THE OPTIMISATION OF THE · XeF XeCl KrF Average power (W) ArF Wavelength (nm) Figure 1.1 Comparison of some commercially available lasers in cw mode or at high-repetition rate. The

THE OPTIMISATION OF THE

MULTI-ATMOSPHERIC AR:XE LASER

The Optimisation of the Multi-Atmospheric Ar:Xe Laser

Gielkens, Serge William Agnew

ISBN 90 365 1070 8

These investigations in the program of the Foundation for Fundamental

Research on Matter (FOM) have been supported in part by the Netherlands

Technology Foundation (STW).

PrintPartners Ipskamp - Enschede

THE OPTIMISATION OF THE

MULTI-ATMOSPHERIC AR:XE LASER

DE OPTIMALISATIE VAN DE MULTI-ATMOSPHERISCHE AR:XE

LASER

PROEFSCHRIFT

ter verkrijging van

de graad van doctor aan de Universiteit Twente,

op gezag van de Rector Magnificus,

prof. dr. F.A. van Vught,

volgens besluit van het College voor Promoties

in het openbaar te verdedigen

op donderdag 15 januari 1998 te 15.00 uur

door

Serge William Agnew Gielkens

geboren op 2 mei 1969

te Heerlen

Dit proefschrift is goedgekeurd door de promotor,

prof. dr. ir. W.J. Witteman,

en de assistent-promotor,

dr. P.J.M. Peters.

Aan mijn moeder Wies, mijn vader Mathje

en mijn levensgezellin Sandra

vii

Contents

1 Introduction..........................................................................................................1

1.1 Types of lasers...........................................................................................................2

1.2 The atomic xenon laser.............................................................................................41.2.1 Excitation techniques ...............................................................................51.2.2 Spectral characteristics.............................................................................7

1.3 Applications...............................................................................................................9

1.4 Scope and summary of this thesis .........................................................................10

2 Electron guns......................................................................................................13

2.1 Introduction ............................................................................................................14

2.2 Plasma anode gun: WIP gun .................................................................................162.2.1 Construction of the WIP gun..................................................................162.2.2 Results and discussion............................................................................18

2.3 Plasma cathode gun................................................................................................272.3.1 Experimental set-up................................................................................282.3.2 Results and discussion............................................................................31

3 Optimisation of the Ar:Xe laser .........................................................................41

3.1 Experimental set-up ...............................................................................................42

3.2 Experimental observations ....................................................................................44

3.3 Quasi-steady state behaviour.................................................................................503.3.1 Kinetics...................................................................................................523.3.2 Laser process ..........................................................................................553.3.3 Discussion ..............................................................................................58

3.4 Temperature effect on the kinetics .......................................................................60

CONTENTSviii

4 Laser spectrum................................................................................................... 65

4.1 Experimental details .............................................................................................. 66

4.2 Results ..................................................................................................................... 674.2.1 Line competition .................................................................................... 694.2.2 Energy loading effects............................................................................ 71

4.3 Discussion ............................................................................................................... 74

4.4 Concluding remarks .............................................................................................. 76

Bibliography........................................................................................................... 77

Samenvatting.......................................................................................................... 83

Dankwoord ............................................................................................................. 87

Curriculum vitae .................................................................................................... 89

Chapter

Introduction

1

1

In 1960 the first successful demonstration of laser operation was achieved by Maiman inruby [1], which is an example of a solid-state laser. Since then numerous other types oflasers have been constructed, like gas lasers, semiconductor lasers, dye lasers, chemicallasers and free-electron lasers (FELs). Each type possesses some unique characteristics,which make it particularly suitable for certain applications that cannot be realised byother lasers. The same holds for gas lasers and in this respect research and developmentis still continuing. In this chapter, first some general features of a few laser types will bedescribed. Next, within the large group of gas lasers the atomic xenon laser, which is thesubject of this thesis, will be highlighted.

INTRODUCTION2

1.1 Types of lasers

Solid-state lasers

The active medium of these lasers is a glass or crystal doped with rare earths or transitionmetals, which is optically pumped by a flash lamp or another laser. Familiar lasers of thistype are based on ruby (Cr3+

: Al 2O3), Nd : YAG (neodymium-doped yttrium aluminiumgarnet) and Ti : sapphire (Ti3+

: Al 2O3). These lasers are of table top size and therefore easyto incorporate in set-ups. The output wavelength ranges from the visible to the near-infrared part of the spectrum. In general the averaged maximum output power isapproximately 100 W, although 10 kW Nd : YAG lasers are available by using several laserrods in series. Because of this high output power the Nd : YAG laser has foundapplications for instance in fabrication processes. An important application of Ti : sapphirelasers is the generation and amplification of femtosecond pulses. In this case peak powersof more than 1014

W are possible. In cw mode the typical performance of this laser is 1 W.Also the large tunability range of about 400 nm exhibited by the Ti : sapphire laser makes ita frequently used laser. Major shortcomings of solid-state lasers are the lack of materialsthat can operate in the UV and thermal problems of the crystals when used at high inputpowers.

Semiconductor lasers

The active region of these lasers consists of the boundary layer between p-type and n-typesemiconductors, called a p-n junction. The thickness of such a transition layer is onlyabout 2 mm, which results in a rather poor beam quality. A large variety of semiconductormaterials has been found to exhibit laser action, resulting in a spectral range covered nowby these lasers that extends from the near UV to the far infrared. Of these lasers the mostextensively studied one is probably the GaAs laser. The emitting area of one laser istypically 1 ´ 5 mm2 and these tiny dimensions demand for efficient cooling. Usually wateris used as coolant to keep the temperature below about 50 ºC, but also liquid nitrogen hasbeen used because at such low temperatures the peak output power and efficiency increasea few times. At room temperature common values of the peak and cw output power of theGaAs laser are respectively 1 W and 50 mW. In this case the efficiency is typically 10 %.To achieve larger emitting areas and higher output powers arrays of, say, 10 of these stripsare used, which on their turn are stacked. In this way several hundred of laser stripsconstitute an emitting area of a few cm2, although it should be kept in mind that in factseveral hundred spots are emitting independently. Because of their small dimensions,compatibility with electronic circuitry and simplicity, semiconductor lasers have alreadyfound large-scale applications, such as in CD players, scanning devices for bar codes insupermarkets and pointers during presentations.

FELs

Because the wavelength of the radiation generated by a FEL depends on the accelerating

CHAPTER 1 3

voltage of the electrons, the FEL is in principle an tunable source of coherent radiation.The tuning range can vary an order of magnitude, a fact which makes them very suitablefor purposes where a large part of the spectrum should be scanned. It should be mentioned,though, that changing from one wavelength to another requires considerable time to adjustvarious parts of the system. Typically, half an hour is needed. The total part of thespectrum covered now by FELs ranges from the UV to almost radio frequency. Peakoutput powers of 1-10 MW are no exception and the fact that the averaged output power atrepetition rate is only 1 W or less, is solely due to practical limitations of the powersupplies. Although the efficiency of the output relatively to the kinetic energy of theelectron beam is about 2 %, the wall-plug efficiency can reach 20 % due to recycling of thebeam energy. Because of this FELs belong to the most overall-efficient lasers.Unfortunately, the money saved by the high efficiency is completely outweighed byinvestments necessary to build the highly complex and bulky systems. Very probably, theuse of FELs will be confined to scientific areas for which no other lasers are available orwhere a large tunability is required.

Gas lasers

In gas lasers the large volume of the active medium and the possibility to flow the mediumthrough heat exchangers facilitate cooling as a consequence of which high averaged outputpowers are possible. CO2 lasers with a CW power exceeding 10 kW are commerciallyavailable. Basically, gas lasers are very simple systems, a characteristic which makes themeconomically attractive. Also the good beam quality is an appreciated property. However,gas lasers are relatively large systems because of the gaseous state of the medium. Becauseof this, sizes of for example CO2 lasers used in industry to cut and weld materials can bequite impressive. Discharge tubes of these lasers are several metres long. At present, thelatest generation CO2 lasers is based on wave guide and slab performances. In non-flowing, convection cooled systems output powers in the range of kW’s are realised.

On the other hand the He-Ne laser, the first gas laser constructed by Javan et al. in1961 at the Bell Telephon Laboratories [2], is only of pocket size. Among the gas lasersthis laser is the most widely spread and is used for alignment purposes, in holography andin interferometric applications. For the latter, the extreme frequency stability of the He-Nelaser is used. The cw output power of this laser is typically a few milliwatts with anefficiency less than 0.1 %. Although the output of gas lasers varies from the VUV to thefar infrared, most of the today research on gas lasers is focused on excimer lasers, whichoperate in the UV and VUV. The lack of other bright, coherent high-power sources of UVmakes these lasers attractive for machining and lithography.

In Figure 1.1 the maximum average output power of some well-known lasers areshown as they are commercially available. So, in laboratory systems in general highervalues have been achieved. The figure for Ar:Xe, however, is taken from Ref. [3] in whichthe principle of operation of a high-pressure Ar:Xe laser at a repetition rate of 60 Hz wasshown in a burst mode. In that experiment the time of operation was merely limited by theelectron gun. In this figure only lasers which generate output powers at moderate or highlevels are displayed.

INTRODUCTION4

1.2 The atomic xenon laser

The first investigations on the atomic xenon laser emitting in the near infrared started inthe early sixties with measurements of the small-signal gain [4,5]. In these earlyexperiments longitudinal discharges in low pressure (10-100 mTorr) gases were applied.Although the gain was extremely high, the laser saturated at low signal levels andconsequently output powers were low. Clark [6] for example, achieved only 4 ´ 10-5

W incw mode using a pure xenon discharge at 75 mTorr. Because of these poor results interestin this laser was fading. Starting from 1970, when Schwarz and DeTemple [7] used atransverse discharge, the atomic xenon laser gradually gained attention again. By applyinga transverse discharge Schwarz and DeTemple were able to increase the pressure of ahelium-xenon mixture to 250 Torr and achieved 0.5 ms pulses of 1 kW peak power with anefficiency of 0.01 %. Soon after, a transversely excited discharge at a repetition rate of 1.4kHz was used to achieve 5.2 W of average power in a helium-xenon mixture with a totalpressure of 300 Torr [8]. The pulses also had a 0.5 ms duration with a peak power of 10 kWand efficiency of 0.12 %. During the seventies a further significant improvement of theatomic xenon laser with respect to output power and efficiency was achieved by using

100 1000 1000010

100

1000

10000

Ar:Xe

CO2

CO

Ho:YAG (s)

Er:YAG (s)

Nd:YAG (s)

Cu vapour

Ar+

XeF

XeCl

KrFArF

Ave

rage

pow

er (

W)

Wavelength (nm)

Figure 1.1 Comparison of some commercially available lasers in cw mode or athigh-repetition rate. The figure for the Ar:Xe laser, however, is taken from Ref. [3]that showed a proof of principle for the high-pressure Ar:Xe laser at a repetition rateof 60 Hz. The letter S between parentheses denotes the solid-state lasers; all othersare gas lasers.

CHAPTER 1 5

argon as diluent instead of helium. Also the use of preionisers enhanced the performanceby giving rise to (multi-)atmospheric discharges [9,10,11,12]. In this way peak outputpowers were increased to 200 kW with an efficiency of 1 % in a 1-bar Ar:Xe mixture [9].From that time interest in the xenon laser really revived and numerous excitationtechniques have been applied since then.

1.2.1 Excitation techniques

A pumping technique for the Ar:Xe laser that much attention was paid to starting in theearly eighties was the electron beam (e-beam) alone [13,14,15]. Usually electrons areaccelerated in a vacuum diode up to energies of 150-350 keV. After penetration of a thinfoil, which separates the high-pressure laser gas from the vacuum inside the electron gun,these fast electrons excite the Ar:Xe mixture. e-Beams with a duration from thenanosecond[16,17] to the millisecond [18,19,20] range have been used. With thistechnique high efficiencies of up to 3-4 % have been achieved [21,22]. Because of thesuccessive efficient absorbing of the highly energetic electrons by argon and transfer ofstored energy from the buffer gas to xenon high specific output powers of 1-2 MW/l arepossible [14,23,24]. Also scaling to large volumes is feasible as shown by Litzenberger etal. [25], who achieved a 650 J pulse from an active volume of 500 l. The major point ofconcern of e-beam pumped systems is the foil. It should be thin, typically 10-50 mm, inorder to be transparent for the fast beam electrons. On the other hand, it should be able tohold a pressure difference of 1 bar or more. When used in a pulsed system at repetitionrate, significant heating by the energy lost by the electrons in the foil results easily in foilrupture. Very probably this will prevent these systems from being commercialised.

A technique quite similar to e-beam excitation is pumping by fission fragments. Inthese lasers fast heavy charged particles are generated by fission of 235U in UO2 coatingswhen it absorbs a thermal neutron. A part of these fission products exits the coating andinteracts with the active medium. Because of a much shorter stopping range in comparisonwith fast electrons, fission fragments deposit a higher specific energy. Nevertheless, inputpowers are usually of a low or moderate level of 1-100 kW/l, although Alford et al. used apump rate as high as 1 MW/l [26]. Because the pump duration is in general in themillisecond range total input energies can still be high. An energy loading of 100’s J/(l×

atm) can be obtained routinely [26,27]. Because fission fragments ionise and excite themedium in much the same way as highly energetic electrons do, characteristics of Ar:Xelasers pumped by fission fragments are expected to be quite similar to the e-beam pumpedones. For example, the highest reported efficiency is 3 % [27], a value quite comparablewith the above mentioned figures for e-beam pumping. Because of the well-knownproblems with nuclear waste and the public resistance to reactor plants it is very unlikelythat these systems will be used on a basis other than a scientific one.

Also excitation by a discharge has been used to generate laser action inatmospheric-pressure mixtures. However, because high-pressure discharges areintrinsically unstable, this pumping method faces some serious problems. Especially withargon as diluent, stable discharge operation is even more difficult because of a highignition voltage, but very low glow voltage. For this reason, at least a preioniser has to be

INTRODUCTION6

used which supplies an initial amount of free electrons as a result of which the ignitionvoltage of the discharge is lowered. This favours a transition to a homogeneous volumedischarge. As sources of preionisation UV light [28], X-rays [29,30] and e-beams [11]have been used. Although not clear, it is very likely that also in experiments in whichauxiliary discharges have been used to obtain a preliminary plasma for the main discharge,UV light plays an important role [10,12]. Of these sources X-rays provide the lowestelectron density and an additional amount of electrons is needed to electrically break downthe gas. In practice this is done by a spiker circuit, which supplies a short high-voltagepulse that accelerates and multiplies the electrons released by the X-rays. After this thedischarge circuit is switched on. With respect to efficiency this so-called prepulse-main-pulse technique showed to be the most promising one of the Ar:Xe laser excited by apreionised discharge. It should be kept in mind that although preionisation provides anefficient and easy starting of the discharge, streamer formation still jeopardises a stabledischarge. Therefore, these self-sustained discharges are usually limited to a fewmicroseconds.

Because the major part of the input power is supplied by the discharge, generalcharacteristics with respect to output power and efficiency are comparable. The maximumefficiency after optimisation is approximately 1 % including the energy deposited by thepreioniser. The resulting specific output powers are several 100’s of kW/l. Thatpreionisation provides an efficient discharge operation is shown by the experiments ofTucker and Wexler, who found an efficiency of 4.1 % with respect to the energy stored inthe discharge circuit [29]. The highest specific output reported so far for the dischargepumped Ar:Xe laser with preionisation is 1.7 J/l [30] with an efficiency of 2.1 % withrespect to the energy stored in the spiker and discharge circuit.

In the preionised self-sustained discharge the external ioniser is only used tostabilise the start of the discharge. Already in the beginning of the development of lasersthe use of an external ioniser was proposed that would be present for the completedischarge duration. Basically, the idea was that electron losses by recombination processesand attachment to the walls and gas species would be accounted for by the ioniser. Thismeans that essentially the electric field is only necessary to maintain the drift velocity. Inpractice the discharge would have to supply much less energy in sustaining itself. Thismode of operation is called the e-beam sustained or e-beam controlled discharge.

In the Ar:Xe laser the situation is different in so far that diminution of the glowvoltage is obtained by making a long-lived electronic level of Xe, a so-called metastablelevel, act like the ground level for the discharge. Because an atom, once being in themetastable level, returns to this level again after ionisation or excitation, it performs aenergy cycle, often referred to as the electro-ionisation cycle. In this case the externalioniser should account for losses out of this cycle. Because ionisation of such a metastableatom requires only about 30 % of the energy needed to ionise neutrals, the dischargevoltage is lowered and stability enhanced. In Chapter 3 these kinetic processes will bediscussed in detail.

In principle, in order to enhance stability during the total duration of the discharge,the pulse length of X-rays and UV light can be extended to match the duration of thedischarge. The reason for not doing so is that the electron production rate by thesepreionisers is orders of magnitude lower than required. Scaling up these sources would not

CHAPTER 1 7

only result in huge, impractical devices, if possible at all, but would also drasticallysuppress the overall efficiency. On the contrary, today electron guns are very well capableof generating the necessary production rates. In the case of the Ar:Xe laser very goodresults with respect to output power and efficiency have been achieved. Until now, thehighest specific output power ever of the neutral xenon laser has been achieved in the e-beam sustained discharge mode by Botma et al. [24], who achieved 8 MW/l in a 8 barmixture with an efficiency of the discharge of 8.5 %. This result is quite impressive takinginto account the quantum efficiency of 20 % relatively to the metastable level. Despitethese very promising results of this excitation technique, it hampers from the sameproblems as the e-beam pumped lasers, namely foil rupture.

The most recent and very interesting one with a view to practical implementation,is the radio frequency (rf) excited system. In this case a transverse ac discharge is appliedat a frequency of typically 100 MHz in gas mixtures with a pressure range of 100 to 500Torr. Because these lasers can be supplied as table top models, they are attractive forapplications, both scientific and commercial. Although already in 1980 Christensen et al.[31] reported on an rf excited Ar:Xe laser in a burst mode during 25 ms, it was only in 1993by Udalov et al. [32] that the first real cw atomic xenon laser was reported on. At that time0.33 W was obtained at an efficiency of 0.2 %. During further optimisation and scaling anefficiency of 0.8 % [33,34] and output power of 5.5 W [34] have been achieved. Becauseresearch has only begun, it is likely that these numbers will be improved in the future.

Besides the above mentioned excitation methods also some unusual techniqueshave been examined. For example, laser or electric-discharge plasmas have been used, inwhich the population inversion results from electron-ion recombination during the rapidexpansion and cooling of the plasma. Also, plasma streams travelling at velocities of about50 km/s have been used to excite mixtures by conversion of the kinetic energy into internalenergy of a shock wave. This energy is mainly emitted as UV and VUV radiation, whichcreates a population inversion by photo-ionisation and subsequent recombination.Although these experiments are interesting from a physical or technical point of view, theyhave never gained much attention because of poor results with respect to output power andefficiency.

1.2.2 Spectral characteristics

Although the gas mixture consists of two or three constituents, laser action takes placeonly on electronic transitions in the xenon atom. In Figure 1.2 a partial energy leveldiagram is shown of Xe. In this figure the arrows indicate transitions which have beenobserved to oscillate in mixtures with diluent Ar. The electronic levels are designated bymeans of the Racah notation. The benefit of the Racah symbols is that they indicate theconstants of motion that identify the energy levels of an excited noble-gas atom in whichonly one electron is removed from the otherwise complete p-shell. So, in this way Racah’snotation describes a physical model whereas the Paschen1 notation is simply a system of

1 Paschen notation was an attempt to fit the neon spectra to a hydrogen-like theory before

the advent of quantum theory.

INTRODUCTION8

shorthand symbols. Racah’s symbols are of the form nl[K]J. Here, n and l represent theprincipal quantum numbers of the outer electron. K is the absolute value of K = Jc + l, withJc the total angular momentum of the core and l the orbital angular momentum of the outerelectron. The total angular momentum J of the atom is obtained by adding S and Kvectorially.

The spectral distribution is a sensitive function of the gas mixture and pumpingrate. The pumping method, on the contrary, has at most a weak influence. For Ar:Xemixtures with a Xe content of less than approximately 1 % at optimised conditions thestrongest lines have wavelengths of 1.73 and 2.63 mm, which carry typically 75respectively 20 % of the total output energy. The remaining 5 % are distributed between2.65, 2.03 and 3.37 mm. The 3.51 mm line is only detected in mixtures with a Xe fraction ofmore than 10 % and in pure Xe. It should be noted, however, that in these cases the outputpower is very low.

When other noble gases are used instead of Ar as buffer, other lines becomedominant. In the case of He the 2.03 mm line is the most intense one carrying 70 % of theoutput energy. Also two new lines oscillating on higher lying states of Xe emerge now,

Figure 1.2 Partial energy level scheme of Xe. The arrows denote transitions betweenwhich laser oscillation has been observed in Ar:Xe mixtures. The thick ones are usually thestrongest lines in the high-pressure laser and in that case carry more than 90 % of the totaloutput energy.

CHAPTER 1 9

namely the 7p[5/2]2 ® 7s[3/2]1 and 7p[1/2]1 ® 7s[3/2]2 transitions radiating at 3.43 mm(few %) respectively 3.65 mm (20 %). When Kr is used the 3.51-mm line is the strongest (>65 %) and the 5d[5/2]3 ® 6p[5/2]3 transition radiating at 2.48 mm carries the remainder ofthe optical output energy. Besides the above mentioned lines also some other lines, havebeen detected at specific conditions; for example 5.57 mm in very low-pressure He-Xe, buteach showed only weak lasing and will therefore never be of practical importance.Although virtually all possible combinations of (He,Ne,Kr):Xe have been investigated,including trinary mixtures, none of these mixtures can compete with the Ar:Xe mixture asfar as efficiency and output power are concerned2. For this reason, most research of thehigh-pressure laser has been focused on this medium.

1.3 Applications

Although the Ar:Xe laser exhibits many features which are interesting from a physicalpoint of view, the fact that its emission lines are in the near infrared, makes this laser alsoattractive for practical use.

Because the 2.63 and 2.65 mm lines fall within the 2.7 mm absorption band of waterwith relatively little scattering of the radiation by human tissue, the laser may find usage asa scalpel for surgery. To this purpose the 1.73 mm radiation has to be suppressed, whichcan be achieved by a grating. Successful single-line operation on the 2.63 mm transitionshas already been shown [35]. In this case approximately 60 % of the energy obtained inmulti-line operation could be extracted as single-line energy. To treat tumours sometimesdyes are used which are photosensitive at wavelengths between 0.6 and 1.7 mm. Irradiationresults in a photo-oxidation process which is toxic to the malignant tissue. In this field thestrong 1.73 mm line could find an application.

Nowadays, CO2 and Nd:YAG lasers have found many applications as machiningdevices. Because of a smaller wavelength of the Ar:Xe laser compared to the CO2 laser thediffraction limited spot is smaller. Together with a three times higher absorption by steel[36], which compensates for the lower efficiency, the Ar:Xe laser emitting at 1.73 mm maycompete with the CO2 laser. Also the fact that the active medium consists of noble gases,gives this laser some advantage over the CO2 laser, which suffers from dissociation. Alsothe Nd:YAG laser undergoes thermal problems of the crystal at high output powers. In theAr:Xe laser, however, the gaseous state of the medium facilitates cooling and does notexperience permanent damage owing to heating. Despite these advantages of the Ar:Xelaser it should be mentioned that the only system which is powerful enough to compete, isthe e-beam sustained laser. As mentioned in § 1.2.1, great difficulties with respect to foilrupture remain to be resolved then.

As a last example of a possible application field may serve the transmission ofnear-infrared radiation through the atmosphere. Although the infrared suffers from

2 For the recent discovered rf excited system, though, the substitution of about 50 % of Ar

by He is necessary to obtain the highest efficiency [32]. Here, the stabilising and coolingproperties of He seem to be essential

INTRODUCTION10

scattering by fog and clouds, scattering by haze is of minor importance because the radii ofthese particles range up to 0.5 mm. Also transmission through rain is surprisingly good[37]. These characteristics together with the fact that the 1.73 mm line fits in a atmospherictransmission window, opens some interesting possibilities, for example incommunications, range measurements and tracking systems.

1.4 Scope and summary of this thesis

As already mentioned above the Ar:Xe laser excited by an e-beam controlled dischargegives the highest performance with respect to output power and efficiency. Previousexperiments in which an e-beam with a duration of about 1 ms was used in combinationwith a discharge that lasted several times longer [24], revealed a sharp drop of the outputwhen the e-beam terminated. This showed that to exploit the full possibility of the Ar:Xelaser it is necessary to excite simultaneously with an e-beam and discharge. Allexperiments performed so far with the e-beam sustained discharge were moreover limitedto a few ms and hardly none of these used an input power constant in time. These factshampered a clear picture of the mechanism of the EBSD laser during quasi-stationaryoperation. Although much work has been carried out to unravel the kinetics and saturationmechanisms of the atomic xenon laser during e-beam or discharge pumping, much is stillunknown. Especially in the case of the EBSD laser theoretical work is almost absent. Tostudy these questions a system was built that could excite the Ar:Xe mixturesimultaneously by an e-beam and discharge with a square-shaped pulse during about 20 ms.With this device the output waveforms were observed as a function of the e-beam currentdensity, discharge power density and gas density.

In this thesis first the construction and working of a suitable electron gun will bedescribed in Chapter 2. First a gun based on a plasma anode was investigated. In thesetypes of guns ions are extracted out of the plasma and subsequently accelerated to acathode at a high negative voltage. Bombardment of its surface by the highly energeticions releases secondary electrons which on their turn are accelerated towards the anodeplasma. After travelling through this plasma they penetrate a foil that separates the low-pressure gun chamber from the high-pressure laser chamber. The main limitation of thisgun was its maximum current density of 100 mA/cm2 after passing the foil. To achievestable discharge operation in the laser at a few tens of kA, a beam current density of up to1 A/cm2 is needed. To this goal a new gun was constructed based on a plasma cathode. Inthis type of gun electrons are extracted from the plasma and next accelerated towards ananode. In the past, such guns have already proven to achieve such high current densitiesduring a few ms. Task was now to extend this operating regime to 20 ms. It appeared that acareful matching of the discharge and high-voltage pulse are necessary with respect toshape and delay. In our set-up a maximum current density after passing the foil of 1.2A/cm2 was achieved. This value is mainly limited by our power supply and currentdensities up to 2 A/cm2 seem to be feasible. With this gun all laser experiments describedin this thesis have been performed.

CHAPTER 1 11

Firstly, a parametric study has been carried out for the laser without investigationof its spectrum. These results are discussed in Chapter 3. As a function of the beam currentdensity, the power density deposited by the discharge and the gas density the outputwaveforms were observed. It is found that although the beam and discharge current areconstant during 15 ms, the laser output may drop earlier. The period during which theoutput power is constant, is called the quasi-stationary period. For this period a analyticalkinetic model is developed which describes well the behaviour of the laser output power asa function of the discharge input power and gas density. With aid of this model it ispossible to detect the main kinetic paths which determine the saturation behaviour of thelaser. In this model also the fractional ionisation defined as the ratio of the electron densityto the gas density appears to be an important parameter for electron collisional mixing ofthe laser levels. Previously, it was already assumed and concluded from Monte Carlosimulations and experiments that this parameter plays an important role. The behaviour ofthe laser after the quasi-stationary period is explained by heating of the gas mixture.Namely, when the temperature rises, the recombination of electrons slows down as aconsequence of which its density rises. When this density surpasses a critical value,electron collisional mixing diminishes the population inversion significantly and theoutput drops. Secondly, the rising electron density causes the glow voltage to drop. Thisresults in a decreasing input power by the discharge resulting in a lower output power. It isshown that the temperature at which the laser ceases to operate in a quasi-stationarymanner, depends strongly on the beam current density.

Finally, the behaviour of the different laser lines will be investigated in Chapter 4.It appears that although the atomic xenon laser with diluent argon emits at 5 different laserlines during multi-wave mode, two of them, the 2.03 and 3.37 mm lines, are insignificant.In our set-up it was not possible to discriminate between the 2.63 and 2.65 mm lines andthey will be denoted by 2.6 mm. The 1.73 and 2.6 mm lines showed a very differentbehaviour. In general the 1.73 mm is the strongest but also the shortest lasting. As a resultthe quasi-stationary behaviour mentioned above is basically determined by the temporalprofile of the 1.73 mm line. Examination of the duration of the 1.73 mm and 2.6 mm linesrevealed that termination occurs at a critical energy deposition energy loading that isconstant regardless of the input power or pressure. This is in sharp contrast with theduration of the stationary period which is shorter at a higher input power, but increases asthe pressure is increased. This behaviour is explained by three-body quenching of thepopulation inversion that at a high energy loading outweighs electron quenching. Thisillustrates that the behaviour of the laser output is the result of a complex interplaybetween heavy-particle and electron processes, the influence of which is controlled by boththe e-beam and discharge current.

Chapter

Electron guns

13

2

As described above, the Ar:Xe laser shows its best performance with respect to efficiencyand thus specific output power when excited by an e-beam sustained discharge. In order toresearch such a system a device is needed that supplies fast electrons, that is an electrongun. In this chapter the research and development of two types of electron guns will bedescribed, which can meet our strong requirements. These are a beam current density upto 1 A/cm2 at an maximum accelerating voltage of 300 kV in a pulse of 20 ms over an cross-sectional area of 5 ´ 55 cm2. It was decided to develop a gun based on a plasma emitter.First, an overview will be given of possible systems to point out why such a gun seems tobe the most suitable choice. Subsequently, a gun based on a plasma anode utilisingsecondary emission of electrons (SEE) will be described with which a maximum currentdensity of 100 mA/cm2 could be achieved. Next, a gun based on a plasma cathode will bediscussed with which a current density of 1 A/cm2 was achieved.

CHAPTER 214

2.1 Introduction

Although interest in electron accelerators has originated before the invention of the laser,the research and development of gas lasers has been a great stimulus. In particular large-area devices that could generate a high current density beam at a high voltage, have beenimproved enormously. For these systems a large variety of sources has been investigated.

The principle of operation is the same for all types. On one hand one needs amedium out of which electrons are liberated; on the other hand a high voltage is applied toaccelerate these electrons to form a beam of highly energetic electrons. The mediumlargely influences beam parameters like uniformity, the maximum current density andeven pulse length. It is basically this medium by which the characteristics and applicationsof one gun distinguish from the others.

The simplest and most early used on a large scale is the cold-cathode gun.Although the name cold-cathode gun is sometimes used for all guns other than those basedon a heated cathode, it is used here exclusively for guns based on field emission from aconductor like graphite or tantalum. When a high voltage is applied, the electric field willbe very high at the sharp boundary, especially at microscale irregularities, calledmicrowhiskers. As a result a huge current density of 108

– 109 A/cm2 starts to emanate and

material from the cathode evaporates. In this way a plasma is formed out of whichelectrons are accelerated towards the anode. So, essentially, this type of gun operates by aplasma cathode. Because this plasma is not bounded, it starts to move towards the anodewith a velocity of about (1-3) ´ 106

cm/s for most cathode materials. This finally results inplasma closure and thus beam termination. This moving plasma causes two maindisadvantages. First, the pulse duration is limited to a few microseconds. It should be keptin mind that a certain field strength is necessary at the cathode to lower the potentialbarrier for liberating electrons. From a practical point of view this limits the diode gap,because the voltage cannot be raised arbitrarily high. Secondly, this gun experiences animpedance collapse during operation. This results from the space-charge-limited currentthat grows as the distance of the gap decreases. For a planar diode in vacuum this isexpressed by the Child-Langmuir law [38], which reads:

2

2

3

0 2

9

4

d

V

m

eJ

ε= , (2.1)

where J is the current density, e 0 is the dielectric constant in vacuum, e and m are therespective charge and mass of the current carriers, V is the accelerating voltage and d isthe distance between the cathode and anode. Equation (2.1) shows that when the gapdiminishes the power supply must either deliver more current or lower the voltage.Consequently, with this type of gun it is impossible to generate a constant current densityat a constant voltage for a long duration. Minor difficulties are a good spatial uniformityand shot-to-shot reproducibility. However, these systems are very simple to construct andare able to generate current densities up to 1000 A/cm2 for which reasons they have beenused extensively in the past.

ELECTRON GUNS 15

A cathode quite similar to the blade type cold cathode is the corona plasma. In thissystem a high field strength is generated at the interface of a metal, in particular a wire,and a dielectric. This results in a macroscopic field strength sufficient to extract amacroscopic current. Further ionisation of the gas by these primary electrons forms aplasma sheath out of which electrons can be extracted. Since no surface protrusions arerequired which are polished off by operation, this cathode lives orders of magnitude longerand provides for a better repeatability and uniformity. However, also this type of gunsuffers from a moving plasma boundary which limits its pulse duration.

A device which lacks this shortcoming of a moving plasma boundary, is thethermionic gun. In these guns, a cathode is heated up to approximately 1500 K which giveselectrons enough energy to overcome the potential barrier of the cathode material. When ahigh voltage is applied, these liberated electrons are accelerated to constitute a beam. Onesuch a cathode is relatively small, typically a few cm2, but by grouping of several of thesecathodes together, large area cathodes have been built. Because the electrons escapeimmediately from the cathode without forming a plasma, no problems correlated withmoving plasma boundaries exist. These cathodes are able to deliver high current densitiesup to 10 A/cm2 during tens of microseconds. The main disadvantage of this gun is itscomplexity. First, a high vacuum of about 10-10

bar is required to prevent the cathode frompoisoning. Secondly, the cathode has to be heated very uniformly. If not, the currentdensity will increase exponentially at points of a higher temperature resulting in even moreheating and finally damage of the cathode. Thirdly, the intense heating asks for a coolingsystem to prevent melting of other parts of the gun. Other disadvantages are a warming uptime of at least half an hour before the gun can be operated, a low efficiency owing to aconstant heating and cooling system, and high expenses to build the gun.

A class which shows to be very promising, are guns based on a plasma. When thisplasma has an open surface, its boundary is not fixed and may move resembling thebehaviour by the cold cathode. To stabilise its position, in particular in large-area emitters,a grid is used. Plasmas have the property that it is easy to extract both electrons andpositive ions. This results in two modes of operation. In the first the plasma acts as acathode, in the second as an anode. In the latter case, these ions are used as high-energyprojectiles. After acceleration they bombard a cathode surface out of which secondaryelectrons emerge. On their turn these electrons are accelerated towards the (plasma)anode.Both systems share desirable properties like virtually infinite pulse duration, large-areaemitting surfaces, high efficiency, and immediate operation. They differ, however, onsome important points. Plasma anode guns can easily be modulated owing to a decouplingof the high-voltage circuit from the low-voltage discharge circuit. In the case of a plasmacathode these circuits are superposed, thereby making the construction more difficult. Theplasma anode operates at higher pressures of about 10-5

bar, diminishing the efficiencyowing to scattering, and resulting in less collimated beams. It also hampers a highelectrical strength. Plasma cathodes operate at pressures of about 100 times lower.Previous investigations showed good perspectives for these systems, encouraging furtherresearch to extend their operating regimes.

Apart from these common guns, also other variants have been built. Examples area gun using a combination of both field and thermionic emission, a gun based on a high-voltage discharge and guns using photocathodes. The first variant suffers of course fromthe same problems as the pure field emission gun. In the second type the cathode layer of

CHAPTER 216

the discharge produces and accelerates electrons or ions to energies as high as 150 keV.When ions are extracted an e-beam is generated by secondary emission of electrons at thecathode. Stability of the discharge is a serious problem on long time scales and alsoaccelerating voltages of more than 200 kV are not - yet - feasible. Photocathodes cangenerate high current densities and have the advantage that the electrons liberated byphotons have a low temperature. For this reason they are used when a low-emittance beamis required. Unfortunately, these cathodes have short life times of typically hours or less.Because they are sensitive to poisoning an ultra-high vacuum of 10-12 bar is necessarymaking the system complicated and expensive. From a handling point of view it ismentioned that the photocathode materials are highly poisonous.

2.2 Plasma anode gun: WIP gun

The acronym WIP stands for Wire Ionised Plasma, which reveals the heart of the gun.Indeed, the main characteristic of this gun is its formation of a plasma by means of wireswhich serve as an anode for the discharge. The purpose of the wire ionised discharge is totrap electrons electrostatically. In this way, the electrons attain long path lengths therebyionising the gas effectively, even at low pressures where the mean-free path is much longerthan the spacing between the anode and cathode. In this regard this kind of dischargeresembles the Penning discharge, in which spiralling around magnetic-field lines enhancesthe path length of electrons. Because ions extracted out of this plasma release electrons bybombardment of a cathode at high negative potential, this gun is a member of the group ofguns based on the Secondary Emission of Electrons (SEE).

2.2.1 Construction of the WIP gun

A schematic transverse cross-section of the electron gun and the laser chamber assembly isshown in Figure 2.1. The total gun volume is about 20 l. During our experiments it wasfilled with helium. The region bound by the foil (1) and the grid (2) acts as an ionisationchamber with dimensions of 4 ´ 9 ´ 55 cm3. Within this ionisation chamber an array ofseven thin tungsten wires with a diameter of 120 mm is mounted and used as dischargeanode (3). The wires are placed longitudinally in a plane halfway between the ionextraction grid and the foil window and are separated one from another by 1 cm. A pulseddischarge is ignited in the chamber by connecting an electrical pulse forming network(PFN) charged to a few kV to the wires using a thyratron switch. Each wire was driven bya separate four-stage PFN with an inductance of about 1 mH and capacitance of 16 nF perstage. In this wire ionised plasma the electrons are trapped both radially and axially[39,40]. The trapping is the result of two mechanisms. First electrons with a velocitycomponent transverse to the radius of the wires miss them and consequently performhelical orbits around the wires. Secondly, the metallic sidewalls of the chamber are onlypierced by small holes to feed through the wires. This geometry results in fieldcomponents inside the chamber that tend to reflect electrons. Thus, the electron orbits to

ELECTRON GUNS 17

and fro across the chamber, until it loses its velocity component transverse to the radius ofthe wire and hits the wire. The generated plasma acts as a source of ions which areextracted through the grid (2) and accelerated to the gun cathode (4). The extraction grid(2) is made of a thin, woven stainless-steel mesh with an optical transparency of 83 %. Thesquare mesh size is 290 mm and the wire diameter is 28 mm.

The electrons produced by SEE at the gun cathode are accelerated to the extractiongrid and travel through the wire discharge chamber and the 25 mm thick Ti foil into thelaser chamber. To withstand gas pressures up to 10 bar the Ti foil is supported by a so-called Hibachi structure with dimensions of 55 ´ 5 cm2. This structure with an opticaltransparency of 81 % has ribs spaced by 8 mm and a depth of 6.5 mm. The gun cathode was53 cm long and was made of aluminium covered by nickel. It was mounted at a distance of3.5 cm from the extraction grid and supported by two PVDF insulators (5).

Figure 2.1 Schematic drawing of the WIP gun in a transverse cross-section: (1) Ti foil withsupporting structure, (2) extraction grid, (3) wires, (4) gun cathode, (5) PVDF insulators, and(6) laser chamber anode. The arrows marked by + denote He that are extracted out of the wireionised plasma towards the cathode. The ones marked by - are the electrons released bysecondary emission upon impact by the ions. The inset is a top-to-bottom longitudinal cross-section of the dashed box and shows more clearly the (1a) Ti foil and (1b) supporting structure.

CHAPTER 218

The electron gun assembly was attached directly to an oil tank containing a high-voltage line type pulser. The main components of the pulser are a five-stage PFN with aninductance of approximately 10 mH and a capacitance of 0.6 mF per stage, a high-voltagepulse step-up transformer with a voltage ratio of 1:13 and an EG&G GPV-6303 vacuumspark gap as a switch. The PFN output pulse was stepped up through the transformer andthen applied to the gun cathode. Because the primary coil of the transformer is a part ofboth the PFN charging and discharging circuits no saturation of the transformer core isobserved. To minimise an impedance mismatch effect a shunt resistor is set parallel to thegun cathode-anode gap. Series and parallel low-inductive resistors in the secondary coilcircuit were used to measure the total output current and gun cathode voltage.

2.2.2 Results and discussion

Paschen breakdown characteristics

A wire discharge in helium is possible in a wide pressure range. However, the heliumpressure must be kept at the left side of the Paschen curve in order to withstand electricallythe high anode-cathode accelerating voltage of the electron gun [Figure 2.2 (a)]. Data forthe Paschen curve in helium are found in the literature but a large scatter in these dataexists. Moreover, these data are measured without any special ionising source like the wiredischarge. Results of our measurements are in good agreement with data of Ref. [41] andshow that our operation point of 17 mbar is sufficiently high at the Paschen left branch. Forexample, at cathode voltages of 150 and 75 kV breakdown occurs at helium pressures ofabout 95 and 120 mbar, respectively. However, it should be mentioned that the breakdowncharacteristics are affected by the wire discharge operation.

Wire discharge features

Oscillograms of the wire discharge voltage and current are presented in Figure 2.2(b). Thevoltage was measured with a Tektronix high-speed voltage probe and the sum of thecurrents in the wire discharges was monitored by a Pearson current transformer. One cansee that after the discharge ignition the wire voltage sharply drops to a quasi-steady glowvoltage of about 250 V, corresponding to the conducting phase. This glow voltage isalmost independent of the PFN charging voltage and the wire discharge current. This is awell-known characteristic of glow discharges [42]. The wire discharge current has a pulseduration of 27 ms (FWHM) with a rise and decay time of 5 and 8 ms, respectively. Thesewere determined by the rise and fall time of the PFN supply.

ELECTRON GUNS 19

The dependence of the ignition and glow voltage for one wire anode on the heliumpressure is shown in Figure 2.3. Apart from the relative low sputtering yields of the He+

ions and desirable high-voltage characteristics helium was chosen because of itsappropriate electrical and SEE characteristics according to references [43,44,45]. Thevalues of the glow voltage in Figure 2.3 correspond to a PFN charging voltage of 2.5 kV.The glow voltage decreases with increasing pressure in accordance with the expected dropof the plasma impedance. The delay of the discharge ignition, usually of the order of a few ms, also decreases with increasing pressure and with increasing charging voltage of thePFN. The wire discharge current of about 10 A is approximately constant in this pressurerange because it is determined completely by the impedance of the PFN (L/C)1/2

» 240 W.Therefore, it increases proportionally to the PFN charging voltage. If we use as a power

0 10 20 30 40 50 60-2

-1

0

1

2

(c)

I beam

[A

]

Time [µs]

-10-505

1015

(b)

I wire

[A

]

-100

-75

-50

-25

0

(a)

Vac

c [

kV]

0

1

2

3 Vw

ire [V]

0.0

0.5

1.0

1.5

2.0

Iion [A]

Figure 2.2 Time evolutions of some typical WIP gun parameters: (a)accelerating voltage at the gun cathode Vacc, (b) wire discharge current Iwire andvoltage Vwire and (c) the electron beam and ion current Ibeam respectively Iion.

CHAPTER 220

supply for the wire discharge a capacitor bank with a capacitance of 64 nF, then the wirecurrent grows proportionally with the pressure increase, in accordance with Refs.[43,46,47]. In this case the wire current is approximately ten times larger but the pulseduration dropped to approximately 2 ms.

The number of wires was varied from 1 to 7. For an effective gun operation it isimportant that all wires are ignited at the same moment and each of them carries an equalcurrent. The parameters of the wire discharge should also be constant from shot to shotand should not be influenced by the high-voltage electric field applied to the gap betweenthe cathode and grid. To ensure this two meshes were mounted at the extraction gridposition at a distance of 5 mm from each other. A small flow rate of helium proved to beuseful. Helium was supplied through a precision leak valve while the gun volume waspumped by a 56 l/s turbomolecular pump. It is possible to operate the discharge atpressures as low as 10 mbar but for a reliable multi-wire operation higher pressures werefound to be beneficial. For this reason most experiments were performed at 17 mbar. Forthe same reason the wire PFN charging voltage should be much higher than the dischargeignition voltage. The main point is that the pressure should be low enough to avoid high-voltage breakdown in the gun.

The purpose of the wire chamber is to produce an ion current pulse. To measurethe ion current [Figure 2.2(c)] we used the gun cathode or the anode of the laser chamberwith the Ti foil removed as an ion collector. The e-beam current was measured either invacuum by the anode of the laser chamber or in air by an aluminium collector placeddownstream of the foil at a distance of 10 mm. The data were corrected for back-scattering

0 25 50 75 100 125 1500

1

2

3

4

ignition voltage

Igni

tion

volta

ge

[kV

]

Helium pressure [µbar]

0

100

200

300

400

glow voltage

Glow

voltage [V]

Figure 2.3 Dependence of the ignition and glow voltage on the helium pressure.

ELECTRON GUNS 21

losses at the collector surfaces [48]. The oscillograms in Figure 2.2(c) correspond to thecase that the Ti foil is absent and the laser anode is used as the ion and electron collector.Here, the e-beam current was measured with a low gun voltage. For this reason one cansee at the tail of the oscillogram a negative part corresponding to the ion current.

When taking into account the ratio of the area of the ion extraction grid to the totalinternal wall surface of the discharge chamber one estimates that the total extracted ioncurrent is approximately one tenth of the total wire current. For a given wire configurationthe increase of the ion current is proportional to the rise of the wire current. The increaseof wire number leads to a less than proportional ion current growth. The time delaybetween the wire and ion current is negligible because the helium ion velocitycorresponding to an energy of 200 eV is about 107 cm/s. The dependence of the ion currenton pressure is in accordance with Ref. [49] very weak, at least in the pressure range ofpractical importance (up to 100 mbar).

The V-I characteristics of the gun

While the WIP gun operates in an idle-run mode, so without wire discharge, its electricalparameters are defined by the shunt resistor of about 1 kW. In this case the gun cathodevoltage and total current in the secondary coil of the transformer are proportional to thecharging voltage of the gun PFN. See Figure 2.4. When the wire discharge was ignited the

0 10 20 30 40 500

100

200

300

, cathode voltage

Vol

tage

at

gun

cath

ode

[k

V]

Charging voltage of PFN [kV]

0

200

400

600

800

total current

Total current [A

]

Figure 2.4 Total current and voltage at the cathode as a function of thecharging voltage of the PFN. The solid squares are the voltage in idle-run mode,whereas the open squares are the voltage during beam generation.

CHAPTER 222

total transformer current increased and the gun cathode voltage decreased compared to thecase of idle run operation. For gun cathode voltages in the higher regime thesedependences showed to be linear with a good accuracy (the case of the lower regime willbe considered later). By subtracting the current through the shunt resistor from the totaltransformer current the gun resistance is estimated to be approximately 2 kW. This valuewas independent of the gun voltage but varied with the wire discharge current; the higherthe total wire current was the lower the gun resistance was.

As the gun voltage increased the total cathode current and electron beam currentalso increased (Figure 2.5). A maximal beam current density Jbeam of approximately100-mA/cm2 was achieved with seven wires carrying a total current of 80 A at a gunvoltage of 220 kV. With a lower beam current the WIP gun could operate at voltages ashigh as 250 kV. Concerning the relationship between the beam current and gun voltage onecan mark only a tendency for the current to saturate at high voltages.

The threshold energy for the electrons to pass the Ti foil is approximately 90 kV.To investigate the gun voltage range below 90 kV we replaced the foil by a mesh. Thevacuum gap permitted a reliable triggering of the PFN at charging voltages as low as 1 kV.In Figure 2.6 the beam current density Jbeam is plotted at several wire currents versus(Vgun)

3/2 with Vgun the accelerating voltage. One can see that at low voltages for all wirecurrents approximately the same linear relationship holds between Jbeam and Vgun

3/2. At

100 150 200 2500

20

40

60

80

100

120

35 A

80 A

Be

am c

urre

nt d

ensi

ty

[m

A/c

m2 ]

Accelerating voltage [kV]

Figure 2.5 The beam current density as a function of the accelerating voltagefor two wire discharge currents, namely 35 and 80 A.

ELECTRON GUNS 23

higher voltages the dependence starts to deviate from a linear one, approaching tosaturation. The higher the value of the wire current the later saturation occurs. So thisbehaviour resembles the classical situation of a vacuum diode current restricted by thespace charge of current carriers [38]. In accordance with Child-Langmuir’s relation for aplanar diode it should be

,)/(

103.222/1

2/36

hmM

VJ

×××=

−

(2.2)

where M/m is the ratio of the current carrier and electron masses, V is the gun voltage in V,h is the cathode-anode spacing in cm, and J is the current density in A/cm2. It should bementioned that although this diode is bipolar, it is not necessary to include anenhancement factor 1.86 associated with a space-charge-limited flow of electrons and ions[50]. Namely, in that case the ratio of the electron to the ion current density reads

,e

i

i

e

m

m

J

J = (2.3)

0 500 1000 15000

50

100

150

200

25060 A

30 A

16 A

10 A

Bea

m c

urre

nt d

ensi

ty

[m

A/c

m2 ]

(Accelerating voltage)3/2

[kV3/2

]

Figure 2.6 Beam current density versus (accelerating voltage)3/2 forvarious values of the wire discharge current.

CHAPTER 224

where J and m denote the current density respectively the mass of the current carriers andthe indices i and e refer to ions respectively electrons. In the case of SEE the electroncurrent density is proportional to the ion current density by the relation

ie JJ η= , (2.4)

with h the coefficient of secondary emission. Because h is typically smaller than 15, whichis much lower than (mi/me)

1/2 = 85.6, space charge neutralisation is of minor importance.

Calculations by Santoru et al. [51] indicate that the ion current increases only by 6 % andClark and Dunning [43] calculated that up to 10 % of the ion space charge could beneutralised by the electron flow. From the linear dependence between Jbeam and Vgun

3/2 wederive the ratio

,

V

A108

2

3

8

2

3

2

×≈× −

V

hJ(2.5)

whereas it should be in the case of ions 2.7 ´ 10-8 and electrons 2.3 ´ 10-6 (A/V3/2). It seemsthat the e-beam current in the WIP gun just triples the ion current, which is limited by itsown space charge, as a result of SEE with coefficient h » 3. It is well known, however, thatthis coefficient for He+ increases with the voltage [52] which would lead to a violation ofChild’s law for the secondary electron current. A possible explanation for the observedlinear relationship between Jbeam and (Vgun)

3/2 at low voltages is that the cross-section forcharge transfer of the He+ ions decreases with an increase of the voltage [53]. In the chargetransfer process helium ions extracted from the grid collide with neutral He atoms andexchange electrons creating a fast neutral atom and slow helium ion. The energeticneutrals have the same velocity as the original ions and produce comparable numbers ofsecondary electrons after collision with the gun cathode [54]. The new low-speed ionsbeing accelerated by the high-voltage electric field, also produce secondary electrons.Hence the charge transfer leads to a larger SEE current. For this mechanism to be effectivethe rise of SEE coefficient h with the voltage should not be very sharp, which is the caseas shown in reference [55]. Estimations based upon a value for the charge transfer cross-section of 5 ´ 10-16

cm2 [56] show that the ratio of cathode-anode spacing to the ion mean-free path is approximately 1. Thus, charge transfer influences the ratio between ion andsecondary electron current and the decrease of charge transfer rate could compensate theincrease of the SEE coefficient with a rising voltage. When the accelerating voltageincreases up to a few hundred kV the cross-section sharply drops to a value of about10-17

-cm2 and the influence of charge transfer becomes negligible.

The relationship e-beam versus wire current

The dependence of the beam current density on the wire discharge current is shown inFigure 2.7. As the wire current increased twice the beam and cathode current increasedless than twice, although at higher discharge currents the beam current density eventually

ELECTRON GUNS 25

grows faster than proportional. The cathode current is nearly five times higher than thebeam current and its flux (cathode current divided by the cathode area in A/cm2)approximately equals the wire current per unit length in A/cm. The data in Figure 2.7 wereobtained with three wires and a total wire length of 150 cm, so the current per unit lengthvaried from 0.2 to 0.4 A/cm. Clark and Cunning [43] investigated the influence of the wiredischarge current on the gun electron current in the ranges (0.3-3) ´ 10-3 and (0.8-5) A/cm.Our data which are in the intermediate range, support the observed linear relationshipbetween wire and gun electron current over four decades variation of these parameters.

Gun efficiency

In any e-beam gun the current behind the foil is only a fraction of the total cathode current.The ratio of the beam and cathode current could be regarded as the efficiency of the gunitself. In addition to the obvious dependence on geometry and foil parameters theefficiency is expected also to depend on the cathode material and gun voltage in the caseof a SEE gun. Only two references about efficiencies of SEE guns have been found withvalues of 0.15 for a gun voltage of 110 kV and a stainless-steel cathode [43] and 0.28 for avoltage of 160 kV [45]. It is not clear whether a molybdenum or stainless-steel cathodewas used here. Our data for the gun efficiency are plotted versus the gun voltage in Figure

30 40 50 6050

60

70

80

90

100

30 kV

35 kV

Bea

m c

urre

nt d

ensi

ty

[m

A/c

m2 ]

Wire discharge current [A]

Figure 2.7 Beam current density versus the wire discharge current forPFN charging voltages of 30 and 35 kV

CHAPTER 226

2.8. One can see that with a Ti foil in the voltage range of practical importance the gunefficiency is approximately 0.22. Interpolating the foil transmission coefficient data of Ref.[57] we recalculated these values for the case when the foil was absent. Together with thevalues measured without foil these data are presented in Figure 2.8. The resultingdependence resembles the voltage dependence of the SEE coefficient [55].

Electron beam guns having high beam current densities (for example cold-cathodeguns) usually operate under conditions of excessive cathode emission obeying Child-Langmuir’s law. In the case of plasma cathode guns Child’s law is also reported to bevalid for short-pulse length conditions [43,46,49] (for long-pulse duration [44,45] no datawere presented). It is reasonable to optimise the characteristics of the wire discharge powersupply together with the gun power supply design. In our case the stored electrical energyin the gun PFN reached 2110 J at a charging voltage of 37.5 kV. As the acceleratingvoltage is 220-250 kV and the pulse duration about 25 ms one derives that the maximumpossible PFN output current equals 350 A. Taking into account the value of the gunefficiency and the losses in the shunt resistor the maximum beam current behind the foil isestimated to be approximately one tenth of the maximum possible value and equals130 mA/cm2. This is indeed close to the experimental value of 100 mA/cm2 and we may

0 50 100 150 200 2500.0

0.1

0.2

0.3

0.4

With foil

Without foil

Gun

eff

icie

ncy


Figure 2.8 Efficiency of the WIP gun as a function of the accelerating voltage withand without Ti foil. Note that the curve labelled by With foil tends to zero at lowervoltages because the threshold energy for electrons to penetrate the foil is about 90 kV.

ELECTRON GUNS 27

say that our gun and wire discharge power supply systems were matched to each other.

Extraction grid aperture

There is a possibility to increase the e-beam current density by decreasing the extractiongrid area. Therefor the external mesh of the extraction grid [(2) in Figure 2.2] has to beremoved and a thick foil shield with a rectangular hole in the centre is placed just over theinner mesh. When a hole size of 1.5 ´ 10 cm2 was used the total beam current reached avalue of 3.6 A at a gun voltage of 220 kV. It was even found that the e-beam was focusedon the longitudinal axis so that the current density on this axis was much higher here thanthe average calculated value of 0.24 A/cm2. As a result it was possible to destroy the foilby only one single shot. However, the current is not so high that the e-beam self-pincheffect could be responsible for the observed focusing effects and current density increase.The observed phenomenon can be explained by assuming an electrical field penetrationeffect. Due to the relatively large grid field factor of about 10, defined as the ratio of meshsquare size to mesh depth, the electrical field penetrates through the extraction grid intothe rectangular aperture creating a cylindrical lens effect, catching and focusing heliumions onto the gun cathode surface. So, the effective cathode emitting area is also verysmall and limited only to the central part of the cathode. For the e-beam there is of coursethe opposite diverging lens effect but it affects the fast high-energy electrons much less.

Spatial uniformity of the electron beam

The distribution of the beam current was measured by a small collector plate for positionsalong and across the longitudinal axis of the beam aperture. The collector plate had across-section of 2 cm2 and was located in air 1 cm downstream of the foil. The uniformityof the current density achieved with a grid with a full extraction aperture was quite good.For example, with a wire configuration consisting of one central wire and two wires atboth sides 2 cm apart from the central wire the variation across the longitudinal axis wasless than 15 %. In the direction of the longitudinal axis the variation was less than 25 %over 50 cm.

2.3 Plasma cathode gun

A plasma cathode is an electrical-discharge device producing a plasma, from whoseboundary electrons are extracted for further acceleration. In comparison with the above-described WIP gun large differences exist with respect to construction and physicalbehaviour which is due to the very different effects of electron instead of ion extraction.

CHAPTER 228

2.3.1 Experimental set-up

The development of high-current electron guns based on a plasma emitter requires the useof high-current discharges. Conventional glow discharges, however, are limited to acertain value of the current in the diffuse phase of operation. Above this value, the well-known glow-to-arc transition sets in. So in this connection, the problem of creating a low-

Figure 2.9 Schematic drawing of the gun: (1) discharge cathode, (2) intermediateelectrode, (3) insulator, (4) hollow anode, (5) extraction grid, (6) vacuum chamber, (7)high-voltage insulator, (8) grid anode, (9) voltage gradient rings, (10) field shapingelectrode, (11) drift section, (12) Ti foil window and support structure, (13) laserchamber, (14) discharge electrode and (15) insulator.

ELECTRON GUNS 29

pressure arc discharge starting from a cathode spot to an expanded anode has to beresolved3. A schematic drawing of the plasma cathode gun is shown in Figure 2.9.

The ignition of a discharge in a long gap, necessary for a large area of the emittingplasma, calls for a special system of discharge initiation. This initiation is impeded by thelow gas pressure which is necessary to ensure a high electrical strength of the acceleratorgap. The simplest method is to create an initiating plasma in the cathode region. In oursystem the initiating plasma is formed by a dielectric surface (1) flashover between acylindrically shaped cathode (2) and a ring shaped intermediate electrode (3). The cathodeis made of magnesium which has a low threshold for arc currents. The plasma jetpropagates with a velocity of about (1-2) ´ 106

cm/s towards the hollow anode and electronemission from this plasma ionises the gas between the boundary of the jet and the hollowanode [58]. The intermediate electrode is electrically connected to the hollow anode (4) bya resistor R = 75 W. This resistor limits the current in the initiating electrode circuitwhereupon the arc discharge switches to the hollow anode. In our set-up two of thesecathode assemblies are used, one located at each end of the hollow anode. This geometry,in which the discharge axis is normal to the beam axis, provides for a more uniformcurrent density distribution and higher electrical strength of the accelerator gap than alongitudinal configuration does [59]. The hollow anode is formed by a cylinder ofstainless-steel foil with a diameter of 20 cm and a length of 65 cm. At one side a windowwith a grid of stainless steel (5) is made with dimensions of 54 ´ 3 cm2. The square meshsize is 290 mm and the diameter of the wires is 28 mm resulting in an optical transparencyof 83 %.

The complete plasma generator assembly is mounted inside a cylindrical vacuumchamber (6) with a diameter of 50 cm and a length of 100 cm. This chamber is filled withargon, the pressure of which was regulated by a precision leak valve while the gun volumewas pumped by a diffusion pump with a pump capacity of 270 l/s. A high-voltage coaxialcable is fed to the discharge assembly through an insulator (7). Equidistant gradient rings(9) increase the threshold for breakdown by protecting the insulators surface andlinearising the voltage drop. A tungsten grid with an optical transparency of 90 % serves asthe gun anode (8). The length of the accelerating gap between the emitter mesh and anodegrid is 10 cm. To focus the electrons a field shaping electrode (10) is mounted at theextraction window. To the gun chamber (6) a drift chamber (11) is attached, which merelyserves as an intermediate flange for connection of the laser chamber to the gun. The field-free path that the electrons travel in this chamber, is 6.5 cm. The chamber is closed by atitanium foil and its support structure (12). The dimensions of the support structure, a so-called Hibachi structure, are 55 ´ 5 cm2. The titanium foil with a thickness of 25 mmseparates the low-pressure gun chamber from the high-pressure laser chamber (13). Thebeam current after passing the foil is measured by a discharge electrode (14) that iselectrically insulated (15) from the laser chamber. This electrode is made from aluminium

3 Much of the technology described in this section has been extensively researched in the

former Soviet Union. Unfortunately, this work is scarcely published in the West. For those readersfamiliar with Russian, the following book is recommended: Þ.Å. Êðåéíäåëü, Ïëàçìåííûåèñòî÷íèêè ýëåêòðîíîâ, Ìîñêâà, Àòîìèçäàò, 1977 (Yu. E. Kreindel’, Plasma Electron Sources,Moscow, Atomizdat, 1977).

CHAPTER 230

covered by nickel and was placed 15 mm from the foil. The angle g as well as the fieldshaping electrode (10) will be discussed below in more detail in the next section.

In Figure 2.10 the complete electrical system is given. The discharge power supplyconsists of a double pulse forming network (PFN) (1) providing synchronised operation ofthe two plasma cathode units. Each PFN consists of four stages with a capacitance of0.5 mF per stage. The first stage is connected by a resistance Rd of 6.5 W and inductance12 mH to the plasma cathode, while the other stages have an inductance of 25 mH per stage.The double PFN is charged by a dc power supply (2) through salt solution resistors Rs ofabout 200 kW. These resistors also protect the dc power supply from high-voltage pulsesgenerated by a high-voltage line type pulser (3). This pulser is the same as described in theprevious section with the exception of capacitors that are twice as high and inductors twiceas low now. To minimise impedance mismatch effects a shunt resistor Rm ofapproxiamtely1 kW is set parallel to the electron gun. The high-voltage pulse is measuredby a resistive voltage divider RHV, while the e-beam current, the discharge and collectorcurrent are measured by Rogowski-type current transformers R1,2,3. During experiments onthe discharge without high voltage the discharge voltage was measured by a high-speedprobe, not shown in this figure. The discharge and high voltage are switched by spark gaps

Figure 2.10 Electrical scheme of the set-up: (1) double PFN for the discharge, (2)dc power supply, (3) high-voltage PFN, T1,2 are trigger generators, G1,2 are spark gaps,R1,2,3 are Rogowski coils and Rx are resistors. See the text for a description.

ELECTRON GUNS 31

G1,2. These are triggered by trigger generators T1,2, for which a delay time can beestablished by a delay generator. To protect this delay generator the trigger generator T2 issupplied with an optical coupling.

2.3.2 Results and discussion

Low-pressure gas discharge features

The plasma discharge parameters have been determined without high voltage at thecathode. In Figure 2.11 oscillograms show the time evolution of the discharge current andvoltage at a pressure of 2 ´ 10-7

bar and a charging voltage of the double PFN of 3.0 kV.The working pressure range for the discharge was found to be (2-20) ´ 10-8

bar. The lowerlimit was set by the base vacuum of the system. At higher pressures instabilities of thee-beam started to grow. The current is the total current supplied by the two plasmagenerators. One can see from these oscillograms that after ignition the voltage sharplydrops to a quasi-stationary glow voltage with a duration of approximately 20 ms. The widthof the current pulse is 34 ms (FWHM).

0 20 40 60 80600

400

200

0

Dis

char

ge c

urre

nt

[A]

Time [µs]

0

1

2

3

4

Discharge voltage [kV

]

Figure 2.11 Oscillograms of the discharge current (solid trace) and voltage(dashed trace). The charging voltage of the double PFN is 3.0 kV and the gaspressure is 2 ´ 10-7

bar.

CHAPTER 232

In Figure 2.12 the glow voltage is plotted versus the flat-top value of the dischargecurrent at a pressure of 2 ´ 10-7

bar. Its appearance resembles the V-I characteristics of thevacuum arc with a metal cathode. From the linear fit one infers a dynamical resistance of0.28 W. This value is much higher than the usual one for vacuum arcs. For example, for alow melting metal like aluminium a dynamical resistance of about 0.01 W is found [42,p.262]. This may be explained by the fact that in this set-up an expanded anode is usedresulting in a volume discharge, whereas usually the arc discharge burns in a much moreconstricted volume with a consequently higher degree of ionisation.

The value of the current is almost completely determined by the impedance of 6.5W of the power supply. For this reason the current rises proportionally with the chargingvoltage of the PFN and increases only by about 3 % when the pressure rises in the range(2 - 20) ´ 10-8

bar. It should be mentioned that the discharge current is only limited by themaximum charging voltage of the capacitors used. By using a perspex window instead ofthe Ti foil one can observe that the plasma fills the hollow anode completely.Nevertheless, the plasma is denser near the cathode assemblies than in the middle of theanode and for this reason an extra mesh with dimensions of 10 ´ 3 cm2 near each cathodewas used to provide for a more uniform e-beam.

200 400 600 800 10000

100

200

300

Glo

w v

olta

ge

[V]

Discharge current [A]

Figure 2.12 The glow voltage as a function of the discharge current.

ELECTRON GUNS 33

Process of extraction

In this section ‘beam current’ refers to the current extracted from the plasma. When thecurrent after passing the foil is meant, ‘collector current’ is used. In Figure 2.13 severaloscillograms are plotted of the time evolutions of the high-voltage pulse and the beamcurrent. For all pictures the delay between the high-voltage and the discharge pulse is zero.In fact, the rising slope of the high-voltage pulse switches the discharge. In (a) however,no discharge is applied. In this case the measured current is the charging and dischargingcurrent of stray capacitors during the rising and falling slopes of the accelerating pulse.This picture shows that these currents can be of significant magnitude. The other picturesshow the change of the behaviour of the beam current when it grows. In (b) it is shownthat at low beam currents, the beam current grows slowly after the charging peak.Moreover, at the end of the accelerating voltage the beam current is still rising and in thiscase its maximum value is merely set by the duration of the high-voltage. When the beamcurrent grows to higher values, (c), the high voltage pulse also exhibits a significant droop,because the impedance drops noticeably during the rising of the beam current. This ishighly undesirable, because at a lower voltage more energy is deposited in the foilresulting in stronger heating and enhanced chance of rupture. It seems that the droop alsoencourages the possibility of a premature ending of the beam. It should be mentioned thatthis does not seem to be a breakdown, but rather a high-voltage discharge. Namely, thefalling off of the high voltage happens in a smooth way without any high-frequencyoscillations and the rise of the beam current is limited. See (d,e). For a comparison, (f) is

0

200

400 (a) (d)

0

200

400 (b)

Be

am

cu

rre

nt

[A]

(e)

0 20 40 60

0

200

400

Time [µs]

(c)

-400

-200

0

Acce

lera

ting vo

ltage

[kV]

-400

-200

0

0 20 40 60

(f)

-400

-200

0

Figure 2.13 Temporal behaviour of the accelerating voltage (dashed curves) and the beam current(solid curves). See the text for explanation.

CHAPTER 234

shown, which shows the rare occurrence of a breakdown. In that case the voltage endsabruptly with high-frequency oscillations – unfortunately not clear from this picture - andthe beam current rises strongly. The difference between the processes of (d,e) and (f) isalso established by the effect on the foil. Whereas the foil shows no traces after an event ofthe (d,e) type, the foil is severely marked by events of the (f) type. This is illustrated byFigure 2.14. The trace in the middle along the foil had a length of 48 cm and height of 0.8cm. These dimensions of the beam in the case of a normal extraction process wererespectively 53 and 3 cm2. So, when a real breakdown occurs mainly a contraction of theheight results, the mechanism of which remains unclear. Finally, it is to be remarked thatonly one such an event already resulted in visible marks on the foil.

It appeared to be possible to enhance the rise of the beam current after the firstpeak by a less fast rise of the slope of the high-voltage pulse. As a result the peak of thecharging current was also lower. This indicates that in some way these charging currentsinherent to application of a high voltage influence on the process of forming the beamcurrent. More important was the influence of the delay between the discharge current andthe high-voltage pulse. By making the accelerator pulse 7-10 ms delayed with respect to thedischarge it was possible to eliminate the slowly rising slope. This is shown in Figure 2.15.Probably two processes play a role. First, the volume discharge needs some time todevelop. As mentioned above the plasma jets travel with a velocity of typically 1-2 cm/ms.This means that in our set-up the plasma needs approximately 15-30 ms to developcompletely. So it is very well possible that approximately 10 ms are necessary beforeextraction may take place. Secondly, the extraction itself also influences on the plasmaparameters. Because the plasma potential may reach 40-50V relative to the walls [60], theelectrons need to overcome a barrier. When the accelerating field is switched on, thebarrier is lowered and, naturally, increases the electron current from the plasma. Topreserve continuity of current in the discharge the current to the anode should decrease.This is provided for by an increase of the plasma potential. Thus, electron extractioninfluences on the plasma potential as well as other plasma parameters [61]. This isprecisely the feature in which a plasma cathode differs from a plasma anode. This makesclear that extraction during the developing phase of the plasma may hamper severely thegrowth of the beam current. As a result the beam current rises only slowly. Whenever the

Figure 2.14 Picture of the Ti foil, when a few real breakdowns have occurred. Notice the sharp trace along the middle as a result of a strong contraction of the beam.

48 cm

ELECTRON GUNS 35

plasma has filled the volume sufficiently, the extraction process does not disturb anymorethe further development. In that case the beam rises immediately and remains constantduring extraction. This is shown in Figure 2.15 by the solid and dashed curves. When thedelay is too small the beam current only slowly rises (solid curves), whereas withsufficient delay the beam current rises immediately (dashed curves). In that case theaccelerating voltage remains constant because the impedance remains constant, andconsequently, no mismatch occurs anymore between the peak of the high-voltage and thebeam current. It should be mentioned that increasing the delay beyond 10 ms enhances thepossibility of a breakdown immediately at the beginning of the beam pulse. This indicatesthat after this time the plasma also starts to penetrate the accelerating gap.

Whereas the problem of a slowly rising beam current can be resolved by applyingan appropriate delay, the high-voltage discharge still remains when the high-voltage pulsefalls off. The remedy to this is a careful matching of the falling slopes of the high voltageand the beam current. This is possible by using a bias current through the primarywindings of the high-voltage transformer. The result is a change in the magnetisation ofthe core, which influences on the rising and falling slope of the accelerating pulse. It isremarkable to see that by adjustment of the value of the bias current it is possible toremove the discharge at the end of the pulse. The above described effects of a slowlyrising beam and discharge at the end of the pulse have already been observed by McGeoch[62]. In that article no attention was paid to the slowly rising slope of the beam current butthe discharge at the end of the accelerating pulse was explained as a consequence of amoving plasma boundary. In his experiments it was seen that the extracted current at acertain voltage was larger than calculated from the Child-Langmuir law on basis of thedistance between the extraction grid and anode of the diode. This could only be extractedif the gap between the plasma boundary and beam anode was smaller than this distance. Itwas therefore suggested that although the grid stabilises the plasma boundary, the plasmanevertheless penetrates the accelerating gap. In this way the diode adjusts to yield a beamcurrent that is controlled by the discharge current. The internal anode mesh serves to fixthe plasma potential regardless of the extraction potential. However, when this potentialdrops, the plasma sheath moves rapidly towards the mesh anode and large excursions start.These resemble our high-voltage discharge closely. In our set-up the space-charge-limitedvalue of the beam current with a diode gap of 10 cm is 334 A at an accelerating voltage of200 kV. The occurrence of a high-voltage discharge at 200 kV, however, already manifestsitself at beam currents as low as 100 A. In this case moving plasma boundaries are veryunlikely. Another possibility is closure of the gap by a plasma emanating from the gunanode; for it should be kept in mind that at an accelerating voltage of 200 kV and a beamcurrent of 100 A the power density on the foil structure is about 105

W/cm2. At such valuessputtering of metal surfaces takes place. In this case the high-voltage discharge wouldoccur sooner at higher currents or voltages, a tendency, however, not observed in theseexperiments.

CHAPTER 236

Gun operation

Because initially the beam diverged at an angle of approximately 6 °, the height of thebeam at the foil window was 6.1 cm and consequently 17 % of the beam current was lost atthe 5 cm high Hibachi structure. To focus the beam an electrostatic electrode was placed atthe extraction window, based on a Pierce type design [50]. Now, the dimensions of the

0 20 40 60

0 20 40 60

14.5 µs7 µs

19 µs

Icol

20 µs

12 µs

Icol

Ibeam

Ibeam

Vacc

Vacc

Icol

Ibeam

Vacc

Idis

Time [µs]

Figure 2.15 Temporal profiles of the discharge current Idis, the accelerating voltage Vacc, beamcurrent Ibeam and collector current Icol. When the accelerating voltage and discharge current startsimultaneously, the beam current rises only slowly (solid curves). With sufficient delay the beamcurrent rises immediately (dashed curves). Finally, by adjusting the falling slopes of the dischargecurrent and accelerating voltage it is possible to eliminate the high-voltage discharge at the end ofthe pulses (dotted curves).

ELECTRON GUNS 37

beam at the collector were 3 ´ 53 cm2. To optimise the spatial uniformity of the beamcurrent, the orientation of the plasma generators was adjusted. This orientation is denotedby g in Figure 2.9. An optimal angle g of 5 ° was found, which resulted in a maximum non-uniformity of 15 %. This value is close to what is previously found [59]. The fact thatslightly changing the orientation of the plasma generators influences on the densitydistribution of the hollow-anode discharge, is illustrative of the complex and sensitiveprocess of forming an arc discharge with an expanded anode.

To make the gun as efficient as possible it is necessary to increase the extractioncoefficient a, which is defined as the ratio of the beam to discharge current. As alreadymentioned above the extraction of electrons increases the plasma potential, therebyredirecting more electrons to the extracting mesh. In Figure 2.16 the dependence of a onthe pressure is shown at an accelerating voltage of 185 kV. The increase of the extractioncoefficient with increasing pressure is associated with a decreasing thickness of the ionsheath in the hollow-anode discharge and consequently with a transition from the mode ofelectron extraction through a potential barrier to emission from an open plasma surface[59,61]. In the latter case the electron emission current tends to the discharge currentwhich is clearly shown in Figure 2.16. Sometimes calculated values of a even exceeded100 % a little. This originates from secondary electrons created in the neighbourhood ofthe mesh [63]. Such high values have been reported already before [59,61]. It should bementioned however, that above about 80 % the possibility of a high-voltage discharge isenhanced. In these cases it is very well possible that cathode spots are formed at the mesh

10-8

10-7

10-6

0

25

50

75

100α

[%

]

Pressure [bar]

Figure 2.16 The extraction coefficient a versus the pressure.

CHAPTER 238

from where a discharge starts. The system resembles then the constricted arc discharge[64], in which a too high current also results in a cascade discharge [61].

Due to the geometrical factors the maximum current behind the foil is limited to65 % of the beam current. In Figure 2.17 the ratio of the collector to the beam current isplotted as a function of the accelerating voltage. The collector current is measureddownstream of the foil by a collector plate. This plate was biased at 130 V. At higher biasvoltages the measured collector current did not rise any further. The generation ofsecondary electrons was measured to be approximately 20 %. Figure 2.17 shows also thevalues of the measurements after corrections have been made for losses in the foil. Forthese calculations results of Seltzer and Berger have been used [57]. The solid linerepresents the mean value of these corrected vales and corresponds to 48 %. When also aback-scattering coefficient of 20 % is taken into account for elastic reflection of high-energy electrons [48], a value of 58 % for the current arriving at the collector plate isfound. This means that about 10 % of the current is lost due to for example collisionsduring acceleration and transportation through the drift section, a value quite reasonable.

Figure 2.18 shows the record result with respect to the collector current density.Notice that the collector current indeed rises immediately which shows that the influenceof the charging peak has now disappeared. So the shape of the beam current is not theresults of a superposition of an extracted and charging current. Notice that the discharge

100 150 200 250 3000

10

20

30

40

50

60

70

I colle

ctor/I be

am

[%]


Figure 2.17 Fraction of the beam current that is available in the laser chamber,as a function of the accelerating voltage. The open circles denote the measuredvalues. The collector plate was biased at 130 V. The solid squares are the valuesafter corrections for losses in the foil.

ELECTRON GUNS 39

current changes slightly its amplitude when the high voltage is switched on. The voltagealso exhibits a small overshoot. This indicates that at such high extraction rates thedischarge inside the hollow anode may be disturbed. The values of the main e-beamparameters for maximum achievable accelerating voltage Vb (1) and e-beam current Ib (2)are presented in Table 2.1. Here, Jb denotes the emission current density, Wb and wb denotethe power respectively the power density of the e-beam at the foil window assembly andJcol denotes the e-beam current density at the collector plate. As can been seen from thetable, the gun is capable of emitting a beam current density of 2.5 A/cm2. In this case, the

0 10 20 30 40 50 60

0

100

200

I col

[A]

Time [µs]

0

200

400

I beam

[A

]

-200

-100

0

Ube

am

[kV

]

0

200

400

600

I dis

[A]

0

1

2

3

Jbe

am [A/cm

2]

0.0

0.5

1.0

1.5

Jcol [A

/cm2]

Figure 2.18 Maximum achieved beam current density with the current set-up. Notethe slight change of the discharge current as the high voltage is switched on and thesmall overshoot of the high-voltage and beam current pulse which indicates that thedelay between the high-voltage and discharge current pulse was not sufficient in thiscase.

CHAPTER 240

current density at the collector is 1.2 A/cm2. It also shows that at maximum ratings thepower density on the foil window assembly is about 5 ´ 105

W/cm2. At such high valuessputtering processes start at the metallic surfaces, resulting in plasma jets filling theaccelerator gap. Although this may give problems in increasing the current density, itshould be possible by a careful design of the Hibachi structure and a more powerful high-voltage power supply to achieve 2 A/cm2 downstream of the foil.

Table 2.1 Values of the main e-beam parameters for maximum accelerating voltage(1) and maximum e-beam current (2). See the text for an explanation of the symbols.

Vb

(kV)Ib

(A)Jb

(A/cm2)Wb

(107 W)

wb

(105 W/cm2)

Icol

(A)Jcol

(A/cm2)Icol/Ib

1 200 400 2.5 8.0 5.0 185 1.2 0.472 270 290 1.8 7.8 4.9 150 0.93 0.51

Chapter

Optimisation of the Ar:Xe laser

41

3

The full exploration of a new system requires a detailed study of its parameters and itskinetic chain of the inversion production. The understanding of the laser and thequantitative information on the kinetics can then be used for the design of an optimisedsystem. As pointed out in Chapter 1 the atomic xenon laser pumped by an e-beamsustained discharge is the most productive with respect to output power and efficiency.Also from an experimental view this method of pumping is attractive, because the e-beamdecouples - at least to a significant degree - effects of the gas pressure from the dischargeparameters. In this respect the e-beam sustained discharge allows to follow more or lessindependently the effects of discharge current, e-beam current and gas pressure. Inpreceding work [24] a short e-beam pulse of only 1.2 ms and a much longer dischargepulse of about 5 ms were used. These experiments showed a fast drop of the output powerafter termination of the e-beam. This clarified the necessity of simultaneous operation ofthe discharge and e-beam. The experiments brought also forward the question to whatextent the quasi-steady state is dealt with during the simultaneous presence of the pulsesand what the saturation mechanisms are. Especially more insight into the quenchingeffects by electrons and atoms is desired. To study these questions the system wasreconstructed to have simultaneous pulses of the e-beam and sustainer for about 20 ms.For this device the output waveforms were observed as a function of the e-beam current,discharge current and gas pressure. A kinetic model is developed to get a betterunderstanding of the kinetic processes.

CHAPTER 342

3.1 Experimental set-up

The electron gun used was the plasma-cathode gun described in § 2.3. Although inFigure 2.8 the laser chamber is also shown, a more detailed picture of the laser set-up isgiven in Figure 3.1. The discharge circuit consists of three capacitors C of 30 mF each andtwo inductors L of 400 nH each. The capacitors are charged by a dc power supply througha resistor of 25 kW which limits the charging current when the capacitors discharge into theplasma. When the e-beam enters the gas mixture, the more or less homogeneous volumeionisation makes the medium conductive. As a result the breakdown voltage drops belowthe charging voltage of the capacitors and the discharge is switched on. The discharge ismaintained between the foil and the discharge electrode. To avoid sputtering of the foil itwas used as anode. If used as cathode sputtering and heating resulted in foil rupture at adischarge current of 20 kA or more. Besides, no difference was seen in the outputparameters of the laser whether the foil acted as anode or cathode.

Although in the testing phase of the gun a 25 mm thick foil was used, it appearedduring the preliminary laser experiments that a 15 mm thick foil reduced the chance of afoil rupture significantly at a high energy loading. This results from a lower temperaturerise compared to the thicker foil. For example, at an accelerating voltage of 200 kV and acollector current density of 1 A/cm2, the calculated temperature of the thinner foil is 510 Kat the end of the e-beam pulse, while that of the thicker one is 630 K [57]. This stems fromreduced energy losses by the electrons in the foil and a lower beam current necessary toachieve 1 A/cm2 after passage of the foil that outweigh the smaller mass. Taking intoaccount that the tensile strength reduces 2.2 times when the temperature rises from roomtemperature to 590 K [65], it is very well possible that the thinner foil keeps a highermechanical strength even during the discharge pulse. The e-beam current density afterpassing the 15 mm thick Ti foil was varied between 0.25 and 0.9 A/cm2.

The resonator consists of a flat totally-reflecting Cu mirror and a planparallel ZnSeoutput coupler with a reflectance of 50 %. With this reflectance an optimal output powerwas observed for this system [35, p.63]. The mirrors are separated by 90 cm. The distancebetween the discharge electrodes is 2 cm and the cross-section of the e-beam is 3 ´ 53 cm2.The laser extraction volume is 0.31 l and the base vacuum in the laser chamber is 5 ´ 10-9

bar. Because air or CO2 impurity concentrations of more than about 0.01 % already cause adrastic drop of the laser output [20], high-purity argon (99.999 %) and xenon (99.99 %) areused.

The discharge current was measured by a Rogowski coil, while the dischargevoltage was measured by a resistive voltage divider. The contribution of an inductiveelement to the discharge voltage appeared to be negligible. A beam splitter BS directs onepart of the laser beam to a fast uncooled InAs photodiode (EG&G J12-18c) and the otherpart to a pyroelectric joulemeter (Gentec ED 500). The photodiode records the temporalprofile of the total output power, that is the power generated by the laser oscillating on theseveral transitions of the 5d and 6p manifolds owing to the broad-band reflectors. In frontof this diode a CdTe window IF and a neutral-density filter ND are placed. The CdTewindow transmits all laser lines but blocks visible radiation, while the neutral-density filterattenuates the beam for a linear response of the photodiode. The joulemeter integrates the

OPIMISATION OF THE AR:XE LASER 43

total output power to give the total output energy. By comparison of this energy with thearea of the waveform detected by the photodiode, the amplitude of this diode signal isconverted into units of power.

Figure 3.1 Scheme of the set-up for the laser experiments. Long arrows representthe fast beam electrons, whereas the short ones represent the low-temperature dischargeelectrons. The main components of the discharge circuit are the capacitors with acapacity of C = 30 mF each and the inductors with an inductance of L = 400 nH each. Thedischarge is switched by the e-beam. The laser beam is directed to a photodiode andjoule meter by means of a beam splitter BS. To attenuate the beam and to block visiblelight a neutral density filter ND respectively interference filter IF are placed in front ofthe photodiode.

CHAPTER 344

3.2 Experimental observations

Before the series experiments were conducted, it was first determined at what xenonfraction the laser showed its optimised output energy. See Figure 3.2. In this graph thetotal output energy is plotted as a function of the xenon fraction at several dischargecurrents. It shows that over a wide range of discharge currents the laser generates thehighest output energy at a xenon fraction of 0.5 %. In previous experiments under similarconditions during 1 - 2 ms values of 0.4 % [35, p. 33] and 0.5 % [66] have been found. In allexperiments described below a fractional xenon content of 0.5 % has been used. Thepressure regime investigated was 2 - 5 bar. At lower pressures the laser showed alreadysaturation behaviour by e-beam pumping only and switching on the discharge strengthenedthis effect. So little information was gained at pressures below 2 bar. Above 5 bar theexperiments were obstructed too much by frequent foil rupture.

0.01 0.1 10

1

2

3

4

5

6

14 kA

28 kA

0 kA

0.5 %

Out

put e

nerg

y [

J]

Xenon fraction [%]

0

3

6

9

12

15

18S

pecific output energy [J/l]

Figure 3.2 The output energy as a function of the xenon fraction at several dischargecurrents. The data are taken at a pressure of 4 bar and a collector current density of 0.75 A/cm2.The numbers to the left of the curves denote the discharge current.


In these experiments the accelerator voltage was kept constant at 185 kV. Thisvoltage was found to be optimal with respect to the output power of the laser. At lowervoltages the electrons do not have sufficient energy to penetrate the foil and subsequentlytravel the distance between the foil and the discharge electrode at the highest pressure of5 bar. This results not only in a strong non-uniform excitation of the medium by thee-beam but also in regions near the discharge cathode that are not ionised at all by thebeam. As a consequence the efficiency of the discharge drops and, more severely, thepossibility of formation of instabilities in the discharge increases. When the voltages wasincreased from 185 kV to 275 kV, the output power at higher pressures dropped about20 %. This can be explained from a slowly decreasing stopping power of the gas mixturewith rising electron energy which results in a lower pumping power. Calculations based on

-10 0 10 20 30 40

0.0

0.5

1.0

1.5

(c)

Pou

t [M

W/l]

Time [µs]

6.2 µs

-10 0 10 20 30 40

0

5

10

15

20

(b)

I dis

[kA

]

-10 0 10 20 30 40

0.0

0.5

1.0

1.5

(a)

J beam

[A

/cm

2 ]

Figure 3.3 Temporal profiles of the beam current density Jbeam (a), discharge currentIdis (b) and laser output power density Pout (c). The pressure is 5 bar. The number 6.2 msdenotes the duration of the stationary period.

CHAPTER 346

stopping power data from Ref. [67] show a drop of the input power by 30 % when theaccelerating voltage is increased from 185 kV to 275 kV. This agrees well with observeddrop of the output power. The fact that such a drop is much less clear at lower pressuresmay be the result of a substantial back-scattering of the electrons at the discharge electrodeowing to the high velocity these electrons still have after passing the gas mixture.

The typical behaviour of the pulsed experiment is the appearance of the outputpulse shortly after the onset of the e-beam, followed by a quasi-steady state regime wherethe e-beam current, discharge current and output are more or less constant, and finally theregion with the premature fall-off of the output pulse whereas the discharge and e-beampulses are still present. See Figure 3.3. The stationary period is then determined by thetime during which the variation of the peak output power is less then 10 %. At the end ofthis period we always observe a continuous fast drop of the output. In this chapter only thetotal laser potential between the two bands is considered by investigation of the laseroperating in multi-wave mode. It is always observed that the total laser power of theoscillator with broad-band reflectors does not show any substantial modulation during thestationary period. In the next chapter it will be shown that the individual lines do exhibitstrong modulation during this period which is due to the well-known line competition.

The experiments give us the stationary duration of the output as a function ofpressure, discharge power and e-beam current. In the following various quantities will beshown as a function of the discharge power for e-beam current densities of 0.4 and0.9 A/cm2. These numbers refer to the flat-top value of the e-beam pulse. The dissipated

0 5 10 15 20 250

5

10

15

20

(a) 0.4 A/cm2

Pressure [bar] 2 3 4 5

Be

am

po

we

r

[MW

/l]

Discharge power [MW/l]

0 10 20 30 40 500

10

20

30

40

(b) 0.9 A/cm2

Figure 3.4 For each experimental condition the corresponding beam and discharge inputpowers are plotted. Note that at high discharge powers the beam input power drops because inthat regime the stationary duration of the laser power is already largely present during thebuild-up time of the e-beam. For the readers convenience a line is drawn which separates theregions of 'long' (more than 5 ms, the left-hand side) and 'short' (less than 5 ms, the right-handside) stationary behaviour.


e-beam power is not simply a constant times the product of the chosen e-beam current andgas pressure because at high input powers when the stationary duration is short, asubstantial part of this duration is already present during the build-up time of the e-beam.For each figure the total input power can be inferred from Figure 3.4. In this figure foreach experimental condition the corresponding beam and discharge input power areplotted. The beam input power is calculated by means of data of the stopping power inargon [67]. To estimate the number of electrons and their mean energy after passing thefoil data from Ref. [57] were used. In argon the losses of the e-beam power by radiationare less than 1 % of the total energy loss in the energy range of interest (0 - 200 kV), whichshows the very efficient transfer of beam power to the buffer gas.

The results of the stationary duration as a function of the discharge power areshown in Figure 3.5(a) and (b) for e-beam current densities of 0.4 and 0.9 A/cm2

respectively. It is clearly seen that the stationary time depends strongly on pressure.Although the experimental data are somewhat scattered owing to experimental fluctuationsthe stationary time at higher input powers is roughly inversely proportional to the inputpower density of the discharge.

Beyond this stationary regime the output power and laser efficiency decrease. Thedependence of the output power in the stationary regime on the discharge power is plottedin Figure 3.6(a) and (b) for e-beam current densities of 0.4 and 0.9 A/cm2 respectively. Thegeneral behaviour of an increase of the output power is, up to a value that depends on thegas pressure, proportional to the discharge power. The higher the pressure the larger thevalue of the discharge power that limits this proportionality regime. Note also that at lowdischarge power the output power drops at the highest pressure of 5 bar. Such behaviour of

0 5 10 15 20 250

5

10

15

20

25

(a) 0.4 A/cm2 Pressure [bar]

2 3 4 5

Sta

tiona

ry d

urat

ion

[µs

]


0 10 20 30 40 500

5

10

15

20

25

(b) 0.9 A/cm2

Figure 3.5 The dependence of the stationary duration of the laser output on the dischargeinput power density for an e-beam current density of 0.4 A/cm2 (a) and 0.9 A/cm2 (b).

CHAPTER 348

a dropping output power at a high pressure and fixed e-beam current has also beenobserved previously [24].

The intrinsic efficiency with respect to the discharge power is plotted in Figure

0 5 10 15 20 250.0

0.5

1.0

1.5

(a) 0.4 A/cm2


Out

put p

ower

[M

W/l]


0 10 20 30 40 500.0

0.5

1.0

1.5

2.0

(b) 0.9 A/cm2

Figure 3.6 The output power density during the stationary duration as a function of thedischarge power density for an e-beam with a current density of 0.4 A/cm2 (a) and 0.9 A/cm2 (b).

0 5 10 15 20 250

2

4

6

8

(a) 0.4 A/cm2


Dis

char

ge e

ffic

ienc

y [

%]


0 10 20 30 40 500

2

4

6

8

(b) 0.9 A/cm2

Figure 3.7 The discharge efficiency versus the discharge input power density during thestationary time of the laser. This efficiency is defined by the ratio of the total output power minusthe output power by e-beam pumping alone and the discharge power.


3.7(a) and (b) for e-beam current densities of 0.4 and 0.9 A/cm2 respectively. These valuesare calculated from the ratio of the total output power minus the output power generatedby the e-beam only and the discharge power. The total efficiency is determined by theration of the output power and the sum of the input power of the e-beam and discharge.When the total efficiency versus the total input power is plotted as is done in Figure 3.8(a)and (b) for e-beam current densities of 0.4 and 0.9 A/cm2, it is seen that the maximumefficiency drops with total input power and that the highest efficiency of about 8 % isreached for input powers below 10 MW/l at a low gas pressure. For each input power thegas pressure can be optimised and the optimised pressure increases with the input power.Note the opposite behaviour of the discharge and total efficiency. Whereas at high inputpower the maximum discharge efficiency grows with rising pressure, the maximum totalefficiency drops. So as far as the efficiency is concerned, the discharge is favoured byhigher pressures but the e-beam by lower pressures. This characteristic of the beam is alsoshown by Ohwa et al. [68] according to whose calculations the maximum e-beamefficiency peaks at 1 bar.

Finally, we plotted the available output energy per pulse during the stationaryperiod as a function of discharge power. See Figure 3.9. It is remarkable that this outputenergy not only peaks as a function of the input power but also as a function of thepressure.

0 5 10 15 20 25 300

2

4

6

8

10

(a) 0.4 A/cm2


Tot

al e

ffici

ency

[%

]

Total input power [MW/l]

0 10 20 30 40 50 600

2

4

6

8

10

(b) 0.9 A/cm2

Figure 3.8 The total efficiency as a function of the total input power density. This efficiencyis defined by the ratio of the output power and the total input power.

CHAPTER 350

3.3 Quasi-steady state behaviour

We shall discuss the kinetic model of the laser process by means of a flow diagram of thekinetics shown in Figure 3.10. It indicates the main species and kinetic reactions that areexpected for a multi-atmospheric Ar-Xe laser with only 0.5 % Xe that is pumped by ane-beam sustained discharge. Although many more reactions take place, these are omittedhere in order to reveal the main processes during operation of the e-beam sustaineddischarge Ar:Xe laser.

Although pressure is used as a convenient experimental parameter, the gas numberdensity will be used in this analysis because this is consistent with the usual description ofkinetic reactions in which rate constant are given with respect to gas number density ratherthan pressure4. The electron beam ionises the argon gas proportional to its density [Ar] sothat the ion production by the e-beam can be written as ceJbeam[Ar] where ce is a constantand Jbeam the collector current density. These ions are lost by three-body collisions with Arto form Ar2

+. The main process suffered by the molecular argon ions is the formation ofArXe+ in collisions with Xe. The recombination of ArXe+ leads to the formation of thehigher excited states of Xe, which are subsequently quenched by atomic collisions to reach

4 The reason for this is obvious since the pressure also depends on temperature.

0 5 10 15 20 250

5

10

15

(a) 0.4 A/cm2


Out

put e

nerg

y [

J/l]


0 10 20 30 40 500

5

10

15

20

(b) 0.9 A/cm2

Figure 3.9 The dependence of the output energy on the discharge power density during thestationary operation of the laser.


the upper laser levels of the 5d manifold. The lower laser levels of the 6p manifold are atmulti-atmospheric pressure mainly quenched by Ar to reach the metastable 6s' level. Thereis also some radiative decay to the metastable 6s level. In the following the 6s and 6s'states will be lumped to one metastable level Xe*. Then, the metastable Xe* atoms willproduce ArXe* excimers in three-body collisions with Ar. These excimers decay byradiative dissociation and form again the ground state.

It is seen that the xenon levels above the metastable level are separated by about1 eV, an energy comparable with the average electron energy of the discharge. For thatreason it is generally accepted that the discharge mainly contributes to the excitation andionisation from the metastable level. In fact, this recirculation of energy between themetastable state and the atomic ion was introduced to explain the high efficiencies found

0

5

10

15

20

Pd Pd

Jbeam

ArAr

2Ar

ee

2ArXe Xe

2Ar,e2Ar

2Ar

Jbeam

Xe(5d)

Xe(6p)

Xe2

+ArXe+Xe+

Xe**

Xe(7p/7s)Xe(6s')

Xe(6s)ArXe*

Ar *

Ar2

+Ar+

Ene

rgy

[eV

]

Pd

Pd

Pd

Figure 3.10 Scheme of the most important kinetic reactions and species for the plasmachemistry of the Ar:Xe laser pumped by an e-beam sustained discharge. The bold names arelabels of the energy levels, whereas the italic ones are the particles involved in the reactionindicated by a solid arrow. The dotted arrows denote radiative transitions.

CHAPTER 352

[9]. Because of the low xenon content the contribution of the e-beam to the formation ofXe+ is negligible compared to the discharge contribution. In this way the discharge iseffective in producing Xe+ which in three-body collisions flows to ArXe+. In principle, thekinetic chain of the discharge and laser process forms a closed cycle bounded by themetastable and ionisation level of Xe. In this steady-state process the supply of metastableXe atoms by the e-beam compensates for the above mentioned loss of metastable atomsthat decay via the excimer to the ground state. It is experimentally observed that after anearly termination of the e-beam the discharge impedance increases drastically and theoutput drops. This shows that the drop of the output pulse after the stationary duration(Figure 3.3) is not the result of a discharge getting unstable. The processes responsible forthe ending of the stationary period will be discussed in § 3.6.

The electrons are delivered by both the e-beam and discharge. The dischargeconditions depend on the e-beam current density. According to calculations the averageelectron energy in the case of mere e-beam pumping increases slightly with increasing e-beam current density. At a lower e-beam current density and constant discharge power thereduced electric-field strength (E/N), the drift velocity and average energy of dischargeelectrons are higher and the electron density is lower. Apart from the formation kinetics ofthe laser inversion which depends strongly on the discharge parameters and gas pressure,there is also a considerable quenching of the inversion by collisional mixing of the 6p and5d manifolds by both electrons and atoms. For that reason the laser performance is astrong interplay of discharge power, e-beam current and gas pressure; each parameter canbe optimised in relation with the other ones.

3.3.1 Kinetics

Below, a kinetic model will be described for the steady-state behaviour of the laser. First,the reactions and mechanism of the e-beam sustained discharge will be considered. Therate equation for Ar+ is mainly given by the following process:

21beame ]Ar][Ar[]Ar[

]Ar[ ++

−= kJcdt

d, (3.1)

where ce is a constant of proportionality, Jbeam is the collector current density and k1 is theformation constant of molecular argon ions. The main process for Ar2

+ in our system isdescribed by

]Xe][Ar[]Ar][Ar[]Ar[

222

12 ++

+

−= kkdt

d, (3.2)

where k2 is the formation constant for molecular ArXe+. The molecular ArXe+ formationin the e-beam chain is described by


ee22

beam

]ArXe[]Xe][Ar[]ArXe[

nkkdt

d +++

−=

, (3.3)

where ke is the recombination rate constant of ArXe+ and ne is the electron density. Themain kinetic chain for Xe+ is dominated by the discharge power density Pd that ionises themetastable Xe atoms, and by its quenching by three-body collisions to form ArXe+. Sincein the model the discharge will ionise the metastable xenon atoms, the production rate istaken to be proportional to the discharge power:

23dd ]Ar[]Xe[

]Xe[ ++

−= kPcdt

d, (3.4)

where cd is a constant of proportionality and k3 is the formation constant for ArXe+. Themolecular ArXe+ formation in the discharge chain is then given by

ee2

3

dis

]ArXe[]Ar][Xe[]ArXe[

nkkdt

d +++

−=

, (3.5)

The formation of xenon metastables is given by

( ) dd2*

4

*

]Ar][Xe[]Ar][[Xe(6p)]Xe[

Pckrdt

d βα ++−−= , (3.6)

where r and k4 are the rate constants for two-body quenching of the lower laser levelrespectively three-body quenching of the metastables and a and b are constants ofproportionality for excitation by the discharge to the upper and lower laser levelsrespectively.

For the stationary state the electron density ne is equal to the sum of the ions, whichcan easily be deduced from equations (3.1) to (3.5) by setting the time derivatives equal tozero:

( )ddbeameee

23

dd

21beamee ]Ar[

1

]Ar[]Xe[

]Ar[

]Ar[

1PcJc

nkk

Pc

kkJcn +++

+= , (3.7)

Under the assumption that ne is maximal 10-15 cm3 the following holds:

85.0]Xe[2]Ar[ 2

21

ee ≤+ kk

nk and 25.0

][ 23

ee ≤Ark

nk, (3.8)

so that to a good approximation

CHAPTER 354

)[Ar](1

ddbeamee

e PcJck

n += . (3.9)

This means that ne increases as the square root of the pump power of both the e-beam anddischarge. Because in rare gases the plasma is recombination dominated, this is preciselywhat one expects. The electron density according to eq. (3.7) is plotted in Figure 3.11 as afunction of the discharge power for various gas pressures. The values of the variousconstants are given in Table 3.1. The values for k1, k2, k3 and ke have been taken fromreference [69]. The value of ce has been calculated from P/W where P is the powerdeposition of the e-beam and W is the average energy expended to create one ion of argonAr+. This W value is taken from Ref. [68].The characteristic time (kene)

-1 of therecombination of the electrons with ArXe+ in Eq. (3.3) and (3.5) determines the lifetime ofthe electrons. Together with an estimated value of ne this allows to calculate theproduction rate by the discharge and thus cd. It is seen in Figure 3.11 that as a function ofthe discharge power ne converges for the various pressures. It should be kept in mindhowever that the discharge power is the product of discharge current and voltage and thatthe voltage increases linearly with pressure at a fixed current.

The metastables are produced by both the e-beam and discharge. In the stationaryregime the production rate by the e-beam is equal to the ionisation rate of Ar. Similarly,the production rate by the discharge is equal to the excitation rate from the metastablelevel:

0 10 20 30 40 500

2

4

6

8


Ele

ctro

n de

nsity

[1

014 c

m-3]


0.9 A/cm2

Figure 3.11 Electron density versus the discharge power density at various pressures ascalculated from equation (3.7).


( ) ]Ar[]Ar][Xe(6p)[ beamedd JcPcr +++= βα . (3.10)

This means that in the stationary regime the density of metastables is not effected by thedischarge and only determined by the e-beam. By substitution of (3.10) in (3.6) one findsfor the density of metastables in the stationary regime:

]Ar[]Xe[

4

beame*

k

Jc= . (3.11)

Also the values for k4 and r are given in Table 3.1. The value for k4 is taken fromRef. [69]. The parameter r will be discussed in more detail in the next section togetherwith other parameters that are related to the kinetic reactions in which the upper and lowerlaser levels involved. This equation illustrates that in the high-pressure regime wherethree-body collisions are important, it is necessary to use higher beam currents atincreasing pressure to maintain a certain level of metastables that can be ionised by thedischarge. In practice this means that if the beam current is too low, the discharge willbecome unstable owing to a lack of easy-to-ionise metastables.

3.3.2 Laser process

In the following the main kinetics of the laser process will be focused on. The inversion isdominated on one hand by the excitation processes of the e-beam and sustainer discharge;on the other hand the inversion is quenched by electrons and atoms. The production rate of

Table 3.1 Values of the reaction constants optimised to match most closely theexperimental results at an e-beam current density of 0.9 A/cm2. The constants in the first columnare discussed in this section. The ones in the fourth column will be introduced in the next section.

Constant Value Unit Constant Value Unit

k1 2.3(-31) cm6/s p1 2.0(-12) cm3/s

k2 2.0(-10) cm3/s p2 3.7(-32) cm6/s

k3 2.0(-31) cm6/s q0 1.35(-6) cm2A1/2/s

k4 6.7(-34) cm6/s r 2.2(-11) cm3/s

ke 1.6(-7) cm3/s a 3.1(18) 1/J

ce 65 cm2/As b 2.2(18) 1/J

cd 5.0(17) 1/J

CHAPTER 356

the upper laser level with density n2 will be in our model proportional to the ionisation rateof argon, i.e. ceJbeam[Ar]. Since the ionisation rate of xenon is taken proportional to thedischarge power, the production rate of the upper laser level is in this model alsoproportional to the discharge power, i.e. (cd+a)Pd. The lasing transitions have highoscillator strengths so that they are tightly coupled by electron collisions. As a result thebuild-up of an inversion is hampered because the electron collisions strive forthermalisation of the 6p and 5d manifolds characterised by the electron temperature. Ingeneral this process is called electron-collision mixing (ECM). The quenching of the upperlaser level by the electrons is proportional to its density as well as the electron density:

2e

e

2 nnqdt

dn−=

, (3.11)

where q is a constant of proportionality. The quenching parameter q depends on theplasma conditions like the average electron energy. At higher average energy the collisionfrequency increases and consequently the quenching rate too. It is expected that the higherthe plasma conductivity determined by the e-beam current, the lower the average energy ofthe electrons and the smaller the quenching parameter. The parameter q will then dependon the e-beam current density. To get a reasonable fit with the experimental observations qwill be approximated by the relation q = q0/Jbeam

1/2. Similarly the quenching by two- andthree-body-collisions with the atoms is given by

22

221

a

2 nNpnNpdt

dn−−=

, (3.12)

where p1 and p2 are proportionality constants and N the gas density which is practicallyequal to [Ar]. Including the stimulated emission the time dependence of the upper laserlevel density is given by

( ) 22

2212e12beamedd2 )()( nNpNnpnqnnnBgNJcPc

dt

dn−−−−−++= νρα ,

(3.13)

where r is the radiation density, g(n) the line shape function and B the Einstein coefficientfor stimulated emission. Since the above mentioned quenching processes strive forthermalisation between the laser levels, we write for the lower laser level with density n1:

122

2212e12d1 )()( rNnnNpNnpnqnnnBgP

dt

dn−+++−+= νρβ , (3.14)

where bPd is the pumping of the lower level and rNn1 the quenching of the lower level,which is proportional to the gas density. To maintain the inversion r must be much largerthan p1 while three-body collisions leading to the decay of the lower laser level arenegligible. The radiation density production W is equal to


( ) ννρ hnnBgW 12)( −= , (3.15)

with the inversion 12 nn − given by

cav12 )(

1

ντν Bhgnn =− , (3.16)

where tcav is the decay time of the resonator determined by its quality factor. The lineshape function can be approximated by

νν

∆≈ 1

)(g , (3.17)

with Dn the gain bandwidth of the laser line. The Einstein coefficient B can be calculatedfrom

hAB

πλ8

3

= , (3.18)

with A the transition probability of spontaneous emission, l the wavelength of the laserline and h Planck’s constant. The decay time tcav is determined by the cavity parametersand is given by

=

R

c

L

1ln

12cavτ , (3.19)

with L the length of the cavity, R the reflection coefficient of the output coupler and c thevelocity of light. Values of Dn and A are calculated in references [70] and [71]respectively. Use of these values and calculation of equations (3.16) to (3.19) gives

12 nn − = 2.5 ´ 1012 cm-3. Because ne = 1014

- 1015 cm-3 the density of n1 and n2 is expected to

be of the same order. This is confirmed by Lawton et al. [11], who did simulations for thee-beam preionised discharge. So, to a good approximation n2 » n1 holds. By adding (3.13)and (3.14) and substituting n2 for n1 one obtains for the quasi-stationary regime:

2ddbeame )( rNncPNJc =+++ βα . (3.20)

By substitution of (3.15) into (3.13) and elimination of n2 the radiation production W in thequasi-stationary regime can be expressed as

CHAPTER 358

( )( ) [ ]

+++++−++=

r

Np

r

p

N

n

r

qcPNJchPcNJchW 21e

ddbeameddbeame )( βαναν .

(3.21)

The initial values for the parameters p1, p2, q0 and r in equation (3.21) are based onRef. [68]. Together with values for a and b the final values of these parameters areobtained by matching the calculated curves with the measured data. These values are listedin Table 3.1. The output power according to equation (3.21) together with ourexperimental data are plotted in Figure 3.12 (a) for an e-beam current density of 0.9 A/cm2.In (b) the optimal output power is plotted versus the pressure for both the experimentaldata and the calculated curves. These figures show that the model agrees well with theexperiments.

3.3.3 Discussion

For small input powers of the sustainer the output power scales proportionally. In thisregime ne is low enough for quenching by electron collision mixing (ECM) to be

0 10 20 30 40 500.0

0.5

1.0

1.5

2.0

2 bar3 bar

4 bar

5 bar

Out

put p

ower

[M

W/l]


0.9 A/cm2

1 2 3 4 5 60.0

0.5

1.0

1.5

2.0

Jbeam

= 0.9 A/cm2

experiment model

Op

tima

l ou

tput

pow

er

[MW

/l]

Pressure [bar]

2

4

6

8

Fractio

nal io

nisa

tion [1

06]

Figure 3.12 (a) Curves of the output power density as a function of the discharge powerdensity at an e-beam current density of 0.9 A/cm2. For various pressures these are calculatedfrom equation (3.21) with values of the constants as mentioned in Table 3.1. The symbols inthis figure coincide with those in Figure 3.6(b). The appearance of the lines connecting thesesymbols coincides with those used for plotting the calculated curve.

(b) Plot of the optimal value of the output power density versus the pressure for the data in(a). Experimental values are indicated by symbols, whereas the calculated points aredepicted by the curve. The dashed line is the fractional ionisation at the optimal outputpower.


negligible. In equation (3.21) this is expressed by the term containing ne/N, which is oftenreferred to by fractional ionisation f. In this regime ne/N is negligible and according to eq.(3.21) the pumping by the discharge reduces to

( ) ( )

+++−+

r

Np

r

pccP 21

ddd βαα , (3.22)

i.e. proportional to the discharge power.At higher discharge powers, however, the output saturates with the discharge

power, as shown in Figure 3.6(a) and (b). It is this regime where the above mentionedECM starts and the fractional ionisation f can no longer be ignored. To what extentelectron quenching influences on the laser process, depends according to this model onlyon the fractional ionisation f = ne/N. Although already suggested by Ohwa et al. [68] andconfirmed by experiments [16] this parameter results here from an analytic study of thekinetics. For the optimal output (Figure 3.12 (b)) f gradually drops from 5 ´ 10-6 to 3 ´ 10-6.At lower e-beam currents f drops; at Jbeam = 0.25 A/cm2 the fractional ionisation at theoptimal input power drops from 3 to 2 ´ 10-6 as the pressure increases from 2 to 5 bar.These values are close to values found for the e-beam pumped systems. Simulations byOhwa et al. [68] gave an optimal f = (2-3) ´ 10-6.

In this respect it is surprising that previously for the EBSD system an optimal f of4 ´ 10-5 is found [72]. In this work ne is calculated from the measured discharge currentand drift velocity calculated for a glow discharge in pure Ar [73]. Because the driftvelocities for Ar and Xe are comparable for a glow discharge in this regime [48, p. 541], itis likely that it will not change significantly in mixtures with only 0.5 % Xe. However, itmay be important that in the EBSD systems a volume ionisation is established by theexternal source. This eliminates significantly the need of high-energy electrons that byionisation compensate for losses. As a result the discharge voltage drops as well as themean energy of the electrons. The drop of the mean energy of the electrons is evenenhanced because the electrons can easily transfer their energy to the metastables. Now, itshould be noted that

m

d νm

eEv = , (3.23)

where vd is the drift velocity, e and m are the charge and mass of the electron, E is the fieldstrength and nm is the mean collision frequency of the electrons with the heavy particles.Although often nm is only taken to be proportional to the pressure, it can be in fact a strongfunction on the electron energy distribution. This is indeed the case for Ar when thecharacteristic electron energy falls in the range of the Ramsauer minimum of the collisioncross-section. For the self-sustained glow discharge this range corresponds to a reducedelectric field E/N in the range of 10-20

- 10-18 V·cm2 [42, p. 13]. The measurements in Ref.[72] were performed at an E/N = 4 ´ 10-18 V·cm2. So at this reduced electric field a shift ofthe electron energy distribution to lower energies may result in a sharply drop of thecollision cross-section and thus a significant increase of the drift velocity. In that case the

CHAPTER 360

fractional ionisation f would be significantly lower, too. Unfortunately no data for the driftvelocity in e-beam sustained discharges in Ar are available in literature [74].

Because quenching by electrons is governed by the ratio of electron to gasnumber density and because to a good approximation ne increases only as the square rootof the gas number density (eq. 3.9) an increase of the pressure has a beneficial effect onECM. This is clearly seen in Figure 3.12: the higher the pressure is, the higher thedischarge input power - and thus ne according to eq. (3.7) - is before saturation of theoutput power occurs. This means that according to equation (3.21) the maximumobtainable power increases strongly with the gas pressure, which is in agreement with theobservations plotted in Figure 3.6. It is also seen in Figure 3.7 and Figure 3.8 that when theefficiency drops it is possible to recoup a high efficiency by increasing of the pressure.This results also from the decreasing fractional ionisation with increasing gas density.

Unfortunately heavy-particle collisions also contribute to quenching. As a matter offact, selective quenching of levels in the 5d and 6p manifolds is dominantly responsiblefor the change of the laser spectrum as a function of gas mixture. Quenching by heavyparticles occurs through two- and three-body collisions. Unfortunately little is knownabout the processes, in particular about the three-body collisions. Equation (3.21) showsthat only at high pressures quenching of the inversion density by atoms becomesimportant. At low pressure depopulation by heavy-particle quenching of the lower laserlevel is also proportional to the gas density, thereby balancing quenching of the upper laserlevel. In eq. (3.21) this expressed by p1/r and p2N/r which are the parameterscharacterising two- and three-body quenching respectively. Evaluation of their ratio gives

pp

Np×= 44.0

1

2 , (3.23)

with p the pressure in bar. This shows that only above 3 bar three-body quenchingoutweighs two-body quenching and that in this regime the output power is hamperedaccording to eq. (3.22) In Figure 3.6 the measurements indicate that only at 5 bar such aprocess takes place. However, both the model and the experiments show that justincreasing the pressure may not necessarily result in higher output powers. This is alsoconfirmed by experiments of Botma et al. [24] who found that at a fixed e-beam currentdensity an increase of the pressure at low discharge pump powers results in a decrease ofthe output.

3.4 Temperature effect on the kinetics

Until now the quasi-stationary regime has been described. In this section the processes thatlimit the duration of this regime (Figure 3.5), will be considered.


Also previous experiments have shown that during long pumping, the laser outputshows a premature drop or even ending [75,76]. These experiments were conducted at lowor moderate pumping rates during a few ms. Our experiments show for the first time sucha phenomenon for the EBSD laser at high pumping rates. The drop of the output poweroriginates from heating of the gas mixture during the pump pulse. This causes an increaseof the electron density ne. Namely, the rate constants of the three-body ion formation, k1

and k3, have a gas-temperature dependence proportional to Tg-3/2, whereas the dissociative

rate constant ke has a temperature dependence proportional to )/exp(1 gv kTε−− , where enis the fundamental vibrational energy [77]. The temperature dependence of ke may be wellapproximated by Tg

-1, because en is only about 6 meV [78]. Substitution of thesedependences into equation (3.7) shows that an increasing temperature results in an increaseof ne.

As mentioned above electrons also have a detrimental effect if their concentrationis too high. So, an increasing temperature leads to a faster drop of the output by ECMaccording to (3.21). To illustrate this the laser output power density and electron densityversus the discharge input power density are plotted for three different gas temperatures ata pressure of 5 bar and an e-beam current density of 0.9 A/cm2 in Figure 3.13(a) and (b).These graphs show that, although the increase of ne due to the temperature is relativelysmall, about 15 % for a temperature difference of 100 K, the decrease of the output powercan be dramatic at high input powers. At 5 bar the drop of the peak output power is morethan 30 %; similar calculations for 2 bar show even a drop of 50 %. These figures show thatgas heating may significantly hamper the output power of the Ar:Xe laser.

0 10 20 30 40 500.0

0.5

1.0

1.5

2.0(a)

500 K

400 K

300 K

Out

put p

ower

[M

W/l]


5 bar, 0.9 A/cm2

0 10 20 30 40 500

2

4

6

8

400 K500 K

300 K

(b)5 bar, 0.9 A/cm2

Ele

ctro

n de

nsity

[1

014

cm

-3]

Figure 3.13 The calculated dependence of the output power density (a) and the electrondensity (b) on the discharge power density at various temperatures. Note the dramatic dropof the output power at high input powers, though the electron density increases onlyslightly.

CHAPTER 362

Because the heat capacity is proportional to the gas density it is expected that thehigher the gas density is, the longer the stationary period is at a fixed power deposition.This is in agreement with Figure 3.5. The temperature for which the laser may operatewithout degraded performance, is a strong function of the e-beam current density. This isshown for a beam current density of 0.4 A/cm2 and 0.9 A/cm2 in Figure 3.14(a) and (b)respectively. Here, the final calculated gas temperature reached at the end of the stationaryperiod, calculated from the dissipated discharge and beam input energy, is plotted versusthe total input power during that period. Thus this figure shows to what extent the gastemperature may be increased at a certain input power level before degradation of theperformance occurs. It is seen that the lower the electron density produced by thedischarge, the less the increased temperature effects the quenching and consequently theoutput. At low input powers, however, the duration of the stationary period is merelylimited by our pump duration of 20 ms and the indicated operating temperature is not themaximum allowable temperature that corresponds with that input power.

These pictures also show that the increase of the e-beam current density, which hasa favourable effect on lowering the electron quenching, allows an increase of the gastemperature before degradation starts. For example, at a beam current density of 0.4 A/cm2

at 5 bar, the maximum temperature increase at the end of the stationary period is about25 K for an input power of 25 MW/l, whereas a density of 0.9 A/cm2 permits an increase ofmore than 200 K at the same power deposition.

Secondly, in the EBSD a second process plays a role, which is absent in the case ofpumping by an e-beam or fission fragments. Namely, an increasing temperature also givesrise to a drop of the discharge impedance; for, if during the discharge the losses of

0 5 10 15 20 25 30300

350

400

450

(a) 0.4 A/cm2


Gas

tem

pera

ture

[

K]

Total input power [MW/l]

0 10 20 30 40 50 60300

400

500

600

(b) 0.9 A/cm2

Figure 3.14 The calculated gas temperature, at the point where the laser output starts todrop, as a function of the total input power for several pressures.


electrons diminish owing to a reduced dimerisation and recombination, a lower ionisationrate and thus lower electron energy is needed. This is shown in Figure 3.15. This figureshows that at low input power the discharge voltage is constant but at high input power agradual drop sets in. This is a well-known phenomenon [42, p. 200] and can lead tocontraction of the discharge finally resulting in an arc. In these experiments, however, suchan event, detectable by a sudden drop of the impedance, has not been observed even whenan e-beam with a duration of 10 ms was used. On the contrary, the discharge extinguishedsmoothly.

A decreasing input power of the discharge seems, however, not to be the maincause of the drop of the output power. This is illustrated in Figure 3.16. Here, it is clearlyseen that the dropping discharge voltage causes a dramatic drop of the discharge inputpower but the total input power does not drop drastically because the e-beam input poweris of the same order of magnitude as the discharge power at the beginning of the pulse.Nevertheless the output power drops more or less linearly and finally even below the valuethat corresponds to mere e-beam pumping. This point is indicated by t1. This means that t1the electron density ne has increased so strongly that ECM severely hampers laser action.

In this figure also the temperature rise is plotted as calculated from the total inputpower. It is assumed that during the excitation pulse the gas mixture is heatedadiabatically. This picture shows that the most important process of limiting the quasi-stationary duration is the enhancement of ECM by the temperature rise. Moreover, itindicates that the drop of the output power is more or less inversely proportional to the gastemperature. This is in agreement with measurements by Hebner [79], who also found aregime in which the output is temperature independent, but thereafter approximatelylinearly drops with temperature. So these measurements are consistent with the measuredtemperature dependence of the gain [80].

-10 0 10 20 30 40

0.0

0.5

1.0

1.5

5.9

2.8

Dis

char

ge v

olta

ge

[kV

]

Time [µs]

12.0 kA

Figure 3.15 Time evolutions of the discharge voltage at different currents. These valuesare taken at the flat part of the current pulse (cf. Figure 3.3). The data are taken at 5 bar and0.9 A/cm2.

CHAPTER 364

Because the stationary duration is limited by the temperature rise and in theseexperiments the beam current density was maximal 0.9 A/cm2, the maximum pulse energydefined as the energy during the stationary period showed a optimum as function of thepressure. According to Figure 3.9 this maximum is about 10 J/l and 16 J/l for e-beamcurrent densities of 0.4 and 0.9 A/cm2 respectively. These results are considerably higherthan previous results obtained with an e-beam pulse of only about 1 ms in which at thesame e-beam current density the maximum value found at 5 bar is 7 J/l [72]. Although inthose experiments an increase of the beam current density up to 2.7 A/cm2 did not result ina higher output energy, it is expected in our case that a higher beam current density at 5 baris beneficial because the stationary period is expected to be longer.

-10 0 10 20 30 40

0.0

0.5

1.0

1.5

t1

(b)

Time [µs]

Pla

ser

[MW

/l]

0

20

40

60-10 0 10 20 30 40

Ptot

Pbeam

Pdis

(a)

Pin

put

[MW

/l]

300

400

500

600

Tem

perature [K]

Figure 3.16 Time evolutions of the input power density Pinput (a) and output power densityof the laser Plaser. (b). In (a) the solid line denotes the discharge power Pdis, the dashed onethe e-beam power Pbeam and the dotted the total input power density Ptot. In (b) the dashedline is the output when pumped by the e-beam alone, the dotted the one when also thedischarge is switched on and the solid line represents the gas temperature during thecombined pumping.

Chapter

Laser spectrum

65

4

In the previous chapter it was shown that the duration of the stationary behaviour waslimited depending on pressure and beam current. It was also argued that the cause of thispremature drop was a rise of the gas temperature during the excitation pulse. In thischapter the behaviour of the various laser lines in multi-wave mode will be investigatedand in particular their contribution to the non-stationary behaviour and sensitivity to thegas temperature.

CHAPTER 466

4.1 Experimental details

Except for the optical part the set-up is the same as described in Chapter 3. Because thedifferent laser lines have to be discriminated the optical part is slightly different from thatin Figure 3.1. See Figure 4.1. By means of beam splitters the laser output is directed to fastInAs photodiodes (EG&G Judson J12-18c) operating at room temperature. In front ofthese photodiodes both Spectrogon narrow-band and neutral-density filters are placed. Thenarrow-band filters each select a single laser line. The 2.6-mm filter, however, was notcapable of discriminating between the 2.63 and 2.65 mm lines. These two lines will bereferred to by the 2.6 mm lines in the remainder of this chapter. The integrated output isdetected by a pyroelectric joulemeter (Gentec ED 500). Whereas the response of thephotodiodes as a function of the wavelength and the transmittance of the optics wasdetermined by the manufacturers specifications, the response of each photodiode has alsoto be corrected for the different attenuation of the optical beam when travelling from thelaser to the photodiode. By removal of the filters the total output power was detected byeach diode by means of which corrections were made for losses by the beamsplitters andtransportation through air. By use of a neutral density filter immediately behind the outputcoupler the detectors still operated in the linear regime. By addition of the integratedsignals of the diodes and comparison of this area with the measured output energy by thejoulemeter the time evolutions were converted into units of power. Because the narrow-band filters attenuated the laser beam by reflecting part of it, great care was taken that thereflections did not interfere with the measurements.

Figure 4.1 Set-up for the measurement of the various laser lines.

LASER SPECTRUM 67

4.2 Results

For the spectroscopic notation of the laser levels the reader is referred to Figure 1.2.In Figure 4.2(a) the temporal profiles of the various laser lines are shown at a

pressure of 2 bar and a collector e-beam current density of 0.25 A/cm2. The 2.03 and3.37 mm lines are at low pressures only present during the rising or falling slope of theexcitation pulse. At pressures of 4 and 5 bar however these lines are much more significantat low pumping rates. Especially the 2.03 mm line grows at the expense of the 1.73 mm lineand has a duration of about 15 ms and an amplitude comparable to the 2.6 mm lines. At thehighest pressures of 4 and 5 bar the 1.73 mm line is even negligible at low pump rates. Thisregime is shown in Figure 4.2(b). Note also that the 1.73 mm line is delayed relatively tothe 2.6 mm lines, a phenomenon that has also been observed by other researchers [70,81].In general the delay increases with rising pressure or decreasing input power. The lowerlevel 6p[5/2]2 of the 1.73 mm line is favourably quenched by Ar [82] and the 1.73 mm

0 10 20 30 40 50

0.0

0.2

0.4

0.6

3.37 µm

Time [µs]

0 10 20 30 40 50

0

50

100

150

2.6 µm

Pow

er

[kW

/l]

0 10 20 30 40 50

0

2

4

6

2.03 µm

0 10 20 30 40 50

0

200

400

600(a) 2 bar, 0.25 A/cm

2

1.73 µm

0 10 20 30 40 50

0

400

800

1200

Time [µs]

23 kA

0 10 20 30 40 50

0

400

800

1200

10 kA

0 10 20 30 40 50

0

400

800

1200(b) 4 bar, 0.9 A/cm

2

0 kA

0

200

400

600

0

200

400

600 Po

we

r [kW/l]

Po

we

r [

kW/l]

0

200

400

600

Figure 4.2 (a) Temporal profiles of the various laser lines at a pressure of 2 bar and acollector current density of 0.25 A/cm2. The data are taken at discharge currents of 0 kA (solidline), 6 kA (dashed line) and 13 kA (dotted line).(b) Temporal profile of the 1.73 (solid line) and 2.6 mm lines (dashed line) in the case of strongline competition between these lines. These data are taken at a pressure of 4 bar and acollector current density of 0.9 A/cm2.

CHAPTER 468

transition has a more favourable ratio of degeneracies5, but the oscillator strength of the1.73 mm line is the lowest [71]. As a result it takes some time before the 1.73 mm line startsto oscillate. When the 1.73 mm line oscillates, the population of the common 5d[3/2]1

upper level of the 1.73, 2.03 and 2.65 mm lines is lowered. In particular the 2.03 mm line isstrongly affected by this decreased population inversion.

The behaviour of the 2.63 and 3.37 mm lines can be understood on similar grounds.These lines share the same upper level 5d[5/2]2 while the 2.63 mm line has the same lowerlevel as the 1.73 mm line, the 6p[5/2]2 level, and the 3.37 mm line shares the 6p[3/2]1 lowerlevel of the 2.03 mm line. So, a rapidly depopulating of the 6p[5/2]2 level but poorquenching of the 6p[3/2]1 level by argon together with a more favourable ratio ofdegeneracies of the 2.63 mm transition allows the 2.63 mm line to dominate over the3.37 mm line.

5 The degeneracy is easily calculated from 2J+1, with J incorporated in Racah notation by

nl[K]J. This shows the usefulness of this notation.

0 10 20 300.00

0.25

0.50

0.75

1.00

3.37 µm

(a) Jbeam

= 0.25 A/cm2

Out

put

pow

er

[kW

/l]

Discharge input power [MW/l]

0 10 20 300

100200300400500

2.6 µm

0 10 20 300

50

100

150

2.03 µm

0 10 20 300

500

1000

1500

2000

1.73 µm

0 10 20 30 40 500.00

0.25

0.50

0.75

1.00

3.37 µm

(b) Jbeam

= 0.9 A/cm2

Out

put p

owe

r [

kW/l]


0 10 20 30 40 500

100200300400500

2.6 µm

0 10 20 30 40 500

50

100

150

2.03 µm

0 10 20 30 40 500

500

1000

1500

2000

1.73 µm

Figure 4.3 The output power of the various laser lines as a function of the discharge powerfor e-beam current densities of 0.25 (a) and 0.9 A/cm2 (b). Note the very different scales of theordinates. The various symbols denote different pressures according to o 2 bar, ▲ 3 bar, ¡ 4bar and u 5 bar.

LASER SPECTRUM 69

Although in these experiments the 2.63 and 2.65 mm lines cannot be distinguished,these arguments explain why the 1.73 and 2.6 mm lines are dominant. It is noted here thatin Ar:He:Xe and He:Xe mixtures the 2.03 mm line dominates because the rate constant forquenching of the 6p[5/2]2 level by He is about 12 times smaller than for quenching of the6p[3/2]1 level [83].

4.2.1 Line competition

Because the 1.73 mm line is dominant when the laser operates near optimum conditionswith respect to output power and efficiency, it is at first instance most interesting toinvestigate the output power of the various laser lines at the point in time where the1.73 mm line exhibits its maximum value. When the 1.73 mm generates the highest powerin comparison with the other lines, this point corresponds to the middle of the stationaryperiod as defined in § 3.2. When the power of the 1.73 mm transition is lower than thepower of other transitions, this point may be anywhere in the stationary period. In Figure4.3(a) and (b) the output power of the various line has been plotted as a function of thedischarge power for beam current densities of 0.25 and 0.9 A/cm2 respectively. Thesefigures show that during quasi-stationary operation the 2.03 mm line is basically absent.Only at higher pressures and at low input power this lines oscillates at a low level. Becausein this regime the 2.6 mm line is dominant, this indicates that the bottleneck for the 2.03 mmline is depopulation of the 5d[3/2]1 upper level by the 1.73 and 2.65 mm lines. It ismentioned that even during single-line operation the performance of this line is very poor

0 10 20 300

50

100

150

200

250

0.25 A/cm2

Ou

tpu

t po

we

r [

kW/l]


0 20 40 600

200

400

600 0.9 A/cm2

Figure 4.4 The output power of the 2.6 mm line as a function of the discharge power at thepoint where the 1.73 mm has just terminated for e-beam current densities of 0.25 (a) and 0.9A/cm2 (b).

CHAPTER 470

[35: p. 59,66] because of the poor quenching of the lower laser level by Ar.The 3.37 mm line is only at high beam current density and high pump power

present. Apparently the diminishing oscillation on the 2.63 mm transition with which the3.37 mm line shares its 5d[5/2]2 upper level, increases the population inversion sufficientlyfor oscillation on the 3.37 mm line. Also other authors have seen such a competition ofthese two lines [22,35: § 3.3,84].

As far as the 2.6 mm lines are concerned, it is seen that essentially these lines showthe same behaviour as the 1.73 mm line, although at 0.9 A/cm2 and the higher pressures the1.73 mm line seems to grow at first instance at the cost of the 2.6 mm line, after which the2.6 mm lines are again allowed to oscillate. It is plausible that this is the result ofcompetition of the 1.73 and 2.65 mm line which have a common 5d[3/2]1 upper level.Previous experiments have already shown a drastic drop of the 2.65 mm line when the1.73 mm line oscillates [66,84]. This also explains that at low input power the 2.6 mm linesincrease after termination of the 1.73 mm line. At high input powers, however, such abehaviour of the 2.6 mm lines is not observed. To illustrate this point the output power ofthe 2.6 mm lines is plotted in Figure 4.4 as a function of the discharge power at the pointwhere the 1.73 mm line terminates. At this point the 2.03 mm and 3.37 mm lines are absent,except for 5 bar with an e-beam current density of 0.9 A/cm2 in which case at low

0 10 20 300.000

0.025

0.050

0.075

0.100

3.37 µm

(a) Jbeam

= 0.25 A/cm2

Re

lativ

e o

utp

ut p

ow

er

[%]


0 10 20 300

25

50

75

100

2.6 µm

0 10 20 3005

10152025

2.03 µm

0 10 20 300

25

50

75

100

1.73 µm

0 10 20 30 40 500.000

0.025

0.050

0.075

0.100

3.37 µm

(b) Jbeam = 0.9 A/cm2

Rel

ativ

e o

utp

ut p

owe

r [

%]


0 10 20 30 40 500

25

50

75

100

2.6 µm

0 10 20 30 40 5005

10152025

2.03 µm

0 10 20 30 40 500

25

50

75

100

1.73 µm

Figure 4.5 The relative output power of the various laser lines as a function of the dischargepower for e-beam current densities of 0.25 (a) and 0.9 A/cm2 (b). The various symbols denotedifferent pressures according to o 2 bar, ▲ 3 bar, ¡ 4 bar and u 5 bar.

LASER SPECTRUM 71

discharge power the 2.03 mm line has a amplitude comparable to the 2.6 mm line.Comparison of this figure with Figure 4.3 shows that at low input power the 2.6 mm linesincrease strongly after termination of the 1.73 mm line. This must be ascribed to thebehaviour of the 2.65 mm line, because in previous experiments it has already beenestablished that the 1.73 and 2.63 mm line do not show strong competition [66,84]. At highinput powers it is seen that also the 2.6 mm lines do not recover after termination of the1.73 mm line. These tendencies indicate that the 5d[3/2]1 upper laser level is affectedduring the excitation pulse, which causes first a termination of the 1.73 mm line and thenof the 2.65 mm line. The 5d[5/2]1 upper level seems to be affected at a much later time asconsequence of which the 2.63 mm line keeps oscillating when the 1.73 and 2.65 mm lineshave already ceased. In the next section more attention will be paid on this differentbehaviour of the upper laser levels.

In Figure 4.5 the relative output power is plotted vs. the discharge pumping powerfor 0.25 and 0.9 A/cm2 respectively at the point of maximum power of the 1.73 mmtransition. These plots show that at higher pressures the 2.6 mm lines become relativelystronger at the cost of the 1.73 mm line. Because the 2.63 and 1.73 mm transitions have thesame lower laser level, which is effectively depopulated by argon, this effect must beascribed to either an enhanced depopulation of the lower level of the 2.65 mm line or netincrease of quenching of the 1.73 upper laser level compared to the upper level of the2.63 mm line. Because Lan et al. [84] already observed that with increasing pressure thecontribution of the 2.63 mm line to the total output energy grows, whereas that of the1.73 mm drops, we also attribute the increase of the relative output power of the 2.6 mmlines to the 2.63 mm line. These results show that quenching by heavy-particle collisionshas a significant influence on the laser spectrum.

4.2.2 Energy loading effects

Because in general the largest part of the laser output energy is carried by the 1.73 and2.6 mm lines, attention will be focused on these lines. As shown in Figure 4.2 the durationof the 1.73 mm line is more sensitive to the input power than the 2.6 mm line. As aconsequence the output power of the 1.73 mm line drops much more quickly than that ofthe 2.6 mm line and comparison with Figure 3.2 shows that the stationary duration is inprinciple determined by the temporal behaviour of the 1.73 mm line. In the previouschapter it was argued that the termination of the stationary behaviour is caused by anincrease of the gas temperature during the excitation pulse. This means that although the1.73 mm line is the strongest line, it suffers mostly from a decreasing pumping rate and arising quenching rate. Contrary to this Patterson et al. [76] found in an e-beam pumpedsystem that the 1.73 mm line terminated at an average energy loading of 200 J/(l×atm)while lasing at the 2.6 mm line terminated at 150 J/(l×atm). In their experiments howeverthe optics were chosen to enhance either the 1.73 or 2.03 mm lines and to suppress otherlines. This possibly explains why in those experiments the 2.6 mm lines ended at a lowerenergy loading than the 1.73 mm. This is also supported by the higher threshold pumpingrate exhibited by the 2.6 mm line compared to the 1.73 mm line in their experiments. When

CHAPTER 472

no line is favoured by the reflectivity of the mirrors, it is the 2.6 mm line that has the lowerthreshold pumping rate.

Till now, most experiments concerning high energy loading effects were carriedout in systems pumped by fission fragments. These experiments focused on the behaviourin single-mode operation of the 1.73 and 2.03 mm lines, which are in general the strongestones in Ar:Xe respectively Ar:He:Xe mixtures. For the first time the behaviour of the 1.73and 2.6 mm lines depending on temperature is investigated, because in our multi-lineexperiments at high pump rate the 2.03 mm line is virtually absent and the 2.6 mm linestrongly present.

In Figure 4.6 the duration of the 1.73 mm line is plotted as a function of the totalinput power. The duration is measured at the base of the optical pulse and the input poweris taken at the time at which the 1.73 mm line terminates. Note that the total duration doesnot depend on the pressure, which is in sharp contrast with the stationary duration (cf.Figure 3.5). Because at high pressures and low pumping rates the 1.73 mm line only weaklylases, the duration under these conditions is consequently short. This regime is indicatedby the dotted boxes in Figure 4.6.

The curves in this figure suggest a duration that depends inversely proportional onthe input power. This means that the 1.73 mm line is terminated at a constant temperaturefor a fixed pressure. In Figure 4.7 the data in the dotted boxes have been discarded becauseof their low gain. The average input power has been calculated from the integrated inputpower divided by the duration of the 1.73 mm line. The integration interval is taken from

0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

25


Dur

atio

n o

f 1.7

3 µm

[ µ

s]

Input power [MW/l]

Figure 4.6 The total duration of the 1.73 mm line versus the input power at the time oftermination of this line. The data are taken at a collector current density of 0.9 A/cm2. Note thatat high pressure and low pump power the 1.73 mm line is only weakly present which manifestsitself by a short duration. These conditions are indicated by the dotted boxes.

LASER SPECTRUM 73

the start of the pump pulse up to the point at which the 1.73 mm line ends. In this wayallowance have been made for the delay of the 1.73 mm, which can be as high as 20 % ofthe duration of the 1.73 mm line at high pressures, and for the rising slopes of the e-beamand discharge current. As a result the product of input power and duration is now directlyproportional to the temperature rise. Figure 4.7 shows that at a fixed beam current densitythe data exhibit the same linear relationship. The dashed curves are linear fits and the slopegives the input energy at which the 1.73 mm line terminates.

In Figure 4.8(a) these slopes are plotted for different e-beam current densities.Although the behaviour of duration the 2.6 mm lines is less clear because at low inputpower this optical pulse had the same duration as the pump pulse and the decrease of theduration takes place at a much lower rate, the data show the same dependence for this line,too. In (b) the results for the 2.6 mm lines are plotted. This figure indicates that the criticalenergy deposition increases with increasing beam current density. It also shows that the 2.6mm lines allow an approximately three times higher energy loading than the 1.73 mm linebefore laser action stops. Patterson et al. [76] also found that termination of the 1.73 and2.6 mm line did not depend on the input power. Because in those experiments the pressurewas fixed at 1 bar this means that the critical energy loading did not depend on the beamcurrent density. As already mentioned above it was found in Ref. [76] that the 1.73 mm lineterminated at an average energy loading of 200 J/l, whereas the 2.6 mm line terminated at150 J/l. The lower value for the 2.6 mm originates from the selective reflectivity of themirrors that suppressed oscillation of the 2.6 mm line, and therefore these result are noteasily compared to our results. The difference may also be the result of a difference in thepumping rate; in Ref. [76] the pumping power was varied between 40 and 1000 kW/l.

0 15 30 45 60 750.00

0.03

0.06

0.09

0.12

0.15

0.25 A/cm2

0.9 A/cm2

Pressure [bar], 2, 3, 4 5

Inve

rse

dur

atio

n o

f 1.7

3 [1

/ µs]

Average input power [MW/l]

Figure 4.7 The inverse duration of the 1.73 mm line as function of the average inputpower. The open and solid symbols correspond to collector current densities ofrespectively 0.25 and 0.9 A/cm2. The dashed curves are linear fits to the data.

CHAPTER 474

4.3 Discussion

The results of Figure 4.7 and Figure 4.8 do not match the calculations by Ohwa et al. [85]for e-beam pumping, according to whose numerical model the laser output is expected toterminate at a lower energy loading as the input power increases. This resulted in thatmodel from an increasing electron density ne during the excitation pulse, which originatesfrom a rising gas temperature causing a drop in the dissociative recombination rate ofArXe+. The fact that termination of the 1.73 mm line always occurs at the same energyloading, even for different pressures, regardless of the input power indicates that heavy-particle collisions play a dominant role6. If ne is the bottleneck, a termination of the1.73 mm line is expected to occur at a constant fractional ionisation f. This means that ahigher pressure would allow a higher electron density, which in the case of a fixed beamcurrent density is equivalent to a higher discharge power. According to Figure 4.7 this isapparently not the case. Because the critical energy loading does not depend on the gaspressure, this implies that the critical gas temperature Tcrit at which laser action ceases, isinversely proportional to the pressure p:

6 It should be kept in mind that termination of the stationary duration, as defined in

Chapter 3, does depend on the input power and pressure. To this difference will be returned at theend of this section.

0.0 0.2 0.4 0.6 0.8 1.0200

400

600

800

1.73 µm

Crit

ical

ene

rgy

load

ing

[J/

l]

Collector current density [A/cm2]

0.0 0.2 0.4 0.6 0.8 1.0800

1000

1200

1400

1600

1800

2.6 µm

Figure 4.8 The critical energy deposition as a function of the e-beam current density forthe 1.73 (a) and 2.6 mm (b) lines.

LASER SPECTRUM 75

pT

1~crit . (4.1)

Possible mechanisms for terminating the laser action on the 1.73 mm line are selectivequenching of the upper (Xe(5dj)®Xe(5dk)), the lower (Xe(6pj)®Xe(6pk)) laser levels orintermanifold quenching (Xe(5dj)®Xe(6pk)). As already shown in the previous section,the dominant process in termination of the 1.73 mm line seems to be a net decrease of theupper laser level. So, a possible cause for the observed behaviour is that during theexcitation heavy-particle quenching becomes stronger owing to a rising gas temperature.As already mentioned in Chapter 3 quenching by heavy particles leading to a reduction inthe total population inversion becomes important according to our model at a pressure ofabout 3 bar. Because the lowest pressure in these experiments is 2 bar, quenching byheavy-particle collisions may become increasingly important or even dominant when therate constant of heavy-particle collisions rises owing to an increase of the gas temperature.According to Equation (3.21) termination of the output power is controlled by

r

Np

r

p

N

n

r

q 21e ++ . (4.2)

If termination of laser action is dominated by heavy-particle quenching, the first term canbe ignored. If in addition the rates for two-body collisions are assumed to have the sametemperature dependence, only the last term on the left-hand side exhibits a temperaturedependence. In view of Equation (4.1) this means that

g2 ~ T

r

p. (4.3)

In other words, because three-particle quenching grows faster than two-particle quenchingat increasing gas temperature, the population inversion diminishes. Unfortunately, little isknown in literature about the gas temperature dependence of the quenching rates. It isplausible that r is mainly determined by the two-body quenching rate of the 6p[5/2]2 level,which is the common lower laser level of the 1.73 and 2.63 mm lines. Calculations byHickman et al. [86] suggest that to a good approximation r ~ (Tg)

0.5. In this case the three-body quenching rate p2 would scale as (Tg)

1.5.Another processes which also may contribute to the termination of laser action are

thermalisation of the levels in the upper or lower manifold and a change in the quenchingfrom the lower laser levels to the metastable 6s' level. Little information of these rateconstants is available, in particular of temperature dependences. Calculations by Hickmanet al. [86] indicate the following. Quenching of the 5d[3/2]1 is negligible, whereasquenching of the 5d[5/2]2 is significant and grows with temperature. This would favouroscillation on the 1.73 mm line in contradiction with the observations. The netdepopulation of the 6p[5/2]2 and 6p[1/2]0 grows, whereas that of the 6p[3/2]1 remainsapproximately constant when the gas temperature rises. So, this also does not support a

CHAPTER 476

ceasing of laser action. In conclusion it can be said that in explaining the laser behaviouras a function of temperature much work need to be done.

As seen in Figure 3.14 the stationary duration drops as the input power increases,which means that the onset of the non-stationary behaviour does result from an enhancedelectron quenching. The cause of a decreasing significance of electron quenching incomparison with heavy-particle quenching at still higher gas temperatures is twofold. First,the electron temperature drops as the gas temperature rises. This has already pointed out in§ 3.4 and manifests itself through a dropping glow voltage, cf. Figure 3.15. As a result therate constant q for electron quenching will drop, too. Because the rate constant fordissociative recombination ke decreases as Tg, ne increases approximately as (Tg)

0.5 (seealso Equation (3.9) and Figure 3.13 (b)). So, because the heavy-particle quenching growsfaster, eventually heavy-particle quenching outweighs electron quenching according toEquation (4.3).

4.4 Concluding remarks

In this chapter the behaviour of the various laser lines has been investigated in a multi-wave mode. It has been shown that in general the 1.73 mm line is the strongest line, but the2.6 mm lines exhibit the longest duration, that means, it is the least sensitive to anincreased gas temperature. This result has been explained by a net quenching by three-body quenching which finally outweighs quenching by electrons. It appears thus that theupper level of the 1.73 mm line suffers more from this dependence on gas temperature thanthe upper level of the 2.63 mm line.

Because the 1.73 mm line is the strongest when the laser operates at high pumppowers, the stationary duration is basically determined by the temporal behaviour of thisline. Because termination of the stationary behaviour shows a different tendency than thecomplete termination of the 1.73 mm line, the performance of this laser is the result of acomplex plasma chemistry.

Finally, it has been shown that in single-line operation the 2.63 mm line is capableof generating about 60 to 70 % [35: p. 59] of the energy generated in multi-wavemode, itmay be interesting to operate this laser on this line with a view to the less sensitivedependence on the gas temperature. In this way a longer stationary duration and acomparable total output power may be achieved and maybe even higher output energiesduring this stationary period.

77

Bibliography

[1] T.H. Maiman, “Stimulated optical radiation in ruby masers”, Nature, 187, pp. 493-494 (1960)

[2] A. Javan, W.R. Bennett, Jr., and D.R. Herriot, “Population inversion and continuousoptical maser oscillation in a gas discharge containing a He-Ne mixture”, Phys. Rev.Lett., 6, pp. 106-110 (1961)

[3] W. Mayerhofer, M. Jung, and E. Zeyfang, in Proceedings of the NATO AdvancedResearch Workshop on Gas Lasers - Recent Developments and Future ProspectsMoscow, Russia, July 2-5, 1995, edited by W.J. Witteman and V.N. Ochkin (KluwerAcademic Publishers, Dordrecht, 1996), p. 225

[4] W.L. Faust, R.A. McFarlane, C.K.N. Patel, and C.G.B. Garrett, “Gas maserspectroscopy in the infrared”, Appl. Phys. Lett., 1, pp. 85-88 (1962)

[5] R.A. Paananen and D.L. Bobroff, “Very high gain gaseous (Xe-He) optical maser at3.5 m”, Appl. Phys. Lett., 2, pp. 99-100 (1963)

[6] P.O. Clark, “Investigation of the operating characteristics of the 3.5 m xenon laser”,IEEE J. Quantum Electron, QE-1, pp. 109-113 (1965)

[7] S.E. Schwarz and T.A. DeTemple, “High-pressure pulsed xenon laser”, Appl. Phys.Lett., 17, pp. 305-306 (1970)

[8] R. Targ and M.W. Sasnett, “High-repetition rate xenon laser with transverseexcitation”, IEEE J. Quantum Electron., QE-8, pp. 166-169 (1972)

[9] L.A. Newman and T.A. DeTemple, “High-pressure infrared Ar-Xe laser system:Ionizer-sustainer mode of excitation”, Appl. Phys. Lett., 27, pp. 678-680 (1975)

[10] P.L. Chapovsky, V.N. Lisistsyn, and A.R. Sorokin, “High-pressure gas lasers on Ar I,Xe I, and Kr I transitions”, Opt. Commun., 16, pp. 33-36 (1976)

[11] S.A. Lawton, J.B. Richards, L.A. Newman, L. Specht, and T.A. DeTemple, “Thehigh-pressure neutral infrared xenon laser”, J. Appl. Phys., 50, pp. 3888-3898 (1979)

[12] V.N. Lisitsyn and A.R. Sorokin, “High-pressure Ar-Xe discharge laser using IRtransitions of xenon”, Sov. Tech. Phys. Lett., 5, pp. 362-363 (1979)

[13] N.G. Basov, V.A. Danilychev, N.N. Ustinovskii, I.V. Kholin, and A.Yu. Chugunov,“Lasing at l = 1.73 mm in an electron-beam-pumped Ar:Xe mixture”, Sov. Tech.Phys. Lett., 8, pp. 256-258 (1982)

[14] Yu. I. Bychkov, V.F. Losev, V.F. Tarasenko, and E.N. Tel’minov, “Intense emissionfrom an Ar:Xe mixture pumped by a microsecond electron beam”, Sov. Tech. Phys.Lett., 8, pp. 361-363 (1982)

78 BIBLIOGRAPHY

[15] V.Yu Baranov, I.M. Isakov, A.G. Leonov, D.D. Malyuta, I.V. Novobrantsev, Yu. B.Smakovskii, and A.P. Strel’tsov, “Effect of pumping conditions on infrared lasing inAr:Xe mixtures”, Sov. Tech. Phys. Lett., 9, pp. 483-484 (1983)

[16] P.J.M Peters, Y.F. Lan, M. Ohwa, and M.J. Kushner, “Impact of electron collisionmixing on the delay times of an electron beam excited atomic xenon laser”, IEEE J.Quantum Electron., 26, pp. 1964-1970 (1990)

[17] O.V. Sereda, V.F. Tarasenko, and A.V. Fedenev, “Lasing due to atomic transitions inxenon during afterglow following pumping with an electron beam”, Sov. J. QuantumElectron., 21, pp. 172-174 (1991)

[18] N.N. Koval’, Yu.E. Kreindel’, G.A. Mesyats, V.S. Skakun, V.F. Tarasenko, V.S.Tolkachev, A.V. Fedenev, A.A. Chagin, and P.M. Shchanin, “Lasing in inert gasespumped by a large-area electron beam with a pulse length to 2.5 ms”, Sov. Tech.Phys. Lett., 12, pp. 16-17 (1986)

[19] T.T. Perkins, “Steady-state gain and saturation flux measurements in a highefficiency electron-beam-pumped, Ar-Xe laser”, J. Appl. Phys., 74, pp. 4860-4866(1993)

[20] E.L. Patterson and G.E. Samlin, “Low-pump-rate multi-millisecond atomic xenonlaser”, SAND93-0057, Sandia National Laboratories (1993)

[21] R.L. Watterson and J.H. Jacob, “Measurements of intrinsic efficiency and parametersof an electron beam pumped ArXe laser”, IEEE J. Quantum Electron., 26, pp. 417-422 (1990)

[22] D.A. Zayarnyi, A.G. Korolev, N.N. Sazhina, N.N. Ustinovskii, and I.V. Kholin,“Influence of the pump power on the spectral and time characteristics of an Ar-Xelaser”, Sov. Tech. Phys. Lett., 21, pp. 488-494 (1991)

[23] N.G. Basov, V.V. Baranov, A.Yu. Chugunov, V.A. Danilychev, A.Yu. Dudin, I.V.Kholin, N.N. Ustinovskii, and D.A. Zayarnyi, “60 J quasistationary electroionizationlaser on Xe atomic metastables”, IEEE J. Quantum Electron., QE-21, pp. 1756-1760(1985)

[24] H. Botma, P.J.M. Peters, and W.J. Witteman, “Intrinsic efficiency and critical powerdeposition in the e-beam sustained Ar:Xe laser”, Appl. Phys. B, 52, pp. 277-280(1991)

[25] L.N. Litzenberger, D.W. Trainor, and M.W. McGeoch, “A 650 J e-beam pumpedatomic xenon laser”, IEEE J. Quantum Electron., 26, pp. 1668-1675 (1990)

[26] W.J. Alford, G.N. Hays, M. Ohwa, and M.J. Kushner, “The effects of the He additionon the performance of the fission-fragment excited Ar/Xe atomic xenon laser”, J.Appl. Phys., 69, pp. 1843-1848 (1991)

[27] W.A. Alford and G.N. Hays, “Measured laser parameters for reactor-pumpedHe/Ar/Xe and Ar/Xe lasers”, J. Appl. Phys., 65, pp. 3760-3766 (1989)

[28] F.S. Collier, P. Labastie, M. Maillet, and M. Michon, “High-efficiency infraredxenon laser excited by a UV preionized discharge”, IEEE J. Quantum Electron., QE-19, pp. 1129-1133 (1983)

[29] J.E. Tucker and B.L. Wexler, “High efficiency, high-energy performance of an X-raypreionized Ar-Xe laser”, IEEE J. Quantum Electron., 26, pp. 1647-1652 (1990)

BIBLIOGRAPHY 79

[30] Q. Mei, P.J.M. Peters, and W.J. Witteman, “Improvement in the performance of anAr-Xe laser using magnetic spiker sustainer discharge excitation”, IEEE J. QuantumElectron., 31, pp. 2190-2194 (1995)

[31] C.P. Christensen, F.X. Powell, and N. Djeu, “Transverse electrodeless rf dischargeexcitation of high-pressure laser gas mixtures”, IEEE J. Quantum Electron., QE-16,pp. 949-954 (1980)

[32] Yu.B. Udalov, P.J.M. Peters, M.B. Heeman-Ilieva, F.H.J. Ernst, V.N. Ochkin, andW.J. Witteman, “New continuous wave infrared Ar-Xe laser at intermediate gaspressures by a transverse radio frequency discharge”, Appl. Phys. Lett., 63, pp. 721-722 (1993)

[33] S.N. Tskhai, Yu.B. Udalov, P.J.M. Peters, W.J. Witteman, and V.N. Ochkin,“Continuous wave near-infrared atomic Xe laser excited by a radio frequencydischarge in a slab geometry”, Appl.Phys. Lett., 66, pp. 801-803 (199 5)

[34] P.P. Vitruk, R.J. Morley, H.J. Baker, and D.R. Hall, “High power continuous waveatomic Xe laser with radio frequency excitation”, Appl. Phys. Lett., 67, pp. 1366-1368 (1995)

[35] H. Botma, Electron-Beam Sustained Discharge Atomic Xenon Laser, PhD thesis,University of Twente, The Netherlands, p. 59 (1993)

[36] T. Fujioka, “Industrial gas lasers between 1.05-10.6 mm range”, Infrared Phys., 32,pp. 81-90 (1991)

[37] See for data of the transmission through the atmosphere: R.D Hudson, InfraredSystem Engineering, John Wiley & Sons, New York (1969), and references herein.

[38] C.D. Child, “Discharge from hot CaO” , Phys. Rev., 32, pp. 492-511 (1911)[39] K.H. Kingdon, “A method for the neutralization of electron space charge by positive

ionization at very low gas pressures”, Phys. Rev., 21, pp. 408-418 (1923)[40] G.W. McClure, “Low-pressure glow discharge”, Appl. Phys. Lett., 2, pp. 233-234

(1963)[41] F.M Penning, “Nieuwe metingen over de doorslagspanningen van edelgassen”,

Physica, 12, pp. 65-82 (1932)[42] See for example: Yu.P. Raizer, Gas Discharge Physics, Springer-Verlag, Berlin

Heidelberg (1991)[43] W.M. Clark and G.J. Dunning, “A long pulse, high-current electron gun for e-beam

sustained excimer lasers”, IEEE J. Quantum Electron., QE-14, pp. 126-129 (1978)[44] D. Pigache, J. Bonnet, and G. Fournier, “A secondary emission electron gun for high

pressure gas lasers and plasma chemical reactors”, in Proc. XV ICPIG, Minsk, pp.865-866 (1981)

[45] J.R. Bayless and C.P. Burkhart, “Long pulse electron gun for laser applications”, inSPIE, Pulse power for lasers III, 1411, pp. 42-46 (1991)

[46] G. Wakalopoulos, “High peak power pulsed WIP electron gun”, Final Report,Contract No. 78-73-09176/E1377-002, Lawrence Livermore Radiation Laboratory,Livermore, California (1978)

[47] D. Pigache, J. Bonnet, and D. David, “A short pulse secondary emission electron gunfor high presure gas lasers and plasma chemical reactors”, in Proc. XVI ICPIG,Düsseldorf, pp. 782-783 (1983)

80 BIBLIOGRAPHY

[48] E.W. McDaniel, Collision Phenomena in Ionized Gases, Wiley, New York (1964), p.668

[49] H. Yasui, T. Tamagawa, I. Ohshima, M. Maeyama, T. Ohsawa, H. Urai, and E.Hotta, “Electrical characteristics of a low pressure wire discharge as an ion source”,in Proc. XXI ICPIG, Bochum, pp. 341-343 (1993)

[50] See, for example, S. Humphries, Charged Particle Beams, Wiley, New York (1990),p. 238

[51] J. Santoru, R.W. Schumacher, and D.J. Gregoire, “Plasma-anode electron gun”, J.Appl. Phys., 76, pp. 5629-5635 (1994)

[52] B. Chapman, Glow Discharge Processes, Wiley, NewYork (1980), p. 87[53] R. Papoular, Electrical Phenomena in Gases, Illife Books Ltd., London (1965), p. 59[54] F. Schwirzke, “Ionisierungs- und Umladequerschnitte von Wasserstoff-Atomen un

Ionen von 9 bis 60 keV in Wasserstoff”, Z. Phys, 157, pp. 510-522 (1960)[55] A.G. Hill, W.W. Buechner, J.S. Clark, and J.B. Fisk, “The emission of secondary

electrons under high energy positive bombardment”, Phys. Rev., 55, pp. 463-470(1939)

[56] S.K. Allison, “Experimental results on charge-changing collisions of hydrogen andhelium atoms and ions at kinetic energies above 0.2 kev”, Rev. Mod. Phys., 30, pp.1137-1168 (1958)

[57] S.M. Seltzer and M.J. Berger, “Transmission and reflection of electrons by foils”,Nucl. Instrum. Methods, 119, pp. 157-176 (1974)

[58] N.N. Koval’, Yu.E. Kreindel’, G.A. Mesyats, V.S. Tolkachev, and P.M. Shchanin,“Efficient use of a low-pressure arc in a grid plasma electron emitter”, Sov. Tech.Phys. Lett., 9, pp. 246-247 (1983)

[59] N.N. Koval, E.M. Oks, P.M. Schanin, Yu.E. Kreindel, and N.V. Gavrilov, “Broadbeam electron sources with plasma cathodes”, Nucl. Instrum. Methods, A321, pp.417-428 (1992)

[60] N.N. Koval’, Yu.E. Kreindel’, and P.M. Shanin, “High-current uniform pulsedelectron beams produced by plasma grid emitter systems”, Sov. Phys. Tech. Phys.,28, pp. 1133-1134 (1982)

[61] E.M. Oks, “Physics and technique of plasma electron sources”, Plasma Sources Sci.Technol., 1, pp. 249-255 (1992)

[62] M.W. McGeoch, “A high-current-density nonclosing plasma cathode”, J. Appl.Phys., 71, pp. 1163-1170 (1992)

[63] Private communications[64] A.F. Zlobina, G.S. Kaz’min, N.N. Koval’, and Yu.E. Kreindel’, “Plasma parameters

in the expander of an electron emitter with a constricted arc discharge”, Sov. Phys.Tech. Phys., 25, pp. 689-691 (1979)

[65] Metals Handbook, 8th Edition, Vol. 1, Metals Park Ohio (1961), p. 1149[66] A. Suda, B.L. Wexler, K.J. Riley, and B.J. Feldman, “Characteristics of the high-

pressure Ar-Xe laser pumped by an electron beam and an electron-beam sustaineddischarge”, IEEE J. Quantum Electron., 26, pp. 911-921 (1990)

[67] J.J. Berger and S.M. Seltzer, Nucl. Sci. Series no 10, NAS-NRC pub. 113 (1964)

BIBLIOGRAPHY 81

[68] M. Ohwa, T.J. Moratz, and M.J. Kushner, “Excitation mechanisms of the electron-beam-pumped atomic xenon (5d®6p) laser in Ar/Xe mixtures”, J. Appl. Phys., 66,pp. 5131-5145 (1989)

[69] N.G. Basov, V.A. Danylichev, A.Yu. Dudin, D.A. Zayarnyi, N.N. Ustinovskii, I.V.Kholin, and A.Yu. Chugunov, “Electron-beam-controlled atomic Xe infrared laser”,Sov. J. Quantum Electron., 14, pp. 1158-1167 (1984)

[70] A. Suda, B.L. Wexler, B.J. Feldman, and K.J. Riley, “Measurements of gain,saturation, and line competition in an electron beam pumped high-pressure Ar/Xelaser”, Appl. Phys. Lett., 54, pp. 1305-1307 (1989)

[71] M. Aymar and M. Coulombe, “Theoretical transition probabilities and lifetimes in KrI and Xe I spectra”, Atomic Data and Nuclear Data Tables, 21, pp. 537-566 (1978)

[72] H. Botma, P.J.M. Peters, and W.J. Witteman, “Saturation studies of the e-beamsustained discharge atomic xenon laser”, IEEE J. Quantum Electron., 29, pp. 2519-2524 (1993)

[73] E. Richley, “Extending the calculation of electron velocity distribution functions forelectrical discharges to large values of E/N”, J. Appl. Phys., 71, pp. 4190-4195 (1992)

[74] It is mentioned though by Lawton et al. [11] that in their model the variation of themetastable density from 0 to 1 % resulted in an increase of the drift velocity by afactor of 3

[75] W.J. Alford and G.N. Hays, “Measured laser parameters for reactor-pumpedHe/Ar/Xe and Ar/Xe lasers”, J. Appl. Phys., 65, pp. 3760-3766 (1989)

[76] E.L. Patterson, G.E. Samlin, P.J. Brannon, and M.J. Hurst, “A study of an electron-beam excited atomic xenon laser at high energy loading”, IEEE J. QuantumElectron., 26, pp. 1661-1667 (1990)

[77] T.J. Moratz, T.D. Saunders, and M.J. Kushner, “High-temperature kinetics in He andNe buffered XeF lasers: The effect on absorption”, Appl. Phys. Lett., 54, pp. 102-104(1989)

[78] A.P. Hickman, D.L. Huestis, and R.P. Saxon, “Interatomic potentials for excitedstates of XeHe and XeAr”, J. Chem. Phys., 96, pp. 2099-2113 (1992)

[79] G.A. Hebner, “Gas temperature dependent output of the atomic argon and xenonlasers”, IEEE J. Quantum Electron., 31, pp. 1626-1631 (1995)

[80] G.A. Hebner, J.W. Shon, and M.J. Kushner, “Temperature dependent gain of theatomic xenon laser”, Appl. Phys. Lett., 63, pp. 2872-2874 (1993)

[81] A.Yu. Dudin, D.A. Zayarnyi, L.V. Semenova, N.N. Ustinovskii, I.V. Kholin, andA.Yu. Chugunov, “Dynamics of the gain and generation of an Ar-Xe laser pumpedby an electron beam”, 23, pp. 578-584 (1993)

[82] J.K. Ku and D.W. Setser, “Collisional deactivation of Xe(5p56p) states in Xe andAr”, J. Chem. Phys., 84, pp. 4304-4316 (1986)

[83] W.J. Alford, “Quenching of 6p[3/2]1 and 6p[5/2]2 levels of atomic xenon by raregases”, IEEE J. Quantum Electron., 26, pp. 1633-1638 (1990)

[84] Y.F. Lan, P.J.M. Peters, and W.J. Witteman, “Spectral line competition in a coaxialelectron-beam-pumped high pressure Ar/Xe laser”, Appl. Phys. B, 52, pp. 336-340(1991)

82 BIBLIOGRAPHY

[85] M. Ohwa and M.J. Kushner, “Energy loading effects in the scaling of atomic xenonlasers”, IEEE J. Quantum Electron., 26, pp. 1639-1646 (1990)

[86] A.P. Hickman, D.L. Huestis, and R.P. Saxon, “Calculations of inelastic collisions ofexcited states of Xe with He and Ar”, J. Chem. Phys., 98, pp. 5419-5430 (1993)

Documents

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