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Effects of anode shape on plasma focus operation with argon

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1996 Plasma Sources Sci. Technol. 5 544

(http://iopscience.iop.org/0963-0252/5/3/023)

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Plasma Sources Sci. Technol. 5 (1996) 544–552. Printed in the UK

Effects of anode shape on plasmafocus operation with argon

M Zakaullah †, Imtiaz Ahmad †, A Omar §, G Murtaza † andM M Beg‡† Department of Physics, Quaid-i-Azam University, 45320 Islamabad, Pakistan‡ PINSTECH, PO Box 2151, 44000 Islamabad, Pakistan

Received 10 October 1995, in final form 10 February 1996

Abstract. X-ray and ion beam emission from a low-energy Mather-type plasmafocus energized by a single 32 µF, 12 kV (2.3 kJ) capacitor is investigatedemploying three different anode shapes and using argon as filling gas. Theradiation yield and the filling gas pressure for good focus are found to be stronglydependent on the anode shape. An appropriate tapering of the anode endenhances the emission threefold for both x-rays and ions. The intensities of thesignals are also found to be correlated mutually as well as with the high-voltageprobe signal intensity. Furthermore, time-integrated pinhole images reveal that thex-rays originate predominantly from the anode end surface. In other words, anappropriate shaping of the anode end switches the device to a high-emission modefor both x-rays and a charged particle beam.

1. Introduction

Dense plasma focus [1] (PF) was developed in the 1960s,independently in the USA and the former Soviet Union.Filippov et al, for example [3], working on a modifieddesign of Z-pinch with a metal wall vacuum chamber,noticed that a noncylindrical high-density high-temperatureplasma filament was formed close to the anode. Theefficiency of the device was further improved when theother electrode of the device was removed and the groundterminal of the capacitor bank was connected to thevacuum chamber itself. Mather [1], working on a coaxialaccelerator, noticed that under certain conditions, a high-density high-temperature plasma develops at the open end,in front of the anode. These configurations were termedplasma focus devices. When they are operated withdeuterium, neutron and x-ray bursts are emitted from thefocus region. Interestingly, both the geometries followidentical scaling laws for neutron emission (Y ∼ E2) whereE is the capacitor bank energy in Joule. PF devices aregenerally operated with deuterium in the pressure rangeof 0.5–10.0 mbar. This has to do with the fact thatthe current sheath (CS) traversal time along the coaxialacceleratorta should synchronize with the current rise timeof the capacitor bank. When the filling pressure is too high,the CS fails to pinch and no focus plasma is formed becausethe magnetic pressure is not strong enough to compress it.The CS traversal time along the acceleratorta follows the

§ Permanent address: Department of Physics, University TechnologyMalaysia, KB 791, 80990 Johre Bahru, Malaysia.

relation [2]

ta =(

4π2z20(b

2 − a2)ρ0

I 20 µ ln(b/a)

)1/2

(1)

wherez0 is the length of the accelerator,b anda are cathodeand anode radii respectively,I0 is the peak dischargecurrent andρ0 is the ambient gas density. If the systemis operated with heavy gases like argon, the pressureshould be low to keepρ0 at the desired value, keepingother parameters the same. Likewise, the system must beoperated at high pressure when hydrogen is used as thefilling gas.

Filippov [3] speculated that to utilize PF as a fusionreactor, the device should be adjusted to work at muchhigher pressures to balance the larger currents achievablein larger machines. For Mather’s geometry, equation (1)suggests that the ambient gas densityρ0 may be increasedby decreasing the anode lengthz0. Beget al [4] worked inthis direction and found that no focus is formed when theanode length is shorter than 110 mm for a 2.3 kJ (32µF,12 kV) system of 80 nH parasitic inductance. An anodelength range of 140–160 mm was reported optimum forhigh neutron emission.

Beget al [5] attempted to broaden the working pressurerange by reducing the parasitic inductance to 22 nH. Theyfound that a 0.8 kJ plasma worked reliably and reproduciblyfor 1–10 mbar deuterium filling pressure. For hydrogen, thesystem was operated at 20 mbar and the high-voltage (HV)signal exhibited a good focus. In this system, the parasiticinductance was found to match the cumulative inductanceof the accelerator and the pinch region.

0963-0252/96/030544+09$19.50 c© 1996 IOP Publishing Ltd

Effects of anode shape

Figure 1. (a) Schematic of plasma focus electrode systemand x-ray and ion beam detectors. (b) The three anodeconfigurations used in the experiment. (c) Magnification ofelectrode structure at the breech end.

Energetic ion and electron beam emission fromPF devices has been reported by many laboratories [6–13]. Bostick et al [7] investigated ion beam and x-rayemission from a 5.4 kJ PF operated with deuterium. Theion beam intensity (inside a small solid angle centred on theelectrode axis) was found to be correlated to the hard x-rayintensity and the neutron yield. Stygaret al [11] studiedelectron and ion beams from a 12.5 kJ PF by employinga Faraday cup, electron magnetic spectrometer and solidstate nuclear track detector, using deuterium as the fillinggas. The charged particle flux was found to be dependenton the discharge current from the main capacitor bank.Feugeaset al [14] demonstrated the use of PF for ionimplantation. PF is also reputed as a reproducible pulsedneutron and x-ray source which may find applications in

Figure 2. Variation of (b2 − a2)/ ln(b/a) with the anoderadius a.

Figure 3. Transmission characteristics of 2 µm and 9 µmthick aluminium filters.

materials research for nuclear fusion reactors [15] and forhigh-brightness sources used in x-ray lithography and x-ray microscopy [16]. Clearly the investigation of ion andx-ray emission with a view to enhance their yield is quiteimportant and is also helpful in understanding the chargedparticle acceleration process.

Generally the anode in a PF device is of cylindricalshape of uniform diameter. However, other shapeshave also been studied. Johnson [17] investigated x-rayproduction in a 375 kJ plasma focus, using a taperedanode. The x-ray emission profile was reported as asmooth Gaussian with FWHM∼ 200 ns. However, nocomparison with a flat-tip cylindrical anode was presented.In this paper, we report the effects on PF dynamics whenthe anode shape is tapered towards the open end. In

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Figure 4. Typical HV probe d/dt(IL), x-ray and ion beam signals for different anode shapes. (a) Cone shape anode at5.0 mbar argon. (i) HV probe signal; 1 V/div, 1 µs/div. (ii) X-ray signal; 1 V/div, 1 µs/div. (iii) Ion-beam signal; 0.2 V/div,1 µs/div. (b) Tapered anode at 2.5 mbar argon. (i) HV probe signal; 1 V/div, 0.5 µs/div. (ii) X-ray signal; 2 V/div, 0.5 µs/div.(iii) Ion-beam signal; 2 V/div, 0.5 µs/div. (c) Cylindrical flat-end anode at 1.25 mbar argon. (i) HV probe signal; 2 V/div,0.5 µs/div. (ii) X-ray signal; 1 V/div, 0.5 µs/div. (iii) Ion-beam signal; 1 V/div, 0.5 µs/div.

section 2, the effects of this change in anode shape onaccelerator inductance, ambient gas pressure and magneticpressure close to the anode surface are described. Section 3describes the experimental set-up and the diagnostics used.Section 4 summarizes the results while section 5 presentsthe conclusions.

2. Plasma focus dynamics with tapered anode

We used anodes of three different shapes: cone-shapedanode (I), tapered anode (II) and cylindrical flat-endanode (III) (shown in figure 1) to investigate their effectson PF dynamics. In cases I and II, the radius of the centralelectrode gradually decreases withz, the distance along thecoaxial accelerator, keeping the outer electrode diameterthe same. The mass entrained by the current sheath alongthe accelerator at any positionz is [2]

ρ0(π(b2 − a2)z

)(2)

whereρ0 is the ambient gas density. When the anode endis tapered,a decreases withz and thus the mass entrainedby the sheath would increase rapidly as the CS propagates.

The magnetic flux density at the surface of the conductorthrough which currentI flows varies with the conductorradius, that is,

B = µ0I

2πr(3)

wherer is the radius of the conductor—the central electrodein our case. This implies that the strength of the magneticflux density at the anode surface increases steadily, as theCS propagates along the accelerator. The inductance of thecoaxial accelerator follows the same relation

La = µ0z

2πln

(b

a(z)

).

The transit time of the CS along the accelerator is

ta =(

4π2ρ0(b2 − a2)z2

0

µI 20 ln(b/a)

)1/2

.

As shown in figure 2, the ratio(b2−a2)/ ln(b/a) decreasesasa reduces.

To synchronizeta with the current rise time from thecapacitor bank, one needs to increase the ambient gasdensity ρ0, that is, the gas pressure. Consequently a PF

546

Effects of anode shape

Figure 4. (Continued)

system with a tapered anode will be operated at higher gaspressures.

3. Experimental set-up and diagnostics

The experiment is conducted on a PF system energized by asingle 32µF capacitor, and charged at 12 kV (2.3 kJ) givinga peak discharge current of about 190 kA. The schematicarrangement of the electrode system is given in figure 1.The anode length in each case is 160 mm, measured fromthe cathode base plate. The diameter of the cylindricalanode is 18 mm. It is surrounded by six 10 mm Cu rodsforming a cathode of inner diameter 50 mm. The cathoderods are screwed to a Cu plate, called the cathode base plate,which has a knife edge near the anode. An insulator sleeveof Pyrex, with a breakdown length of 25 mm, is placedbetween the anode and the cathode at this end. The lengthsof the insulator sleeve and the anode are chosen fromthe experimental results reported previously [4, 5, 18]. Todetect the ion beam generated in the PF region, a Faradaycup is used. To avoid unnecessary plasma jets reaching theion beam collector, the plasma gun chamber is masked bya copper plate with a hole in the centre. The ion beamhad to pass through a 100 mm long cylindrical channel ofdiameter 5 mm to reach the Faraday cup to be detected. Thetime-resolved x-ray emission is monitored by a pin diode

Figure 5. Variation of x-ray signal intensity with respect toargon filling pressure for the three anodes.

BPX-65 with slight modifications. The safety glass coverof the diode was removed, and 9µm thick aluminium foilwas used to screen the visible light. A 45 cm long stainlesssteel pipe of 4.0 cm diameter serves as the black box of thecamera to contain a prism-shaped film holder of aluminium150 mm long and a triangular base of 25 mm each side. Thewhole assembly is adjusted in such a fashion that movingand/or rotating the film holder and recording 15 snapswithout disturbing the vacuum is possible. A pinhole of0.5 mm diameter was found adequate for reasonable imageintensity in our experiment. The pinhole was covered with2 µm aluminium foil. We could not employ the same filterfor both the pinhole camera and the pin diode because theintensity of pinhole images with a 9µm filter was toolow to obtain any significant information, whereas the x-ray flux from a 2µm filter was too high for the diode tosustain. The absorption characteristics of the 2µm and9 µm aluminium foils are given in figure 3. This curveis obtained by using the data of Henkeet al [19]. Torecord the d/dt (IL) signal, a simple resistor divider isused. Three signals, that is, HV probe signal, ion beamand x-ray emission profile are recorded simultaneously bya four-channel 200 MHz GOULD 4074 oscilloscope, and ahard copy of the oscillograph is obtained on a multicolourHP 7475 plotter.

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Figure 6. Behaviour of HV probe signal versus argonpressure for the three anodes.

4. Results and discussion

For the three anode configurations, we scanned the argonfilling pressure and recorded ten shots for each selectedpressure value. After every ten shots, the previous gas waspurged and fresh gas was filled to minimize the effects ofimpurities accumulated in the working gas.

Figure 4 shows a typical HV probe and x-ray and ionbeam signals for each anode shape. In these oscillographs,the time interval between breakdown and appearance ofHV probe spike indicates that CS collapse is about 4µs.This time interval is pressure dependent, as expected. Thedepicted oscillographs are selected for having almost thesame time interval, which in turn requires argon fillingpressures of 5.0 mbar, 2.5 mbar and 1.25 mbar for the threeanode shapes I, II and III respectively. This reflects thatthe magnetic pressure increases faster than the mass densityresistance in accordance with figure 2. In figure 5, the x-ray signal intensity and the x-ray pulse width (FWHM) asdetected by the pin diode versus argon filling pressure arepresented. The error bars are not added to pulse widthpoints so as to avoid overlapping with the x-ray signalintensity error bars. Figure 6 contains the variations ofthe HV probe signal, whereas figure 7 gives the ion beamsignal intensity against the argon pressure. Figures 8 and9 compare the x-ray signal intensity with HV probe signaland that of the ion beam with the x-ray signal for all the

Figure 7. Variations of ion beam signal intensity versusargon pressure for the three anodes.

three anodes. Figure 10 presents the x-ray pinhole imagesfor each filling pressure.

Compared to the standard flat-ended cylindricalanode (III), the intensity and pulse width (FWHM) of x-ray emission are higher for both the cone-shaped (I) and thetapered (II) anodes. This observation demonstrates that thex-ray yield from PF devices may be enhanced by modifyingthe anode shape.

The pinhole images help us to identify the region ofintense x-ray emission, though the information is ratherlimited due to the large diameter (500µm) of the pinholeaperture. The cylindrical anode (III) has a wider emittingzone at a lower pressure of 0.25 mbar accompanied bya significant amount of x-rays originating from the anodesurface, probably via a thick bremsstrahlung mechanismby the impact of the plasma CS. With increased filling gaspressure, the zone squeezes to the pinch filament axis andthe emission is lowered. For different filling pressures, hotspots are visible along the pinch axis distributed from theanode end to about 22 mm away. However, at 2.25 mbar,just one spot of very low brightness can be seen. For thecone-shaped anode (I), most of the x-rays seem to comefrom the anode end, where the linear current density mayrise to 0.75–1.0 MA cm−1. At these linear current densities,each discharge will cause significant damage to the anodetip. This damage is visible after a few shots. At 0.25 mbar,a very faint image of the anode tip appears. With increasedfilling gas pressure, the image intensity is enhanced. Inthe pressure range corresponding to high x-ray emission,intense x-ray emitting spots also appear in front of theanode tip. The location of intense x-ray emitting hot spotsdepends on the filling pressure to some extent. At 2.0 and

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Effects of anode shape

Figure 8. Correlation of x-ray signal intensity with the HV probe signal for the three anodes.

8.0 mbar, one such hot spot appears close to the anode tip.In the range 3.0–7.0 mbar, two or three hot spots appearalong the axis, distributed from anode tip to about 20 mm;the exact position changes from shot to shot. At 9.0 mbarargon, the x-ray emission drops again, leaving a faint imageof the anode tip. From figure 5, we notice that with anode Ithe PF operates in two modes—one at high pressure (5–8 mbar) and the other at low pressure (2–3 mbar). Thex-ray signal intensity is large in the high-pressure mode,

whereas the pulse width (FWHM) is comparatively broaderin the low-pressure mode.

For the tapered anode (II), a significant amount of x-rays originates from the end, which appears bright in all thepinhole images. At 1.5 mbar only, the x-ray emitting zoneextends to the pinch axis also, and one hot spot is locatedat about 10–12 mm from the anode tip. Superimposedupon the anode tip images for each filling pressure, anaxially elongated bright dot appears at the centre. That

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M Zakaullah et al

Figure 9. Correlation of ion beam signal and x-ray signal intensity for the three anodes.

probably is due to x-ray emission by the impact of theelectron beam which interacts with the high-density plasmaclose to the anode tip, or copper vapours that may besputtered by the electrons in the CS and are swept to theaxis during implosion. This indicates the dominance ofthe thick bremsstrahlung mechanism with this anode. Thisresult is also reported by Johnson [17]. Figure 7 indicates ahigher ion beam intensity. If we associate a high ion beamintensity with a high electron beam intensity, it may explainthe intense x-ray emission from the anode tip providingsupport to our speculation regarding the dominance of

the thick bremsstrahlung mechanism. It further suggestsanode II to be a charged particle/x-ray optimized modefor the Mather-type plasma focus. However it is difficultto speculate whether neutron yield with anode II willincrease. Although one expects an increase in ion beaminduced neutron emission, a more intense electron beammay increase the copper evaporation and hence a higherimpurity level in the PF plasma results. Experiment withdeuterium is under way to this end.

As is evident from figure 7, the ion beam intensity isstrongly influenced by the anode shape. With the tapered

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Effects of anode shape

Figure 10. X-ray images of the focus plasma region with2 µm aluminium filter for the three anodes.

anode (II), the ion beam current increases appreciablycompared to the flat-end anode (III), whereas it dropssubstantially in the case of the cone-shaped anode (I). Onemay infer from this that in plasma focus, the phenomenoninvolved with the radial collapse of the CS is responsible

for intense charged particle beam generation. Since in thecone-shaped anode (I) the radial collapse phase is almostabsent, the intensity of the ion beam signal is quite low.

The HV probe, which is a simple resistor divider, isconnected across the cathode–anode headers outside theaccelerator. It records voltage proportional to d/dt (LI) andhelps to obtain useful information about the status of theCS collapse, focus formation and its timing. The intensityof this signal with respect to working gas pressure for thethree anodes is shown in figure 6.

Figures 8 and 9 demonstrate that in PF with anode II,the correlation of x-ray emission with ion beam emissionand HV probe signal intensity is quite pronounced. Thissuggests that the device with anode II approaches a modeof operation giving high radiation yield. In this mode thehigh voltage recorded by the HV probe is also correlatedwith the charged particle beam formation.

5. Conclusions

X-ray and ion beam emission from a low-energy (2.3 kJ)plasma focus using argon as the filling gas are studied.Special attention is paid to the effects of anode shape onradiation yield. As the anode radius towards the end isreduced, the filling gas pressure has to be increased so as totime the peak current at the end of the central electrode. Thedata show the tapered anode (II) to be the best x-ray emitter.A significant part of the x-rays seems to originate from theanode end, probably via a thick bremsstrahlung mechanismby electron impacts. Furthermore, for this anode shape (II),the intensity of the HV probe signal, x-ray signal and ionbeam signal are clearly correlated, while for the cylindricalanode (III) there appears some correlation and for the cone-shaped anode (III) there appears some correlation and forthe cone-shaped anode (I) no correlation at all. The effect ofelectrode shape on neutron emission requires further work.

To conclude, proper shaping of the central electrodeof a low-energy Mather-type plasma focus can establish ahigh mode of operation, enhancing the ion beam and x-rayemission manyfold.

Acknowledgments

This work was partially supported by a QAU ResearchGrant, Pakistan Science Foundation Project No C-QU/Phys(92), PAEC Project for plasma physics, TWAS RGNo 93-371 RH/Phys/AS, ICAC project AC-7 Islamabad andICSC World Laboratory Project CHEPCI, E-13, Islamabad.We are grateful to the referees for their valuable suggestionsto improve the manuscript.

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