Characterization of the plasma on dielectric fiber (velvet) cathodes

JOURNAL OF APPLIED PHYSICS 98, 093308 �2005�

Characterization of the plasma on dielectric fiber „velvet… cathodesYa. E. Krasik,a� J. Z. Gleizer, D. Yarmolich, A. Krokhmal, V. Ts. Gurovich, S. Efimov, andJ. FelsteinerPhysics Department, Technion, 32000 Haifa, Israel

V. BernshtamPhysics Department, Weizmann Institute of Science, 76100 Rehovot, Israel

Yu. M. SavelievPhysics Department, University of Strathclyde, Glasgow G4 0NG, United Kingdom

�Received 30 March 2005; accepted 26 September 2005; published online 16 November 2005�

An investigation of the properties of the plasma and the electron beam produced by velvet cathodesin a diode powered by a �200 kV, �300 ns pulse is presented. Spectroscopic measurementsdemonstrated that the source of the electrons is surface plasma with electron density andtemperature of �4�1014 cm−3 and �7 eV, respectively, for an electron current density of�50 A/cm2. At the beginning of the accelerating pulse, the plasma expands at a velocity of�106 cm/s towards the anode for a few millimeters, where its stoppage occurs. It was shown byoptical and x-ray diagnostics that in spite of the individual character and nonuniform cross-sectionaldistribution of the cathode plasma sources, the uniformity of the extracted electron beam issatisfactory. A mechanism controlling the electron current-density cross-sectional uniformity issuggested. This mechanism is based on a fast radial plasma expansion towards the center due to amagnetic-field radial gradient. Finally, it was shown that the interaction of the electron beam withthe stainless-steel anode does not lead to the formation of an anode plasma. © 2005 AmericanInstitute of Physics. �DOI: 10.1063/1.2126788�

I. INTRODUCTION

There has been a continued interest in velvet and carbonfiber cathodes that can be used in the generation of electronbeams with current densities of several tens of A/cm2 atmoderate accelerating electric fields of 104–105 V/cm andpulse durations in the range of 10−7–10−5 s.1–28 The mainadvantages of these cathodes are the low electric-field thresh-old �E�104 V/cm� and the small time delay ��10−8 s� inthe onset of electron emission. In spite of the large number ofexperimental papers devoted to this subject, the mechanismsgoverning electron emission and the uniformity of the cross-sectional current density of the electron beams generated bythese cathodes are not fully understood at present and requirefurther research. In a recent publication by Shiffler et al.,27

the electron emission from CsI-coated carbon velvet cath-odes was suggested to be a “pure field emission” with thecathode plasma playing a minor role only. These authorssuggested also that the electron beam had a uniform current-density distribution across the cathode area, and that theelectron current density from velvet cathodes exceeds theChild-Langmuir value due to the formation of an anodeplasma and the establishment of a bipolar flow in thediode.18,21–24 In contrast, Saveliev et al.26 and Krasik et al.17

have observed intense light emission from individualbright spots that appear on the surface of velvet and carbonfiber cathodes. These observations indicate that the electronemission from velvet and carbon fiber cathodes is of plasmaorigin.

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A number of recent experiments14–27 employed varioustypes of velvet and carbon fiber cathode materials and differ-ent techniques for CsI coating. This could be potentially thereason behind the differences in the results related to mecha-nisms governing electron emission, uniformity of the elec-tron beam, and appearance of an ion flow in the diode.Deeper understanding of these mechanisms could beachieved and some contradictions in the results by differentresearch groups could be settled by direct time-and-space-resolved nondisturbing measurements of the surface plasmaparameters, ion flow in the diode, and electron-beam current-density cross-sectional distribution.

In this paper, we present the results of an investigation ofa high-current planar electron diode with cathodes made oftwo types of polymer velvet, with and without CsI coating,and a solid carbon cathode. The polymer velvet fabrics usedin the present experiments were similar to those studied inthe experiments by Shiffler et al.15,16,18,21–24,27 and Savelievet al.25,26 A number of various time-and-space-resolved elec-trical, optical, x-ray, and spectroscopic diagnostics were usedto characterize the operation of the cathodes and the gener-ated electron beams. We will show that the investigated cath-odes are characterized by the formation of a nonuniform sur-face plasma with a density in the range of 1013–1014 cm−3

and an electron temperature of several eV. Despite the cath-ode plasma nonuniformity, the electron current densityacross the anode surface was found to be sufficiently uni-form. A model explaining this apparent “contradiction” willbe discussed. The conditions for the bipolar flow formationalso have been investigated by direct measurements of the

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093308-2 Krasik et al. J. Appl. Phys. 98, 093308 �2005�

II. EXPERIMENTAL SETUP AND DIAGNOSTICS

Circular cathodes made of two various types of velvetfabric, blue and black, have been investigated. Velvet fabricsconsist of fiber bunches distributed uniformly with densitiesof �12�12 cm−2 �black velvet� and �14�14 cm−2 �bluevelvet�. Each bunch consists of approximately 20 polymerfibers of �17 �m diameter and �1.5 mm �black velvet� and�1.8 mm �blue velvet� lengths. The total thickness for boththe velvet materials was �2 mm. The blue velvet was testedwith and without CsI coating. A CsI coating was made by anapplication of a saturated CsI water solution on the velvetsurface followed by heating it to �80 °C during severalhours. In several experiments, a solid carbon cathode of25 mm diameter was also used.

Each velvet cathode had an emission area of D=60 mm diameter. The velvet material which was dried andcleaned by dried air was glued with conductive-silver-loadedepoxy produced by Chemtronics® �resistivity of 5�10−3 � cm and cure cycle of 24 h at 24 °C� along theedge of a 2-mm-thick aluminum disk. This disk was attachedto the cathode holder having a polished aluminum screeningring of 10 cm outer diameter. The edge of the velvet diskholder was screened by the cathode screening electrode. Thesurface of the velvet was offset by �1 mm with respect tothe ring surface. Special care was taken to stretch the mate-rial only enough to ensure that the velvet surface was asplanar as possible.

A planar diode �Fig. 1� was operated at moderate40–90 kV/cm electric fields. Normally, a stainless-steelplate was used as an anode. In some experiments the anodewas a 140 mm diameter stainless-steel grid with 70% trans-parency. The grid was placed inside a 200 mm diameter alu-minum ring holder. In these experiments a 120-mm-diam.carbon collector was positioned at 30 mm behind the anode.The anode-cathode gap dak was varied within the range of15–51 mm. The diode was placed inside a vacuum chamberof 50 cm diameter and 55 cm length. A vacuum of �1�10−5 Torr was maintained by two Edwards rotary pumps

FIG. 1. Experimental setup.

�pumping speed of 12 m /h� and two turbomolecular pumps

�pumping speeds of 500 and 350 l / s�. In these experimentswe did not measure the change in the background pressure inthe experimental chamber during and after the diode opera-tion. These data can be found in Ref. 17.

The diode was supplied by a high-voltage �HV� genera-tor with output voltage amplitudes up to 300 kV, pulse du-ration of �300 ns, and internal impedance of 84 �.17 Theexperiment was run in a single pulse regime of the generatoroperation, i.e., one generator shot per 1–5 min. A rep-rateoperation of the diode with a velvet cathode was studied inour earlier research �see Ref. 17� when the diode with thevelvet cathode was triggered at 1–5 Hz in a nonstop mode ofthe generator operation during 4–5 h.

No special conditioning procedure was used for the vel-vet cathode. Namely, these cathodes were operated at fullgenerator voltage. The data concerning the diode, plasma,and electron-beam parameters were collected after approxi-mately 20–25 “conditioning” shots. In most of the experi-ments the data were averaged over several �4–6� generatorshots.

The diode voltage �ak was measured by an active volt-age divider. The diode current Ik and anode current Ia weremeasured by self-integrated Rogowsky coils and the collec-tor current Ic was measured by a current-viewing resistor�Fig. 1�. The side and front images of the light emitted fromthe cathode and anode were registered with a fast-framingcamera 4Quik05A having a frame duration of �20 ns. Thefront images of the cathode were obtained with the collectorremoved and a pair of SmCo magnets �B�150 G� installedat a distance of �50 cm from the cathode outside a drift tubeof 160 mm inner diameter �see Fig. 1�. The purpose of themagnets was to deflect a small part of the beam electronsreaching this location. Otherwise these electrons could dam-age the Plexiglas window. Side images were obtained with astainless-steel plate anode.

The time-and-space-resolved electron-beam current-density distribution was obtained by fast x-ray imaging ofthe electron beam. In this case, instead of the anodegrounded grid, a 125-�m-thick Ta foil with a fast EJ-200plastic �polyvinyltoluene of 2 mm thick� scintillator, whichwas attached to the back of the Ta foil, was used as an anodeat ground potential. The mean path of the electrons �electronenergy �300 keV� in the Ta foil is less than the Ta foilthickness. Therefore, electrons do not interact with the scin-tillator. However, the mean path of the x rays produced bythe electrons inside the Ta foil is larger than the foil thick-ness. The interaction of these x rays with the scintillator�maximum emission at �=425 nm, rise time of 0.9 ns, anddecay time of 2.1 ns� produces a time-and-space-resolvedimage which was obtained using the 4Quik05A camera. Themicro- and macrodivergences of the electron beam weremeasured by using a multipinhole camera and by analyzingthe patterns of the electron microbeams on a sensitive dielec-tric film. The multipinhole camera was installed at astainless-steel disk collector with 15 holes, each being 1 mmin diameter and at a distance of 5 mm from each other. Thedistance between the grid anode and the sensitive dielectricfilm was either 8 or 10 mm.

The ion flow in the diode was measured by an array of

four collimated Faraday cups �CFCs�. Four holes, 1 mm indiameter, were made in the blue velvet and aluminum cath-ode plate, and the CFCs were placed at a distance of 1 mmbehind these holes. Thus, the resulting distance of these CFCcollectors from the velvet front surface was �5 mm. TheCFCs had a radial separation of 10 mm from one another.The CFCs were loaded by 50 � resistors. The sensitivity ofthe CFCs was �0.5 mA/cm2 being limited by electromag-netic noise. In these experiments a solid stainless-steel anodewas used, and the HV generator operated with a positiveoutput pulse, i.e., the cathode was grounded.

The spectroscopic investigations of the light emitted bythe velvet and carbon cathodes were made using a 250 mmChromex spectrometer �1800 grooves/mm grating and spec-tral resolution of �0.4 Å/pixel� and a 750 mm Jobin Yvonspectrometer �2400 grooves/mm grating and spectral resolu-tion of �0.1 Å/pixel�. The light collection was madethrough a Plexiglas window �see Fig. 1�. A light transmittedthrough the window was focused on a 20 mm height and0.1-mm-width entrance slit of the spectrometer by an achro-matic lens of 5 cm in diameter and 15 cm in focus length.The Chromex spectrometer having a less spectral resolutionbut a larger sensitivity than a Jobin Yvon spectrometer wasused to measure the relative intensity of different spectrallines. A Jobin Yvon spectrometer was used to study the spec-tral line profiles. The spectral line images at the output win-dow of the spectrometers were recorded by the fast-framingcamera 4Quik05A. In these experiments the frame durationwas varied in the range of 50–400 ns. The duration of theframe was determined by the flux of light which was neces-sary to collect in order to obtain a reliable spectral line pro-file. The spectral dispersion and the instrumental full width athalf maximum �FWHM� of the spectral lines in the range of3000–6600 Å were calibrated by Oriel spectral lamps, andthe relative spectral sensitivity of the Chromex-4Quick05Acamera system was calibrated using a tungsten light source.

III. EXPERIMENTAL RESULTS

A. General characteristics of an electron diodewith a velvet cathode

In line with the results presented earlier,1–28 an applica-tion of the accelerating pulse caused the appearance of anintense electron emission from both types of the velvet cath-ode, beginning at an average electric field �15 kV/cm. Thetypical wave forms of �ak, Ik, Ia, and Ic at dak=4 cm areshown in Fig. 2 for the case of the circular blue velvet cath-ode. In Table I, we present the average electric field Eav

=�ak/dak the diode current Ik, the average electron currentdensity jk= Ik /Sk where Sk is the cathode emitting surfacearea, the space-charge-limited current density jsc, and the to-tal space-charge current Isc= jscSk for different values of dak

for a diode with the blue velvet cathode. Here the values of Ik

were measured at the maximum of the accelerating voltage.Similar values of Ik were measured with the circular blackvelvet cathode and the blue CsI-coated velvet cathode. In therange of dak=16–51 mm the value of jk varied in the rangeof 55–20 A/cm2, thus covering the range of average current

cathodes.15,18,20,22,25–27 The measured diode current Ik alwaysexceeded the calculated value of Isc with the difference get-ting larger while increasing dak �Table I�. This is the result oftwo effects, i.e., �i� a two-dimensional �2D� experimentalgeometry20,29–35 as opposed to the one-dimensional �1D�model used to evaluate jsc and �ii� cathode plasma expansionin the beginning of the accelerating pulse during the first�150–200 ns before the measurement of Ik is made. Thelatter can be neglected for large values of dak where the in-fluence of the plasma expansion plays only a minor role inexcess of Ik above Isc �see Sec. III D for further details�.However, at larger values of dak, the 2D effect becomes im-portant. For instance, at D /dak=1.2 that corresponds to dak

=51 mm, the increase in Ik over Isc could be as high as 30%�Refs. 20 and 29–33� due to the 2D geometry factor alone.

In the space-charge-limited regime,36 Ik= P�ak3/2, where

P=2.33�10−6�Sk /dak2� is the diode perveance. The value

of P depends only on the diode geometry and remainsconstant during the accelerating pulse if there are nochanges in Sk and dak. In Fig. 3, the experimental P�t� of thediode with the blue velvet cathode is shown for dak

=16 mm �jk�50 A/cm2 and Eav�90 kV/cm�, dak=25 mm�jk�35 A/cm2 and Eav�75 kV/cm�, and dak=40 mm�jk�20 A/cm2 and Eav�50 kV/cm�. The temporal depen-dencies P�t� show that at jk=20–35 A/cm2 the diode pre-veance remains almost unchanged during a major part of thepulse. We made a comparison between the experimental pre-veance and the preveance calculated as P=kla /�ak

3/2, wherek=0.3145�dak/D�−0.0004�dak/D�2+1 is the coefficientwhich accounts for 2D effects.29,30 One can see in Fig. 3 a

FIG. 2. Wave forms of the accelerating voltage �ak and of the cathode Ik,anode Ia, and collector Ic currents. The anode-cathode gap is dak=40 mm.The cathode is made of the blue velvet.

TABLE I. Average electric field Eav, average electron current density jk,amplitude of the diode current Ik, calculated space-charge-limited values ofthe electron current density jsc, and the total current Isc for the differentanode-cathode gaps dak in the case of the circular blue velvet cathode withthe diameter of 60 mm.

dak �cm� Eav �V/cm� jk �A/cm2� jsc �A/cm2� Isc �A� Ik �A�

16 89 55 51 1440 156019 83 45 42 1190 120025 73 35 33 935 99031 65 28 25 710 79041 48 20 15 425 57051 45 18 13 365 510

good agreement between the experimental and calculated�dotted lines� preveances for dak=25 mm and dak=40 mm, aswell as with the data presented by Saveliev et al.25,26 Thus,these data indicate the constant temporal behavior of Sk /dak

at a time delay �d�150 ns with respect to the beginningof the accelerating pulse. At lower dak=15 mm, the pre-veance is not temporally stable and increases with time dur-ing the pulse. This increase in P could be due to either thecathode plasma expansion or the generation of ions on theanode that compensates the electron space charge thus in-creasing the electron current. It is reasonable to suggest thatthe cathode plasma density and temperature are higher atjk�50 A/cm2, leading to a higher expansion rate of thecathode plasma �this issue will be discussed further in Sec.III D�. An increase in the electron current density may at thesame time facilitate the creation of the anode plasma with acorresponding ion flow towards the cathode. �We note thatthis latter mechanism was suggested by Shiffler et al.23,24 toexplain the elevated current densities up to a bipolar flowlimit found in their experiments.�

To evaluate a potential effect of an ion flow on the diodeoperation, the ion current was measured in the cathode sur-face. It was found that for a value of jk up to 50 A/cm2 ameasurable ion flow, i.e., above �0.5 mA/cm2, does not ap-pear in the diode. In these experiments we used an anodemade of a stainless-steel plate. The test of the circular bluevelvet cathode with and without the CsI coating did not leadto an ion flow production. The ion flow towards the cathodewas obtained only when a polyethylene sample was placedon the anode. In this case an ion beam with a current densityof ji�1 A/cm2 was obtained �see Fig. 4�. This ion currentdensity corresponds to the calculated value of the space-charge-limited ion �proton� current density in a planar diodewith a bipolar flow37 jibp�93�ak

3/2�MV� /dak2�cm�

�0.7 A/cm2 at �ak=0.24 MV and dak=4 cm. Also, in Fig. 4the diode current calculated in accordance with the bipolarflow mode of the diode operation36,37 Ibpk=1.86P�ak

3/2 isshown. One can see a satisfactory agreement between theexperimental and calculated current wave forms.

We therefore conclude that under normal operating con-ditions no appreciable ion flow was detected in the diode

FIG. 3. Variation of the diode perveance P�t�= Ik /�ak3/2 during the accelerat-

ing pulse for three anode-cathode gaps dak: 16 mm �jk=50 A/cm2�, 25 mm�jk=35 A/cm2�, and 40 mm �jk=20 A/cm2�. The dotted lines are the per-veance calculated from 3/2 law with corrections for the 2D effect.

with the velvet cathodes, with or without CsI coating, at

electron current densities of up to 50 A/cm2. Therefore, thetemporal instability of P�t� at dak�15 mm should be attrib-uted to cathode plasma expansion.

B. Optical observation of light emission fromthe cathode surface and x-ray imagingof the electron beam

An important characteristic of any electron source is itselectron emission cross-sectional uniformity. In Fig. 5 wepresent the front and side view images of the circular bluevelvet cathode observed at several �d. Similar images wereobtained for the other investigated velvet cathodes. Theseimages are very similar to the images presented in the papersby Saveliev et al.,25,26 Krasik et al.,17 and Shiffler etal.16,21,22,27 Namely, one can see in the front view a practi-cally uniform distribution of small bright spots which appearwhen the average electric field in the diode reaches�20 kV/cm �see Fig. 5�a��. For a larger �d, the brightnessand sizes of the spots at the periphery of the velvet cathodesurface increase as compared with the brightness and sizes ofthe spots at smaller radii �see Figs. 5�b� and 5�c��. Similar

FIG. 4. Typical wave forms of the diode voltage, diode current �1�, calcu-lated bipolar current �2�, and ion current density in the diode with a dielec-tric anode. dak=40 mm.

FIG. 5. Typical front and side images of the light emission from the bluevelvet cathode at different time delays �d with respect to the beginning ofthe accelerating pulse. Frame duration of 20 ns, �ak�200 kV, Ik=850 A,and dak=40 mm. Front view: �a� �d=30 ns, �b� �d=250 ns, and �c� �d

=400 ns. Side view: �d� stainless-steel grid anode. �d=250 ns, �e� stainless-steel plate anode. �d=250 ns, �f� side view framing image for the polyeth-

patterns were obtained in the case of other dak, and the re-moval of the cathode screening ring did not change the tem-poral and spatial evolution of these patterns.

Side view observations which were made with grid an-ode showed only a bright thin ��1 mm� layer in the vicinityof the cathode surface within the first few tens of nanosec-onds of the accelerating pulse. The thickness and brightnessof the bright layer did not change during the acceleratingpulse �see Fig. 5�d��. At dak15 mm only, when the averageelectric field became E�90 kV/cm �jk�55 A/cm2�, an in-crease in the thickness of this bright cathode layer was ob-served with the increase of �d. In the case when instead ofthe grid anode a stainless-steel anode was used, the side viewimages indicate also some light coming from the anode re-gion �see Fig. 5�e��. This light appeared at the beginning ofthe accelerating pulse and becomes more intense at smallerdak. Because we did not notice an ion flow within the wholerange of dak, it is reasonable to suggest that this light is areflected light coming from the cathode plasma which be-comes more intense at smaller dak.

A bright layer of anode plasma was obtained with thedielectric anode only at dak�40 mm. Moreover, at dak

�20 mm, fast-expanding cathode and anode bright layerswere observed �see Fig. 5�f��. At dak�10 mm these cathodeand anode plasma layers bridge the anode-cathode gap at�d�200 ns. At that time the amplitude of the acceleratingvoltage drops to zero. This supports the conclusion that thelight emission observed in the diode with the dielectric anodeis the light emitted by the cathode and anode plasmas.

The above data demonstrate that, in spite of the satisfac-torily uniform side view image of the light emission from thecathode, the front view of the cathode light emission is uni-form only at the beginning of the accelerating pulse. Later inthe accelerating pulse, the main light emission is in the formof bright spots concentrated on the cathode periphery. Thus,if these spots are associated with the locations of the mostdense and hot plasma, one can expect the electron emissionto be significantly nonuniform.

In order to study the electron-beam current-density dis-tribution on the anode we used a fast x-ray imaging of theelectron beam at the Ta foil anode �see Sec. II�. Due to thefast decay time of the organic scintillator ��10−9 s� and therelatively short frame duration of the 4Quik05A camera��20 ns�, one can consider that the x-ray image is producedby electrons having approximately the same energy. Also,one can expect to obtain a ring structure on the x-ray imagewhich will correspond to the structure of the light on thecathode surface. Surprisingly, the obtained electron-beamx-ray images demonstrated satisfactory cross-sectional uni-formity �see Fig. 6� in spite of the individual spot structureon the velvet surfaces. Let us note that the diameter of theelectron-beam x-ray image is slightly larger than the diam-eter of the velvet cathode �see Fig. 6�a��. For example, thediameter of the x-ray image increases up to 7 cm for dak

=4 cm and up to 6.5 cm for dak=2 cm. This diameter in-crease can be explained by the electron-beam divergence.The latter was supported by 2D numerical simulations andthe measurement of the electron-beam divergence. At the

diameter which are connected to the central light zone byluminous rays �see Fig. 6�b��. It can be supposed that theserays are images of the electron beamlets emitted from theplasma sources located at the cathode periphery. Indeed, us-ing different time delays in the 4Quik05A camera operationwith respect to the beginning of the accelerating pulse, wedid not obtain any detectable difference in the radial lengthof these rays. Also, it was checked that the appearance ofthese rays was not related to the discharges along the surfaceof the organic scintillator. Indeed, a Pb screen placed behindthe anode grid showed a sharp replica of these rays as meltedtraces after ten HV generator shots. This replica entirely cor-responds to the x-ray image, including an interchange ofbright �luminous rays� and dark strips at the periphery. Thisindicates reproducibility of the appearance of emission cen-ters at the cathode surface which can be explained by thecarbonization of the discharge channels between the cathodeholder and the velvet.26

In order to understand the contradiction between the in-dividual emission spots obtained on the cathode surface andthe almost-uniform electron-beam density distribution at theanode and the appearance of the radial luminous rays wecarried out additional experiments. Namely, we investigatedthe light emission from the surface of a blue velvet cathodemade in the form of a ring with outer and inner diameters of46 and 22 mm, respectively. Also, we studied the x-ray im-ages of the electron beam generated by this cathode. Thecathode has rounded edges with a radius of 3 mm. Two con-figurations of the cathode were investigated �see Figs. 7�a�and 7�b��. In the first configuration, the velvet was at thesame plane as the central uncovered aluminum base �Fig.7�a��. In the second configuration �Fig. 7�b��, the velvet was4.5 mm above the central uncovered aluminum base. Oneshould expect the central uncovered aluminum base not to

FIG. 6. X-ray images of the electron beam generated in the diode with theblue velvet cathode at time delays of �a� �d=70 ns and �b� �d=250 ns withrespect to the beginning of the accelerating pulse. Frame duration of 20 ns,�ak�200 kV, and dak=40 mm.

FIG. 7. Schematic diagrams of the three types of velvet cathodes.

contribute to electron emission at an accelerating field�60 kV/cm and, therefore, an annular electron beam shouldbe formed by these types of cathodes.

A typical framing image of the velvet cathode �see cath-ode configuration presented in Fig. 7�a�� luminosity is pre-sented in Fig. 8�a�. Similar images of the cathode luminositywere obtained in the case of the cathode configuration shownin Fig. 7�b�. These images are characterized by a ring patternof bright spots located at the outer diameter of the velvet ringand less bright spots at the inner diameter of the velvet ring.In the beginning of the accelerating pulse the brightness ofthe outer and inner spots was the same. Further with theincrease of �d, the brightness of the outer spots increased incomparison with that of the inner spots and this difference inbrightness persisted during the accelerating pulse.

One might expect to obtain a similar structure in thex-ray imaging of the electron beam emitted by the structureof these bright spots. However, we obtained quite differentx-ray images �see Figs. 8�c� and 8�d��. In the case of thecathode configuration shown in Fig. 7�b�, the x-ray imageshows an intense circular spot of �10 mm in diameter at thediode axis, less intense �30 mm in the diameter ring, andconvergent radial rays �see Fig. 8�d��. Similar x-ray imageswere obtained in the case of the velvet cathode shown in Fig.7�a�. In this case, at �d�50 ns the x-ray image also showed�30 mm in the diameter ring pattern with radial rays �seeFig. 8�c��. In addition, a ring pattern with a smaller diameter��7 mm� was obtained at the anode center. It was found thatthe diameters of the both ring patterns decreased with theincrease in �d. Namely, at �d�250 ns the diameter of theinternal and external ring patterns decreased down to �3 and�25 mm, respectively.

In order to decrease the edge effect related to the forma-tion of bright spots at the inner radius of the ring velvetcathode, we studied a 60 mm in diameter velvet cathode hav-ing a screening ring and a Mylar sheet of 0.2 mm thick and32 mm in diameter between the velvet and the aluminumcathode holder �see Fig. 7�c��. According to Saveliev et al.26

the use of an insulator between the velvet and the metalprevents the uniform formation of bright plasma spots on the

FIG. 8. Front view of the ring-type blue velvet cathode: �a� see configura-tion in Fig. 7�a�,�b� see configuration in Fig. 7�c�. The x-ray images of theelectron beam generated in a diode with the ring-type blue velvet cathode:�c� see configuration in Fig. 7�a�,�d� see configuration in Fig. 7�b�,�e� seeconfiguration in Fig. 7�c�. Frame duration of 100 ns, �d=150 ns, and dak

=30 mm.

surface of the velvet. Indeed, in the framing images of the

cathode one can see bright separate radial rays and an ab-sence of bright spots in the central part of the cathode �seeFig. 8�b��. However, these separate rays lead to an almostuniform current-density distribution on the anode �see Fig.8�e��, similar to the case presented in Fig. 6.

Finally, we carried out experiments with a 25-mm-diam.carbon cathode having several circular concentric grooves atits front emission surface at dak=20 mm. The typical waveforms of �ak and Ik are shown in Fig. 9�a�. In these experi-ments we also obtained a ring structure of bright spots lo-cated at the outer cathode radius and almost uniform lumi-nosity of the electron-beam x-ray image �see Figs. 9�b� and9�c�� with the similar radial ray structure.

There are two factors that could contribute to the ratheruniform electron-beam current-density distribution obtainedin spite of the nonuniform character of the separate brightspots at the cathode surface. The first could be related to thelarge electron-beam divergence within the anode-cathodegap. The second is related to a fast radial expansion of thesurface plasma that serves as an electron source.

C. Electron-beam divergence

The divergence of the electron beam was studied with amultipinhole camera �see Sec. II�. In this set of experiments,about ten shots were needed in order to obtain reliable mi-crobeam patterns on the dielectric film. With the circular bluevelvet cathode, 60 mm in diameter and having a screeningring, the microbeam divergence was found to be �� /h�3°, where � is the difference between the diameters of thepinhole and the microbeam pattern and h is the distance be-tween the pinhole plate and the sensitive film. One can writethe transverse velocity of electrons as V�=V�tg� /2��V�� /2�, where V� is the longitudinal velocity of electronsand is the deflection angle of the micro-electron-beam

FIG. 9. �a� Typical wave forms of the diode voltage and current in the diodewith the carbon-made cathode. �b� Front view framing image of the carboncathode and �c� x-ray image of the electron beam. Frame duration of 20 ns,�d=100 ns, and dak=20 mm.

from its axial direction. Taking into account that V��V�,

one estimates the longitudinal velocity as V� =c� 2−1�1/2 / ,where is the relativistic factor, =1+ �e�ak/m0c2�, e andm0 are the charge and mass of the electron, respectively, andc is the speed of light. For our experimental conditions,�ak�200 keV, one obtains V� =2�1010 cm/s and, respec-tively, the transverse electron energy is �30 eV. In addition,these experiments showed that the center of each microbeamimprint on the sensitive film deviates from the center of thecorresponding pinhole �see Fig. 10�a��. This data indicate aweak divergence of the electron beam inside the acceleratinggap that was confirmed by the x-ray measurements �see Sec.III B�. This divergence is caused by the Coulomb repulsionforces of the electron-beam uncompensated space charge.Similar dependencies of the electron-beam macrodivergencewere obtained with cathodes made of the blue velvet with

FIG. 10. �a� Dependence of the electron-beam microdivergence on the beamradius for the blue velvet cathode. �b� Dependence of the microbeam patternrelative intensity on the beam radius for the blue velvet cathode. �c� Depen-dence of the microbeam pattern relative intensity on the beam radius for theblue velvet cathode with CsI coating. �ak�200 kV and dak=40 mm. �d�Typical microbeam imprints for the ring blue velvet cathode �see configu-ration in Fig. 7�b�� on the sensitive dielectric film.

CsI coating and black velvet.

The radial electron-beam density distribution measuredwith the multipinhole camera for the blue velvet cathodewithout and with CsI coating is presented in Figs. 10�b� and10�c�, respectively. One can see that the CsI coating im-proves the uniformity of the radial distribution of theelectron-beam current density.

Thus these experiments showed that one cannot use thedivergence of the electron beam generated by the planar vel-vet cathode with a screening electrode as an explanation forthe cross-sectional uniformity of the electron beam. How-ever, in order to understand the effect of the beam divergenceon the structure of the x-ray images produced by the electronbeam emitted from the ringlike velvet cathode, we carriedout experiments using the multipinhole camera. Typical setof microbeam imprints for the blue velvet cathode �see Fig.7�b�� are shown in Fig. 10�d�. One can see that the centralmicrobeam imprints have a circular form. The latter can beascribed to electrons emitted from the ringlike pattern of thebright spots located at the inner radius of the velvet cathode�see Fig. 8�a�� and having trajectories inclined towards thecathode axis. The measured divergence of these electronsreaches 35°. However, for the blue velvet cathode with theMylar film �see Fig. 7�c�� the divergence of the electronbeam was found to be the same as in the case shown in Fig.10�a�, i.e., not exceeding a few degrees. Thus, this set ofexperiments showed that the electron divergence inside theanode-cathode gap becomes significant only in the case of anonplanar structure of the cathode emission surface.

The experimental data concerning beam divergence wereconfirmed by a simulation of the electron trajectories in theaccelerating gap using the EGUN2 code which accounts forself-space-charge effects.38 The equipotential lines and elec-tron trajectories and the radial electron current-density distri-bution are shown, respectively, in Figs. 11�a� and 11�b� and

FIG. 11. Simulated equipotential lines, electron trajectories, and relativeradial electron-beam current density at the anode in the cathode configura-tions shown in Figs. 7�a� and 7�b�, respectively.

in Figs. 11�c� and 11�d� for the diode configurations shown

in Figs. 7�a� and 7�b�. One can see a good agreement withthe experimental results. Namely, the simulation of the tra-jectories of the electrons emitted by the annular cathode �Fig.11�a�� showed an electron beam of circular structure withradial rays, similar to the x-ray image shown in Figs. 8�c�and 9�c�. Also, the simulation of the trajectories of the elec-trons emitted by the ringlike cathode �the configuration ofthe cathode is shown in Fig. 7�b�� placed 1 mm above thecathode holder showed maximum intensity of electron-beamcurrent density at the center of the anode �see Fig. 11�c��.Current-density calculation results �see Fig. 11�d�� showedmaximum intensity of electron-beam current density at thecenter of the anode. The latter explains the circular brightspot registered at the center of the x-ray image �see Fig.8�d��. Thus, one can conclude that the electron-beam focus-ing and electron rays are the result of the fringe electric fieldat the edge of the cathode emission surface as was observedin experiments with velvet cathode having screening elec-trode �see Fig. 6�. At present we do not know the contribu-tion of these electronic rays to the total beam current and thisremains a subject of further investigation.

In the cathode configuration shown in Fig. 7�a� the x-rayimage obtained in the beginning of the accelerating puls-eshowed an absence of the electron beam at the anode centralpart of 7 mm diameter. The decrease of this diameter later inthe accelerating pulse could be explained by the expansion ofthe plasma cathode spots.

D. Spectroscopic measurements of thecathode plasma

The parameters of the plasma produced at the surface ofthe velvet and carbon circular cathodes �plasma electron den-sity ne and temperature Te, plasma ion temperature Ti, andplasma axial expansion velocity Vp� were obtained by non-disturbing spectroscopic measurements and by comparisonof the experimental data with the results of collision-radiative modeling �CRM�.39 Different spectral lines �H,H�, and C II� were observed in the vicinity of the velvetsurface ��2.5 mm� at different values of dak and, respec-tively, at different jk �see Table I�. The spatial resolution�0.2 mm was limited by the intensity of the collected light.Note that while the H and H� spectral lines were observedin the vicinity of the velvet cathode surface for the wholerange of dak=15–50 mm, the C II �6578 Å� spectral line wasobserved only for dak�20 mm �jk�50 A/cm2� in the vicin-ity of the cathode surface with the sensitive Chromex spec-trometer �see Sec. II�. The observed spectral lines of excitedhydrogen and carbon ions prove the suggestion14,17,25,26 thatthe source of electrons is the cathode surface plasma.

The main part of the experiments with spectroscopicmeasurements was carried out with the circular cathodemade of the blue velvet and with the screening electrode. Atthe beginning of this set of experiments we also checked thespectral lines emitted by the plasma produced at the surfaceof the blue velvet cathode with CsI coating. However, due tothe large background fluorescence of CsI only the H spec-tral line was obtained with reasonable spectral resolution.

solvable. Therefore, spectroscopic measurements were car-ried out with uncoated blue velvet cathode that allows thedecrease of the background light by more than twice.

The broadening of the H and H� spectral lines was usedto determine the values of ne and Ti of the cathode plasma.These measurements were carried out using the 750 mmJobin Yvon spectrometer at a distance of 0.1±0.1 mm fromthe velvet cathode surface at different dak of 20 and 30 mm.The results obtained in these experiments were the same forthe black and blue velvets. At larger distances from the cath-ode, the H� spectral line intensity decreases that makes spec-tral line analysis rather uncertain. The obtained broadeningsof the H and H� spectral lines were treated by the methodwhich is described in detail in Ref. 40 and is based on acomputer iteration procedure to achieve the best fit of boththe H and H� spectral line profiles with the Voigt profile.The latter is obtained as a convolution of the Gauss andLorentz profiles. The Gauss profile results from the convolu-tion of the Doppler spectral line broadening and the instru-mental broadening of the apparatus. The Lorentz profile re-sults from the spectral line broadening which is caused bythe Stark effect due to the electric microfields of chargedparticles in the plasma.41 Here it is assumed that the Dopplereffect plays a major role in the H spectral line broadeningand that the Stark effect is more pronounced in the H� spec-tral line broadening. These are reasonable assumptions be-cause the H spectral line broadening is more sensitive to theDoppler broadening due to its longer wavelength than is theH� spectral line. Also, the H� spectral line is more sensitiveto the Stark effect due to the bigger dipole moment of itsupper level of the transition. The temperature obtained fromthe H spectral line profile is used in the calculation of theH� spectral line FWHM and its fitting to the Voigt profile.Further, the density obtained from the H� spectral line Starkbroadening is inserted into the calculation of the H spectralline FWHM and the fitting of this spectral line profile to theVoigt profile. From this step the recursion continues, up tothe step when the change in the FWHM of both the H andH� spectral lines becomes smaller than the spectral resolu-tion. The plasma ion temperature was determined as41 Ti

=1.8�108��D /��2 �eV�, where � is the H wavelengthand ��D is the Doppler broadening of the H spectral line.Here it was assumed that neutral hydrogen is in thermalequilibrium with the plasma ions. Indeed, assuming thatwithin a few tens of microns in the vicinity of the cathodesurface the plasma density could be �1016 cm−3, one obtainsan ion-neutral collision time �5 ns. Here it was supposedalso that the plasma is formed as a result of a flashover alongthe surface of fibers which contain neutral monolayers �sur-face density of one neutral surface monolayer is ��1–3��1015 cm−2 and the amount of these monolayers is in therange of 15–20�. It was found that Ti�0.5±0.2 eV and doesnot change significantly for all the tested values of dak. TheStark broadening obtained by this procedure, i.e., the FWHMof the spectral line Lorentz profile, was found to be�0.03 Å. This FWHM was determined as42 wl=C�Te ,ne��ne

2/3, where C�Te ,ne� is a coefficient which dependsweakly on the plasma parameters. The values of C�Te ,ne�

was found that the increase in dak from 20 to 30 mm, i.e., adecrease in jk from 40 to 25 A/cm2, leads to a decrease in ne

from �3.5±2��1014 to �5.5±3��1013 cm−3.The plasma electron temperature was determined by a

comparison between the measured H /H� spectral line inten-sity ratio and the results of the CRM.39 The H /H� intensityratio measured by the Chromex spectrometer in the vicinityof the cathode surface was found to be 1.82±0.2 for valuesof dak in the range of 20–30 mm. For our optical experimen-tal setup, this intensity ratio corresponds to a population ratioof 2.5±0.5 of the hydrogen excited levels. In Fig. 12, thedependencies of the modeled H /H� population ratio on thevalue of Te for a different value of ne are shown as curvesand the experimentally obtained H /H� population ratio isshown as a horizontal line. One can conclude that for theplasma densities of �3�1014 and �5�1013 cm−3 whichwere obtained from the Stark broadening analysis, theplasma electron temperature is Te��7±1� eV.

One can expect to observe excited ion spectral lines inthe velvet cathode plasma, for instance, the spectral lines ofcarbon ions. However, only a C II �6578 Å� spectral line witha rather small intensity was registered. Therefore, a spectro-scopic investigation of the plasma produced at the surface ofthe circular carbon cathode �see Sec. III A� was conducted.These experiments allowed us to compare the parameters ofthe plasma produced by circular carbon and velvet cathodes.In this set of experiments, the spectral lines of H, H�, andC II ��4267 Å and ��6578 Å� were observed reproduc-ibly at a distance of �0.2 mm from the cathode surface withdak=15 mm. However, the intensities of the H and H� spec-tral lines observed by the Jobin Yvon spectrometer were in-sufficient for analyzing their FWHM. Therefore, theChromex spectrometer was used in order to obtain theH /H� and the carbon ion spectral line intensity ratios. Thus,in these experiments only CRM was used for the determina-tion of the plasma parameters. However, a comparison of themeasured intensity ratio of a pair of spectral lines with theresults of the CRM gives several pairs of ne and Te valueswhich can be realized in the plasma with the same popula-tion ratio of the excited upper levels. Therefore, one shouldmeasure the intensity ratio of at least two pairs of differenttransitions. The CRM results of the population ratios of theH /H� and C II �6578 Å� /C II �4267 Å� for different ne andTe and the experimentally obtained intensity ratio with ac-

FIG. 12. Results of the CRM �inclined curves� and the experimentally ob-tained data �horizontal line� of the H /H� excited level population ratio.dak=30 mm. The blue velvet cathode.

counting for the level degeneracy of these transitions are

shown in Fig. 13. The best fit of the CRM and the experi-mental results for the H /H� and C II �6578 Å� /C II

�4267 Å� population ratios is obtained for ne��3±2��1014 cm−3 and Te�5±1 eV. At a distance of 1 mm fromthe cathode surface, these spectral lines have been also ob-served but the intensity of the C II spectral lines decreaseddramatically. Moreover, the error bar in the determination ofthe ratio of the C II spectral line intensities increases and,respectively, significantly increases the uncertainty in the de-termination of the set of ne and Te values. At a distance of2 mm from the cathode surface, the C II spectral line be-comes irresolvable and only the H, H�, and C II �4267 Å�spectral lines were observed. At this distance, the populationratio of the H /H� spectral line was found to be �2.5. Thus,one obtains a plasma density similar to that obtained with thevelvet circular cathodes, namely, �1013–1014 cm−3 �see Fig.12�, assuming that Te does change significantly at this dis-tance as compared with its value in the vicinity of thecathode.

A dense cathode plasma expands towards the anodeleading to the mismatch between the diode and HV generatorimpedances and to the accelerating gap closure. The plasmaexpansion velocity was studied by recording the appearanceof the H spectral line at different distances from the bluevelvet circular cathode with a screening electrode using theChromex spectrometer coupled with the 4Quik05A camera�frame duration of 50 ns�. Using a time delay in the appear-ance of the H spectral line at difference distances from the

FIG. 13. �a� Results of the CRM �inclined curves� and the experimental data�horizontal line� of the H /H� excited levels population ratio. �b� Results ofthe CRM �inclined curves� and the experimental data �horizontal line� of theC II �3d 2D−4f 2f0 and 3s 2S−3p 2P0� excited level population ratio. dak

=20 mm. Carbon cathode.

velvet surface, the plasma average expansion velocity was

estimated. This average velocity was measured at distancesup to 3 mm from the cathode surface in the case of gapsdak=20–30 mm, which corresponds to jk values in the rangeof 40–25 A/cm2, respectively. Here it was assumed that theappearance of the excited hydrogen spectral line manifeststhe appearance of a plasma at the same location. Indeed, theEinstein coefficient for the H upper level transition is�15 ns. Therefore, in order to obtain the H spectral lineone should suppose the presence of plasma electrons atthe same location �the excitation cross section of energeticelectrons are negligibly smaller than the excitation cross sec-tion of the plasma electrons�. It was found that in theseranges of jk, the average plasma expansion velocity is��1±0.2� cm/�s.

At a distance from the cathode surface of l*, the intensityof the H spectral line decreases to the noise level even at a4Quik05A camera frame duration equal to the duration of theaccelerating pulse. Namely, it was found that l*=3 mm fordak=20 mm and l*=1.5 mm for dak=30 mm. This decreasein the H spectral line intensity was � ten times and � fourtimes with respect to that of the spectral line intensity mea-sured at a distance of 0.2 mm from the cathode for dak of 20and 30 mm, respectively. These data indicate a fast decreasein the plasma density with increasing distance from the cath-ode. One can assume that at l* the plasma stops its expansiondue to the fact that at those distances the condition of jk

� jpl is satisfied. Here jpl�0.25eneVth is the saturationplasma electron current density and Vth�6.7�107Te

1/2�2�108 cm/s is the thermal velocity of the plasma electrons.42

In fact, this distance could be slightly larger than that mea-sured by the spectroscopic method. Indeed, the density ratednH

* /dt of excited hydrogen atoms is proportional to�nenH�exVth where �ex is the excitation cross section and nH

is the hydrogen density in the plasma. Assuming approxi-mately the same Te for different distances from the cathode,one can estimate the population ratio of the same excitedlevels n1en1H/ �n2en2H�=n1e / �n2e��. Here n1e and n1H and n2e

and n2H are the plasma electron and hydrogen atom densitiesat two distances from the cathode, respectively, and ��1 isa coefficient which accounts for the decrease in the hydrogenatom density versus the distance from the cathode. For dak

=20 mm the H population ratio is n1e / �n2e��10 at a dis-tance of 3 mm, and for dak=31 mm, n1e / �n2e��4 at a dis-tance of 1.5 mm. Thus, one estimates the plasma density at l*

as �−14�1013 cm−3 and �−11.5�1013 cm−3 at dak values of20 and 31 mm, respectively. The maximal density of thecurrent-carrying plasma electrons can be estimated as ne

�4jk /eVth that gives plasma densities of �5�1012 and�3�1012 cm−3 for the jk values of �40 and �25 A/cm2,respectively. One can see that these plasma densities aresmaller than the minimal measurable plasma density. Thisindicates that plasma stoppage occurs at a larger distancefrom the cathode surface than would be assumed based onspectroscopic measurements. Nevertheless, the obtained ten-fold decrease in ne within a distance of 3 mm �dak=20 mmand jk�40 A/cm2� and four-fold within a distance of1.5 mm �dak=30 mm and jk�25 A/cm2� indicate that theplasma stoppage occurs at distances �6 and �3 mm for the

in the effective dak, i.e., between the plasma emission bound-ary and the anode, as well as an increase in the effectiveemission cross-sectional area due to the plasma radial expan-sion should be taken into account in any explanation of theexcess of the diode current amplitude above its space-charge-limited value as reported in recent publications.23,24 Let usalso note that the experimental dependence P�t��const at�d�150 ns is a result of the stoppage of the cathode plasmaexpansion.

IV. DISCUSSION

The experiments carried out with an electron diode, thecathode of which was made of black and blue velvets, withand without CsI coating �see Sec. III A� showed generallythe same electrical parameters �amplitudes of the diode cur-rent and voltage, average current density, and perveance� asthose obtained in the earlier experiments.14–27 Also, the samestructure of the bright spots on the velvet surface and theuniform side view bright cathode layer were observed in thepresent experiment, similarly to the results described in Refs.16, 17, 21, and 25–27. It is reasonable to assume thereforethat approximately the same phenomena occur in the diodestudied in this work as in those used in the earlier research.

Several main conclusions can be drawn from the experi-mental data presented here.

�1� Time-and-space-resolved spectroscopic measurementsshowed that the source of electrons is the cathodeplasma �see Sec. III D�. The plasma formation was sug-gested and described in Refs. 14, 17, and 26. Accordingto the mechanism proposed in Ref. 14, the plasma formsas a result of the surface discharge of polymer fibers.The density and expansion velocity of this plasma de-pend on the density of the emitted electrons, i.e., thelarger the density of the emitted electrons, the faster isthe expansion velocity and the larger is the plasma den-sity. It was shown that the density and temperature of theplasma electrons do not exceed 4�1014 cm−3 and 8 eV,respectively, in the vicinity of the velvet surface for jk

�45 A/cm2. During the first part of the acceleratingpulse, this plasma expands towards the anode with avelocity of 1±0.2 cm/�s. Plasma expansion stops at adistance where the condition jpl= jk is satisfied. In ourexperiments this takes place at a distance of �6 mm inthe case of jk�50 A/cm2.In the present experiments we did not succeed in thespectroscopic measurements of the parameters of theplasma produced on the surface of the circular velvetcathode with CsI coating �see Sec. III D�, except to ob-serve the H spectral line in the vicinity of the velvetsurface. However, a similarity with the H spectral lineintensity and broadening obtained in the case of the vel-vet cathode without CsI coating allows one to speculateapproximately the same plasma parameters for the casewith CsI coating. At present we intend to apply inducedfluorescence spectroscopy by the use of a dye laser. Thelatter should significantly increase the sensitivity of the

parameters of the plasma in the case of a velvet cathodewith CsI coating.

�2� It was shown that there is a fast change in the intensityof the bright spots on the velvet surface during the ac-celerating pulse �see Sec. III B�. These bright spots rep-resent individual plasma sources that produce separateelectron beamlets. At the beginning of the acceleratingpulse these sources have similar sizes and brightness anddistributed with satisfactory uniformity on the velvetsurface. Further into the pulse, the peripheral plasmasources increase their brightness and size while at thesame time the brightness of the plasma sources locatedin the central part decreases.

�3� In spite of the individual character of the cathode plasmasources, the distribution of the extracted electron beamis satisfactorily uniform. The beam uniformity cannot beexplained by electron divergence in the accelerating gap,which does not exceed a few degrees in the case of thecathode with the screening ring and slightly offset velvetsurface. It was shown that a large electron divergence��30° � appears only when the cathode is made in theform of a ring with a central nonemitting area �see Sec.III C�. It was also shown that the x-ray image of theelectron beam generated by the cathode without ascreening electrode is characterized by radial rays.

�4� It was shown that, in the nanosecond time scale, theinteraction of the electron beam having a current densityup to 50 A/cm2 with the stainless-steel anode does notlead to the formation of an anode plasma and the appear-ance of ion flow in the diode �see Sec. III A�.

We now discuss possible mechanisms for the electron-beam uniformity obtained with the circular velvet cathodeand screening electrode, in spite of the individual characterof the plasma sources on the cathode surface. By excludingelectron divergence inside the accelerating gap �see item 2above�, we suggest a fast radial expansion of the plasmatowards the center which covers the cathode surface withsatisfactory uniformity that results in continuous, cross-sectionally uniform electron emission. This radial plasma ex-pansion should be much faster than the plasma expansiontowards the anode which occurs at a typical ion-sound ve-locity Vs�106 cm/s for plasma which is composed of pro-tons and carbon ions and has a temperature of a few eV. Forour experimental conditions, Ik=1 kA, the azimuthal mag-netic field of the current flowing through the plasma can beestimated at the cathode periphery of r=3 cm as B��70 G.This azimuthal magnetic field decreases towards the cathodeaxis. A gradient of B� could be a reason for the fast radialplasma expansion similar to the z-pinch effect.44 The plasmaexpansion occurs in a form of a collisionless shockwave hav-ing a wave-front width of approximately one electron Lar-mor radius, which is 2–3 mm in our case. The typical veloc-ity of this wave is close to the velocity of a magnetoacousticwave45 Vm=B� / ��0��1/2, where �0 is the absolute magneticpermeability and � is the plasma density. Here we assume aproton plasma with �=MHni, where MH and ni are the mass

�1012 cm−3, one obtains Vm�107 cm/s. This fast radial ve-locity makes the plasma at the central velvet part to have thenecessary density for jk=10–50 A/cm2.

It is understood that the less intense plasma sources ap-pearing in the central part of the velvet �see Sec. III B� can-not be excluded from participation in the electron emission.It is reasonable to assume that less intense plasma sourcesalso have less density and temperature as compared with thebright peripheral plasma sources. Therefore, the plasma pro-duced by these less intense sources should have a smallerexpansion velocity. The latter dictates a nonplanar emittingplasma boundary and, respectively, a nonuniform beamcross-sectional distribution. However, at large dak values thisnonplanarity in the plasma emitting boundary could be ne-glected.

The phenomenon of the increase in brightness of indi-vidual plasma sources at the cathode periphery during theaccelerating pulse needs additional investigation. At presentwe can suggest only a qualitative explanation based on a 2Deffect that necessitates larger electron current density at thecathode edges for the establishment of a space-charge-limited electron flow.26

It was shown that the CsI coating of the velvet cathodeimproves the uniformity of the electron emission �see Sec.III C�. Thus, one can suppose a more uniform surface plasmaformation in the case of the CsI coating. At present, the exactmechanism which is responsible for this phenomenon is notknown, and a further specialized research is necessary. Wecan only speculate that the application of the CsI coatingcould improve significantly photo- and secondary electronemissions as well as decrease the work function of electrons.On the other hand, the CsI coating cannot have a long life-time because of a polymer fiber flashover phenomenonwhich causes surface erosion. Finally, let us note that thedifferences in the cathode materials used in the present ex-periments �polymer fibers� and in the experiments cited inRefs. 18, 21, 22, and 27 may not be a decisive factor sincethe creation of plasma on both is due to flashover along thefiber surface.17,19 However, the differences in the materialstructures would affect the cathode lifetime.

ACKNOWLEDGMENTS

The authors would like to thank K. Chirko for fruitfuldiscussions and H. Sagi and L. Iomin for assistance in theexperiments.

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Characterization of the plasma on dielectric fiber (velvet) cathodes

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Evidence of nonclassical plasma transport in hollow cathodes for electric propulsion

Chemical and Electrochemical Lithiation of LiVOPO 4 Cathodes for Lithium-Ion Batteries

Large dielectric permittivity and possible correlation between magnetic and dielectric properties in bulk BaFeO3−δ

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Behavioural interference between ungulate species: roe are not on velvet with fallow deer

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Jurassic-Pliocene biogeography: testing a model with velvet worm (Onychophora) vicariance

Insert Heating and Ignition in Inert-Gas Hollow Cathodes

Kiloampere and microsecond electron beams from ferroelectric cathodes

Ion Exchange Membrane Cathodes for Scalable Microbial Fuel Cells

EQCM study of oxygen cathodes in DMSO LiPF6 electrolyte

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Optical and dielectric response - sciforum

Low-k dielectric materials

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Dynamic dielectric analysis of solids

Sphagnum (velvet) species used by rural communities at the Guaratuba EPA, Paraná State, Brazil

Unexplored Character Diversity in Onychophora (Velvet Worms): A Comparative Study of Three Peripatid Species

Dielectric Material Characterization up to Terahertz