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Imaging of Fusion Protons from a 3 kJ Deuterium Plasma Focus

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2005 Jpn. J. Appl. Phys. 44 4117

(http://iopscience.iop.org/1347-4065/44/6R/4117)

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Imaging of Fusion Protons from a 3 kJ Deuterium Plasma Focus

Stuart Victor SPRINGHAM�, Siew Pheng MOOy, Paul LEE, Rajdeep Singh RAWAT,

Alin Constantin PATRAN and Sing LEE

Natural Sciences, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616

(Received July 10, 2004; accepted March 7, 2005; published June 10, 2005)

This paper reports a study of the proton emission from a 3 kJ, 14 kV plasma focus device operated with deuterium gas at400 Pa. A filtered pinhole camera with a 1.8mm diameter hole is placed axially downstream of the plasma focus, and imagesof the proton-emitting region are recorded using CR-39/PM-355 nuclear track detectors. The detector plates are scanned usingan automated track measurement system and the spatial track density profile is acquired. The resulting density distribution isinterpreted with the help of a simple pinhole imaging model that assumes the 2H(d; p)3H reaction protons are emitted from aconical region extending from the tip of the anode to a fixed distance downstream. Comparison of the experimental trackdensity profile with the model calculations supports the view that the beam-target mechanism is the dominant fusionproduction mechanism in this small plasma focus device. [DOI: 10.1143/JJAP.44.4117]

KEYWORDS: plasma focus, deuterium fusion, beam-target fusion, fusion imaging, nuclear tracks, CR-39, PM-355, automatedtrack measurement, fusion diagnostics

1. Introduction

The plasma focus (PF) is essentially a pulsed electric gasdischarge between coaxially arranged electrodes. Althoughdeveloped almost four decades ago, independently byFillipov1) and Mather,2) it has continued to attract interest.This is due in large part to the great variety of phenomenaoccurring in the plasma focus, and to its potential applica-tions as a source of intense radiations (energetic ions andelectrons, soft and hard X-rays). In the deuterium plasmafocus energetic neutrons and protons are produced in nearlyequal quantities from the fusion reactions 2H(d; n)3He and2H(d; p)3H, respectively. Hence neutron and proton meas-urements can yield valuable information concerning thefusion reaction mechanisms occurring within the PF. In thepast, research on the deuterium PF has concentrated almostexclusively on the study of the neutron emission. Theneutron yield, the neutron energy spectrum, and the neutronemission in time and space have been investigated by avariety of techniques.2–5) However, as pointed out by Jageret al.,6) studies of the complementary proton reactionchannel can yield even more refined results than neutronmeasurements. This has been attested by the series ofexperiments on a large PF device, the 280 kJ, 60 kVPoseidon plasma focus.6,7) These experiments employedthe solid-state nuclear track detector material CR-39 for thedetection of protons. CR-39 was used in conjunction withthin metal foils of varying thickness to deconvolute theproton energy spectrum, while the location and structure ofthe proton source were deduced from a pinhole cameratechnique—the camera being positioned to record the side-on view of the PF pinch region (i.e., � ¼ 90�).

At our laboratory we have carried out extensive work on asmall plasma focus, employing a variety of diagnostics andtechniques.8–11) These include current and voltage measure-ments; plasma dynamics studies using optical interferome-try; soft X-ray measurements using PIN diodes, pinholecamera and a crystal spectrograph; hard X-ray measurementsusing scintillator-photomultiplier detectors; neutron meas-

urements using an indium foil activation detector, and time-of-flight scintillator-photomultiplier detectors; and deuteronspectra measurements using a magnetic spectrometer. Tofurther elucidate the nature of the fusion reaction mechanismin the plasma focus we now investigate the proton emissionusing a proton pinhole camera. Unlike the studies on thePoseidon device, we position our pinhole camera on theforward axis of the plasma focus (� ¼ 0�) in order toinvestigate the relative contributions of beam-target andpinch fusion to the total fusion yield.

2. Experiment

The plasma focus used in this work is the 3 kJ UNU/ICTPPFF.8) It is of the Mather-type,2) with a hollow copper tubeof 160mm length and 19mm diameter as the anode.Surrounding and concentric with the anode is a set of sixcopper cathode rods arranged in a squirrel cage configu-ration. A Pyrex glass tube insulates the anode from thecathode. For the present investigation the plasma focusdevice is operated at 14 kV with deuterium gas at 400 Pa.Neutron yield measurements are made using an indium foilactivation detector. A proton pinhole camera is placedaxially downstream of the plasma focus, 120mm from thetip of the anode. The pinhole has a diameter of 1.8mm and itis covered with a 50 mm thick Kapton film. On the other sideof the pinhole, 34mm away, is placed a PM-355 (PageMouldings, U.K.) nuclear track detector. This is a super-grade form of the CR-39 track detector material. The Kaptonfilm serves to protect the PM-355 detector from the hotplasma and the large flux of low energy deuterons emittedfrom the PF pinch; it also stops the energetic 3He and 3Hions.

It is found that five to seven plasma focus shots arerequired to produce a sufficient number of tracks on the PM-355 detectors. The exposed PM-355 is etched in 6.25 molarNaOH solution at 90�C for 5 h. Each detector is scannedusing our automated track measurement system, based on anoptical microscope (with CCD camera, motorised stage andfocus-adjust) interfaced to a PC computer.11) A computercode has been written to process the captured images,measure relevant track parameters and determine theabsolute position of each proton track on the surface of the

�Corresponding author. E-mail address: svsprin@nie.edu.sgyOn leave from University of Malaya, Kuala Lumpur, Malaysia.

Japanese Journal of Applied Physics

Vol. 44, No. 6A, 2005, pp. 4117–4121

#2005 The Japan Society of Applied Physics

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detector. The system is able to discriminate very effectivelybetween genuine proton tracks and spurious track-likefeatures.

3. Results

A dozen PM-355 detectors have been exposed, processedand analyzed. In total, approximately 54,000 proton trackswere recognised and measured by the scanning system. Theresults obtained are similar for all the detectors. A typicalplot of track positions measured by our scanning system forone PM-355 detector plate is shown in Fig. 1. Thisdistribution of tracks represents the on-axis projected imageof the PF proton emitting region, and it is clear that thedistribution has high degree of rotational symmetry. Foreach detector the centroid of the distribution is computed,and the density of the tracks is determined as a function ofthe radial distance from the centroid for concentric annularbins of 0.5mm width. Each detector distribution is thencorrected for the effect of track overlap, before the per-detector average track density distribution is computed.Figure 2 shows a plot of this overall average distribution.

The track overlap correction is necessary because thescanning system does not separate overlapping tracks; it

records the positions of only circular non-overlapping trackshaving diameters within a suitably defined range. The scandata therefore initially gives an uncorrected track density�scan. For a given track area At and true track density �t theprobability that a track will not be overlapped by any othertracks is, from Poisson statistics, Pno ¼ expð�4At�tÞ, andtherefore �scan ¼ Pno�t. Since track diameter is also meas-ured by the scanning system, At is known, and the correctedtrack density can be found from the iterative formula �iþ1

t ¼�scan expð4At�

itÞ, using the starting value �0

t ¼ �scan. Thetrack diameters vary slightly between detectors (in the range15.2 to 16.5 mm) due to small variations in the etchingprocedure. At the centre of the most densely tracked detectorthe highest value of �t is 260mm�2, while the average trackdensity for the central region of all detectors is 152mm�2.Following track overlap correction, the determined values of�t are in the range 9 to 21% higher than �scan at the centre ofdetectors. The overlap correction becomes progressivly lessimportant with increasing radis; beyond r � 4mm trackoverlap is negligable and �t ’ �scan.

As shown in Fig. 2 the track density drops sharply withradial distance—at 2mm from the centroid the track densityis about half of the centroid value. The statistical uncertain-ties in the track densities are 2% or less for all of the datapoints, except the r ¼ 0:5mm point for which the uncer-tainty is 2.8%. The exposed region of the PM-355 detector isa circle of radius 10.5mm, hence the detector recordsprotons passing through the pinhole at angles up toapproximately 18� with respect to the camera axis. Theenergy of the protons will depend on the reaction mecha-nism. For thermonuclear fusion the protons will have anenergy ’3MeV, while for beam-target reactions withdeuterons of �50 keV, the protons emitted in the forwarddirection are expected to have an energy of �3:3MeV.Calculations using the TRIM code12,13) show that the 50 mmthick Kapton window will completely stop all 3He (�0:8MeV) and 3H (�1MeV) ions, but will transmit the fusionprotons with an energy loss of 0.9MeV and an averageangular deflection of 1.5�. The detection efficiency of thePM-355 for protons in the present experiment is expected tobe 100%

If thermonuclear fusion in the pinch were the dominantfusion mechanism in the plasma focus then the proton imageon the PM-355 detectors would be confined to an isolatedcentral spot of diameter slightly greater than that of thepinhole (�2mm)—since scattering in the Kapton foil hasonly a minor effect, and the magnetic field enclosed by thecurrent sheath has no effect on the forwardly directedprotons. Figures 1 and 2 show clearly that an isolated centralspot is not what is observed. Hence it can already be saidthat, for our 3 kJ plasma focus, these results indicate thatthermonuclear fusion is not the dominant fusion mechanism.

4. Proton Imaging Calculations

The proton pinhole imaging calculations to be presentedare guided by the following considerations:(1) In a previous work9) with an identical plasma focus

also operated at 400 Pa deuterium but at a marginallyhigher voltage of 15 kV, it was found that: (i) less than15% of the neutrons are produced in the region 0–20mm from the end of the anode, (ii) more than 85%

Fig. 1. Plot of measured track positions (x, y in mm) for one PM-355

detector plate exposed to seven consecutive PF shots inside the on-axis

pinhole camera. The rectangle represents the area of the detector scanned

by the automated system.

Fig. 2. Plot of proton track density (per mm2) vs radius.

4118 Jpn. J. Appl. Phys., Vol. 44, No. 6A (2005) S. V. SPRINGHAM et al.

of the neutrons are produced in the 20–60mm region,and (iii) the neutron production is highest in the region30–40mm from the anode. From this study it isconcluded that the neutron production mechanism isprincipally beam-target[deuterium gas] interaction, andthat most of the neutrons are produced in a rather shortregion up to 60mm from the end of the anode.

(2) The deuterium ion or atom density in the pinch columnand its vicinity varies greatly, depending on time andposition. It changes from a maximum of about 1� 1019

cm�3 at the pinch column (of approximate dimensions:length 10mm and diameter 2mm) to a minimum of1:98� 1017 cm�3 corresponding to the ambient gaspressure at 400 Pa. Calculations using the TRIMcode12,13) show that, for the ambient gas, the specificenergy-loss for 50 keV deuterons is dEd=dx ¼ 1:1 keV/cm, and that the path length required for 50 keVdeuterons to be slowed down to 10 keV is about46.5 cm. The TRIM code is not applicable for plasmatargets and connot therefore be used to calculate theenergy-loss for deuterons in the pinch, but (for similarpinch density and temperature) Jager7) states thatdEd=dx is in the range 0.9 to 10 keV/cm for Ed �20 keV.

(3) Published results on the Poseidon plasma focusdevice6,7) have shown that the fast deuterons producedin the plasma focus are trapped by the presence of astrong magnetic field. The gyromotion of the deuteronslengthens considerably the particle paths, resulting in asignificant enhancement of the fusion yield bycomparison with a beam-target model in which thedeuterons travel in straight line paths.

Based upon these considerations, we propose for thepinhole imaging calculation a simple model in which acombination of gyromotion of the deuterons and an effectiveion/gas density exceeding that of the ambient gas (but lessthan the density at the pinch column) essentially confines thefusion reaction region to a length L (of several cm)downstream from the anode. We also make the followingsimplifying but reasonable assumptions:

(i) The fusion reactions take place downstream of theanode in a cone of half-angle �0.

(ii) This cone can be approximated by a series of ‘‘thinproton emitting discs’’ situated at equal intervals. Ineffect the fusion cone is sub-divided into several10mm wide segments and the fusion reactions takingplace in a particular segment (say the i’th segment)are considered to have originated uniformly from thedisc representing the intersection of the i’th segmentmid-plane and the cone of half-angle �0. The fusionprotons are taken to be emitted isotropically.

(iii) The fractional fusion yields are given by the set {yi}where yi is the yield in the i’th segment such thatP

yi ¼ 1. This is illustrated graphically in Fig. 3 forL ¼ 70mm.

The pinhole imaging is a straightforward geometricalimaging in which the area of the pinhole and the effect ofsolid angle are taken into account. By means of this simpleimaging calculation, the sensitivity of the track densitydistribution to variations in �0, L, and {yi} have beeninvestigated. Values of the cone half-angle �0 which are

modeled, range from 10� to 50�. The length L of the cone isvaried from 70mm to a maximum of 120mm (i.e., to thefront face of the pinhole camera).

Moreover, two different distributions of the fractionalfusion yields {yi} are investigated—the first is a flatdistribution and the second a Gaussian distribution—asshown in Fig. 4 for the case of L ¼ 70mm. The flatdistribution corresponds to equal fusion yields from eachsegment of the fusion cone. The fractional fusion yield fromthe first 20mm of the cone is 28.6% for L ¼ 70mm, 20% forL ¼ 100mm and 16.7% for L ¼ 120mm. The Gaussiandistribution with L ¼ 70mm corresponds more closely to theexperimental observation mentioned in consideration (1)above. The fractional yield from the first 20mm of the coneis 15%.

Figure 5(a) shows the calculated track density profiles fora flat fusion yield distribution with L ¼ 70mm for �0 ¼ 20�,

Fig. 3. Graphical illustration of the proton emission cone of half-angle �0

for the case where the length L ¼ 70mm.

Fig. 4. Two cases investigated for fractional proton yield distributions

{yi}, for 10mm wide contiguous segments of the proton emission cone.

Jpn. J. Appl. Phys., Vol. 44, No. 6A (2005) S. V. SPRINGHAM et al. 4119

30�, and 40�. Also shown in this figure is the experimentaltrack density profile. For comparison, the calculated trackdensities have been multiplied by scaling factors so that theyagree with the experimental value at the first radial point.These scaling factors are indicators of the total proton fusionyield. Similarly, Fig. 5(b) shows the calculated track densityprofiles for a flat fusion yield distribution with �0 ¼ 30� forL ¼ 70, 100 and 120mm. Comparison of the experimentaltrack density profile with calculated profiles for a Gaussianfusion yield distribution with L ¼ 70mm for �0 ¼ 15�, 20�

and 25� is shown in Fig. 6.

5. Discussion

The measured proton track density of the pinhole image,as plotted in Fig. 2, shows a high density at the centre of theimage. The track density drops rapidly with increasingradius, becoming typically �3% of the central density forpoints near the edge of the exposure (i.e., radius ’ 10mm).This general trend is reproduced in our simple protonimaging calculations. In the calculations, however, there area number of adjustable parameters: the half-angle �0 of thecone, the length L of fusion reaction cone, and the fractionalyield distribution {yi} of protons from the different segmentsof the cone. As is to be expected, the calculated track densityat the centre of the pinhole image is higher when a narrowercone angle is used in the imaging calculation. As the coneangle widens the tracks become more widely spread.Figure 5(a) illustrates this sensitivity of the simulated trackdensity distribution to the cone half-angle �0. In the case of aflat fusion yield distribution with L ¼ 70mm, the bestagreement with the shape of the experimental track densityprofile is for �0 ¼ 30�. The corresponding calculated totalproton yield is 3:5� 107 per shot.

In general for a given value of �0, increasing the value ofL results in a decreased track density at the centre of thetrack distribution, and a higher track density away from thecentre. In the case of a flat fractional fusion yield distributionwith �0 ¼ 30�, the changes are slight as shown in Fig. 5(b)for L ¼ 70, 100 and 120mm. All the three calculated curvesagree well with shape of the experimental track densityprofile. The corresponding calculated total proton yieldsobtained from the scaling factors are 3:5� 107, 5� 107 and6� 107 per shot. The calculated proton track densitydistribution is also sensitive to the shape of the fractionalyield distribution {yi}. As shown in Fig. 6, for the case of aGaussian fractional yield distribution with L ¼ 70mm, thebest fit is obtained for �0 equal to 20�. The correspondingtotal proton yield is about 2:8� 107 per shot.

6. Conclusions

In principle, by adjusting �0, L and {yi} it is possible toobtain a calculated track density profile which is in goodagreement with the experimentally measured distribution.The imaging calculations also show that the total protonyield is very sensitive to the choice of these threeparameters. Clearly, to be of value, the choice of L, �0

and {yi} must be guided by measured values. Furtherexperimental work could be carried out to improve upon thevalues of L, �0 and {yi}. Absolute neutron yield measure-ment would be particularly important in this respect. Thetotal proton yields predicted from these calculations are inthe approximate range ð3{6Þ � 107/shot; which is signifi-cantly lower than the average neutron yield of �1� 108/shot, as measured using the indium activation detector. But,as the magnitudes of the (d; n) and (d; p) reaction cross-sections are very similar over a wide range of energies, thetotal neutron and proton yields are expected to be almostequal. More work will be required to resolve this disparity.The experimental data can only be satisfactorily explained ifthe fusion protons originate from a conical region in front ofthe pinch. The volume of this conical fusion emission zoneis very much greater than the volume of the pinch column,

Fig. 5. Comparison of the calculated track density profiles for a flat

fractional yield distribution with measured track density profile. (a)

L ¼ 70mm and �0 ¼ 20�, 30� and 40�. (b) �0 ¼ 30� and L ¼ 70, 100,

and 120mm.

Fig. 6. Comparison of the calculated track density profile for a Gaussian

fractional yield distribution of L ¼ 70mm and �0 ¼ 15�, 20�, and 25�,

with the measured track density profile.

4120 Jpn. J. Appl. Phys., Vol. 44, No. 6A (2005) S. V. SPRINGHAM et al.

and the temperature and density in this extended sourcecannot be high enough for thermonuclear fusion to occur.Therefore we must conclude that for this 3 kJ plasma focusdevice, beam-target fusion is the dominant fusion mecha-nism. We cannot however exclude the possibility of a minorcontribution resulting from thermonuclear fusion occuring inthe pinch column. This conclusion is in agreement with theresults obtained previously using a completely differenttechnique.9) Further work, both experimental and theoretical,will be required to determine more precisely the location andstructure of the fusion emission region.

Acknowledgement

The authors would like to acknowledge financial supportfor this work by the International Atomic Energy AgencyCoordinated Research Programme on Dense MagnetizedPlasmas (Contract number 12412).

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