Evidence for the buffer zone in a plasma acceleratorKeith A. Thomas and Eugène J. Clothiaux Citation: Journal of Applied Physics 70, 3467 (1991); doi: 10.1063/1.349239 View online: http://dx.doi.org/10.1063/1.349239 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/70/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Erratum: “Evidence of photon acceleration by laser wake fields” [Phys. Plasmas13, 033108 (2006)] Phys. Plasmas 13, 079901 (2006); 10.1063/1.2218327 Determination of the ionization and acceleration zones in a stationary plasma thruster by opticalspectroscopy study: Experiments and model J. Appl. Phys. 91, 4811 (2002); 10.1063/1.1458053 Particle acceleration in magnetic reconnection zones AIP Conf. Proc. 558, 815 (2001); 10.1063/1.1370883 Evidence of Turbulence in the Reaction Zone of Detonating Liquid Explosives J. Appl. Phys. 37, 4798 (1966); 10.1063/1.1708140 Plasma Acceleration Am. J. Phys. 29, 336 (1961); 10.1119/1.1937772

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Evidence for the buffer zone in a plasma accelerator Keith A. Thomas and Eugene J. Clothiaux Department of Physics, Auburn University, Alabama 36849-5311

(Received 2 January 1991; accepted for publication 8 July 199 1)

The existence of an absorbing layer, or buffer zone, of weakly ionized gas between the rear of the projectile and the front of the plasma arc armature in a plasma accelerator has been postulated. In the studies reported here a technique for finding the position of the projectile as a function of time is given and compared to the plasma armature position as determined by inductive probes. Analyses of these signals provide the basis for a description of the in- bore motion of the projectile with respect to the plasma arc armature. The experimental evidence appears to support the existence of a buffer zone.

I. INTRODUCTION

Kinetic theory models of the plasma arc armature of a plasma accelerator predict equilibrium temperatures in the range of 30-50 000 K,‘,* and in-bore spectral measure- ments show this plasma to be optically thick over the wavelength region of 2300-6300 A, consisting of a contin- uum spectrum laced by a few absorption lines.3’4 If the spectrum observed is due to an equilibrium plasma at a temperature of 3-4 eV, say, then the Planck radiation has a peak in the vicinity of l-2 x lo3 A. The strong ultravi- olet radiation associated with this plasma is believed to be the direct cause of ablation.5 The projectile and the side insulators are frequently made of polycarbonates, and whereas the side insulators show signs of heating, the rear of the projectile usually appears unaffected. It is this latter observation which has led to the hypothesis that there ex- ists an absorbing region, or buffer zone, between the rear of the projectile and the front of the plasma arc armature.

The movement of the plasma arc down the accelerator is tracked with inductive. probes which sense the magnetic field of the plasma arc, B,, or the magnetic field of the rail current, Brti,. The use of these probes has been reviewed by Parker in a recent article,6 wherein he assesses the strengths and weaknesses of both types of magnetic probes.

Some investigators have inferred an arc current density distribution from the B,, probe signals.7-11 Jamison et a1.7P8 assumed an of priori form for the current distribution to fit a series of B,, signals. ebbgl” developed a least- squares routine to fit a series of B,, probe signals to obtain the current distribution. He correlated the signal. of a pho- todiode detector directly across the bore from a B,, probe and found the appearance of light about 6 ps before the occurrence of the first maximum of the B,, probe. lo From the claim that the sharp rise in the photodiode signal cor- responded to the passage of the rear of the projectile and the assumption that the first peak in the B,, signal corre- sponded to the passage of the front of the plasma arc, he was able to infer the existence of a buffer zone of < 10 mm in length.

Clothiaux et aZ.‘* found values for the buffer zone in two different ways. The sensitivity to light emission as the

projectile passes was increased by using a spectrograph- photomultiplier tube viewing at 4000 A. As the projectile clears the viewing port a weak light signal appears, fol- lowed thereafter by the sudden onset of a large signal, which was taken to correspond to the arrival of the leading edge of the plasma arc armature. From the speed of the projectile and the time interval for the weak light signal, these authors deduced a buffer length of ~24 mm. In a second method, a photodiode signal was compared with a conductivity probe located at the same accelerataor port position. Figure 2 of Ref. 12 shows the photodiode re- sponding before there is any conducting material detected at this port. The time interval between the two measure- ments gave a buffer length of z 13 mm.

A difficulty common to all attempts to detect the pres- ence of a buffer zone and to determine some of its proper- ties has been the lack of precision of the location of the rear of the projectile. In this paper we review the technique of embedding small magnets in the projectile to track its motion,13 and combine this approach with information de- rived from inductive probes to search for a buffer zone.

II. EXPERMENTAL APPARATUS

The plasma accelerator has a length of 60 cm and a 1 cm square bore, and the electrodes are held horizontally so that the plasma arc current flows in a vertical direction between the electrodes, as shown in Fig. 1. The electrodes are made of copper, and the side insulators are made from a clear polycarbonate (Lexan) . There are 11 ports on 2-m centers along both sides of the accelerator providing access for a variety of diagnostics, for example, B,, probes and optical fibers. There are also 11 ports along the top of the accelerator for Brai, probes, with each of these ports in the same vertical plane as the two corresponding side ports (Fig. 2). The Brai probes are placed in an offset position to maximize the signals according to the recommendation given by Parker.6

The projectile is 5 cm long and is fabricated from a black polycarbonate material with the tradename Zelux. The total mass is approximately 6 gm and there are three holes in the projectile at 2, 3, and 4 cm from the front face

3467 J. Appl. Phys. 70 (7), 1 October 1991 0021-8979/91/073467-05$03.00 @I 1991 American Institute of Physics 3467 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

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FIG. 1. Cross-sectional view of the plasma arc accelerator. The electrodes are copper; the side insulators supporting the electrodes are Lexan; the top and bottom insulators shown are a fiberglass material (G-10); the containment structure is aluminum.

with which a measurement of the injection speed can be made using light gates. Two rare-earth magnets are located 1 cm from the front end of the projectile, one on each side. The magnets are ~5 mm in diameter and are z 1.5 mm thick. The forward location is desirable in order for the magnetic field of the magnets to be discernible in the B arm probes from the magnetic field of the plasma arc ar- mature. Once mounted in the projectile, the magnets are coated with epoxy which provides support and electrical insulation. An aluminum foil is mounted on the rear of the projectile from which the initial plasma arc armature is formed once the projectile is in the bore of the accelerator.

The projectile is generally injected into the plasma ac- celerator with some initial velocity provided by a light gas gun. This device can provide injection speeds of 250-450 m/s using helium gas compressed at 1200-2000 psi in a small gas bottle which is released with a fast acting valve; The injection speed of the projectile is measured with light gates mounted along the injector bore, and with the B,, probe located ‘at port 1 in the accelerator. The use of this B - probe is possible since the power source triggering

LIGHT GATES Rl R2 R3 . Rll

FIG. 2. Top view of the schematic layout of the plasma accelerator. The light gates are part of the gas injector. There are eleven ports on each side of the plasma acceleration section and eleven ports on the top. The top ports are offset from the bore axis for the mounting of rail inductive probes.

___-.-.-

I- ---- --- 0.0 1 .o --. r-- -l

2.0 3.0 TIME (ms)

FIG. 3. Typical signals from armature inductive probes at ports R2-R6. This is a subset of the eleven signals obtained on a shot. The arrowheads indicate the position of the signal from the magnets embedded in the projectile nose. The passage of the center of the magnet can be determined to within * r mm.

(foil explosion) occurs at a time after the embedded mag- nets have passed by port 1.

Ill. EXPEMMENTAL RESULTS

A. Projectile position

The position of the projectile is found by detecting the passage of the embedded magnets located near its nose. In the standard accelerator configuration the B,, probes were located a distance of ~16.5 mm from the bore and were carefully oriented to detect only the magnetic field of the plasma arc armature. It was found that these probes could not reliably detect the embedded magnets at this position. However, on relocating the B,, probes to a dis- tance of 10 mm from the bore, the magnetic field of the embedded magnets was readily detectable on every shot. The characteristic signature of these magnets is symmetric and easily identifiable at every port along the accelerator. The position of the center of the magnet is taken to corre- spond to the peak in the signature and this point can be located to within * 1 mm. A series of five B,, probe sig- nals is shown in Fig. 3, where the signal due to the embed- ded magnets is indicated by an arrowhead.

B. Inductive probes

For a uniform current density distribution the leading edge of the plasma arc armature has *been shown to coin- cide with the first extremum of the B,, inductive probe. This extremum may be either a maximum or a minimum depending on the orientation of the probe coil. The zero crossing corresponds to the plasma arc centroid, while the second extremum is generally the rear of the armature. The actual current density distribution is not likely to be uni- form and the interpretation that the first extremum of the Barn, signal gives the location of the leading edge of the plasma arc armature is suspect.

3468 J. Appl. Phys., Vol. 70, No. 7, 1 October 1991 K. A. Thomas and E. J. Clothiaux 3468

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An estimate of the variation possible in locating the several different current density distributions. The filament leading edge of the plasma if the current density is not model of Parker6 was integrated over an assumed current uniform was made by calculating the expected Barm for density profile J(c) ,

(1)

where the notation is that of Parker with z, the position of the probe, zp the position of the leading edge of the plasma arc, Z, the length of the plasma, and 6 the location of the generic point in the plasma. Equation ( 1) was numerically integrated to give Bann signals for a probe located at the origin of coordinates (z, = 0) and for several different func- tional forms for the current density distribution, namely: uniform, linear, sine, x4, e-“, and e- ‘. The results are shown in Fig. 4 for a plasma arc of length 2 cm. These plots show that for the various current density distribu- tions tested, the individual B,, signals do not vary much, and that it will be difficult to infer a unique current density distribution from an inversion of the ;B,, signals alone.14 Moreover, the first maximum in the B,, signal can occur either before, or after, the leading edge of the plasma arc passes the probe location. However, the first maximum for the assumed distributions lies within z f 1 cm of coinci- dence of the leading edge of the plasma arc and the probe. The corresponding time interval depends on the speed of the projectile, and for a plasma arc with a velocity of 800 m/s (typical for our experiments), this interval is =!= 15 ps.

We do not know the actual current density distribu- tion, but assuming it does not substantially differ from the aforementioned ones, it is possible to bracket the position of the leading edge of plasma arc armature relative to the

-10.0 -8.0 -60 -4.0 -2.0 0.0 2.0 4.0

DISTANCE - Z, (cm)

FIG. 4. Superposition of calculated armature inductive probe signals, B Bn,,, for diierent assumed current density distributions. The distributions listed in the order in which their curve crosses the x axis are: (1) 2, (2) x, (3) e. ‘, (4) sin(x), (5) uniform, (6) eeX. The first maximum or peak of these distributions falls within the interval z f 10 mm of the probe location at the origin.

I

first maximum of the. i,, signal. Therefore, from the lo- cations of the eleven B - probes, the position of the rear of the projectile and of the leading edge of the plasma can be determined as a function of time. From these curves the appearance, or nonappearance, of a gap between the two is inferred. In Fig. 5 the position versus time of theembedded magnets, the first maximum or peak of the Q,,, probe signal, and the zero crossing of the same signal are plotted for the case of a typical shot. From these curves, correcting for the location of the rear of the projectile relative to the embedded magnets, the length of the gap or buffer zone between the plasma arc and the projectile is determined and these results are shown in Fig. 6 for four different shots, each at a different peak current as indicated in the figure. The length of the buffer zone is observed to decrease as the accelerator current increases.

IV. DISCUSSION OF RESULTS

The projectile is injected into the breech of the accel- erator with some initial velocity, which in our shots varied between 250-450 m/s. During the time interval required

0 200 400 600 800

TIME (us)

FIG. 5. Temporal plots of the position of: i-the magnets in the projec- tile. 2-the first peak of the B,,, signal, and 3-the zero crossing of the B,, signal. The zero crossing is sometimes used to determine the speed of the plasma arc armature.

3469 J. Appl. Phys., Vol. 70, No. 7, 1 October 1991 K. A. Thomas and E. J. Clothiaux 3469 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

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g 7.0-

z F? 5

6.0-

2. - 2 I& 5.0.

F. - 3 Lj 4.0-

DISTANCE (cm)

,_ .-

FIG. 6. Length of the buffer zone at four different accelerator peak’&- ;_L._ rents: (a) 32 kA, (b) 60 kA, (c) 124 kA, and (cl) 150 kA. ~The honzontal axis is the time axis measured in units of the distance of the projectile magnet from the breech of the accelerator. The buffer zone was deter- mined using plots as shown in Fig. 5 for each of the accelerator currents.

for the aluminum foil to ‘explode and for the plasma to form, the projectile is observed to suddenly accelerate away from the explosion region while the forming plasma arc suffers a small deceleration. Shortly thereafter the plasma arc begins to accelerate under the action of the JxB force, and as seen in Fig. 6 the buffer zone decreases. If the JXB force could be maintained constant, the buffer zone should achieve some terminal length, however, there seems to be no correlation bettiekn the decrease in the total accelerator current (Fig. 7) and t& length of the buffer zone.

It is important to note that the plots in Fig:. 6 are for four different total currents to the accelerator, and in each case the total in-bore transit time for the projectile and for the arc was different. Therefore, the horizontal axis is not explicitly a time axis but is normalized to the distance between the instantaneous position of the embedded mag- net and the breech of the accelerator.

0.9-

z$ 0.8- E

s5 0.7-

$ -o,6

3 9 0.5-

0.4-

I- 0.3 ~-- 10 r 2b-- -_ --xi-

L 1

DISTANCE yirn) 50 60

FIG. 8. Velocity of the projectile for the currents (a)-(d) of Fig. 6. Curve (e) was obtained at’ an accelerator current of 185 kA during which shot the occurrence of a secondary plasma arc was seen on the B,, probes, /

Plots of the velocity of the projectile and of the first maximum of the B,, signals are shown in Figs. 8 and 9, respectively. As the current into the accelerator increases, the velocity of the projectile versus position is observed to increase and in each case the-exit velocity is greater. Curve (e) in Fig. 6(a) is an exception, but a secondary arc oc- curred in this shot, which changed the behavior of the system.- The acceleration of the projectile versus position inferred from ‘the velocity plots gives a slightly increasing acceleration for curve (a), a constant ‘acceleration for curve (b), and slowly decreasing acceleration for curves (c) and (d). A comparison with the plots for the velocity of the plasma arc? as defined by the velocity of the first maximum of the B - probes, shows that once the plasma arc has formed it moves with ‘a slightly greater velocity than that of the projectile at the same position. However, the arc velocity decreases faster than that of the projectile, and the minimum observed in the buffer zone plots, Fig. 6,

TIME (ms)

FIG. 7. Typical curve of the accelerator current. The projectile was in the FIG. 9. Velocity of the plasma arc armature for the currents (a)-(d) of accelerator bore from t = 0 ms until the time indicated by the arrow at Fig. 6. The vertical bar indicates the indeterminacy of the leading edge of t-O.95 ms. The peak current on this shot was about 124 kA. the arc for the current density distributions discussed.

Cd) A------

F 0.8 E

o.3,~-~~._.--7- L I

DIl;ANCE ;arn) 50

3470 J. Appl. Phys., Vol. 70, No. 7, 1 October 1991 K. A. Thomas and E. J. Clothiaux 3470

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occurs at the point where the plasma front (the first max- imum of B-) has the same velocity as that of the projec- tile.

Although the acceleration curves associated with the velocities of Fig. 6 do show some increase or decrease for the projectile, the change is small in all cases, particularly late in the motion of the projectile. It is reasonable to take the force acting on the projectile as essentially constant for each shot, regardless of the velocity or acceleration of the. plasma arc armature, or of the length of the buffer zone. Since it is the pressure in the buffer zone which provides the projectile acceleration, it follows that no change in the pressure behind the projectile is expected, even though the length of the buffer zone is observed to change. The impli- cation is that in the early stages of the motion, as the buffer zone decreases, the accelerating plasma arc is absorbing the buffer zone without any gross change in the buffer zone pressure. While in the later stages of the motion, the de- celerating plasma arc is either feeding ,material into. the buffer zone or otherwise heating it so as to keep the pres- sure constant. Obviously; temporally resolved pressure measurements along the length of the plasma accelerator. are needed.

A standard diagnostic technique frequently used is an in-bore photodiode (PD) which monitors the light emis- sion from the accelerator bore. It is generally assumed that a sharp rise in the PD signal is caused by the passage of the rear of the projectile in front of the PD port. Our signals are comparable to those reported by Cobb” and will not be shown here. We consider the case of the 124-kA’ shot, where the PD shows a sharp increase in light beginning 4 ,us before the first maximum in the B,, probe located directly across the bore. From a position versus time plot it is found that the rear of the projectile passes the PD port 4 ps before the appearance of a signal in the PD and that the projectile is moving at a speed of 633 m/s at that point. If the observation that little or no light is emitted for the first half of the buffer zone holds true in’general, then the as- sumption that this sharp rise in the PD signal is due to the passage of the rear of the projectile appears to underestii mate the size of the buffer zone.”

V. CONCLUSIONS

We have reported an accurate technique for measuring the in-bore position of the projectile in a plasma accelerator using B,, p robes. The BiotSavart law is numerically in- tegrated for several different current density distributions to provide an estimate of the accuracy of using the~first peak of the &.,,, signal as defining the leading edge of the plasma. In these calculations the leading edge is taken as a sharp, well-defined boundary which may not be the case in an actual shot.

From the position of the projectile and the front of the plasma as’a function of time, a buffer zone can be inferred. The results of these buffer zone measurements, for several shots with different currents, show the length of the buffer zone to be varying as a function of the projectile position in the accelerator.

The velocities of both the projectile and the plasma can also be found from the position versus time data. It is from these velocity plots that we see the motion of the projectile shows only small changes in acceleration implying that the driving force is also nearly constant. From this observa- tion, we conclude the plasma arc armature may be either absorbing material or flowing material, and heat into the buffer zone as it changes its length, thereby maintaining a constant pressure on the rear of the projectile. This will require an experiment, using calibrated pressure transduc- ers at many bore positions, to measure the pressure of the buffer zone.

The results reported here were for a rather short ac- celerator (60 cm), and the behavior in a longer device may be different. Experiments to test the phenomena described here are currently planned using a 2-3-m accelerator.

ACKNOWLEDGMENTS

The authors wish to acknowledge the assistance of S. C. Boyd, C. Wilson, E. Ogar, J. W. Rogers, and G. Arnold in operating the accelerator and in making the measure- ments. This work was supported by the Innovative Science & Technology Division of SD10 through contract No. DNA-001-85X-0183 with the Defense’ Nuclear Agency.

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elsewhere. ~,

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