IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. PS-15, NO. 6, DECEMBER 1987
Simulations of a Plasma Flow Switch
J. BUFF, M. H. FRESE, A. J. GIANCOLA, R. E. PETERKIN, JR., AND N. F. RODERICK
Abstract-In a portion of the experimental program using the SHIVAStar capacitor bank at the Air Force Weapons Laboratory (AFWL), acylindrical foil load is imploded using an inductive store and a plasmaflow switch. We have performed a number of two-dimensional simu-lations of the switch and load using the MHD code MACH2. In addi-tion to explaining the data from the first series of experiments, thesimulations led to design modifications of the basic plasma flow switchthat resulted in improved current delivery and in enhanced radiationyield. The experimental results are reported in a companion paper byDegnan et al. The key modification was closing portions of the vanestructure. The switch must be sealed shut or else substantial currentwill flow in the diffuse gas that is ablated from the walls of the switchbarrel.
I. INTRODUCTIONIN THE QUICK-FIRE series of experiments at the Air
Force Weapons Laboratory (AFWL), a fast capacitorbank, an inductive store, and a plasma flow switch wereused together to produce multimegampere currents withsubmicrosecond rise time in cylindrical foil loads. Thecapacitance of the SHIVA Star bank is 1.3 mF, and thetotal initial inductance including the plasma flow switchand inductive store is 16.5 nH. In this series, the bankwas charged to 95 kV which resulted in 5.9 MJ of storedelectrical energy. Details of the QUICK-FIRE series ofexperiments may be found in Baker et al. [1], [2]. As aresult of our simulations of the QUICK-FIRE shots, wemade suggestions for geometry changes that predicted im-proved current delivery to the load. These ideas weretested in subsequent shots that are described in a compan-ion paper by Degnan et al. [3]. It is the purpose of thispaper to document the simulations that led to the im-proved current delivery.A drawing of the plasma flow switch is shown as Fig.
1; the configuration is coaxial with the axis of symmetryat the left. A chordal array of 120, 2.0-mil aluminumwires is used to initiate the gun plasma. Below the wirearray is a barrier foil of 0. 12-mil Mylar film which servesto limit travel of a plasma precursor generated by the ex-plosion of the wire array. The total mass of the wire arrayand barrier foil is approximately 120 mg. The load con-sists of a thin cylinder of copper- or aluminum-platedFormvar with a mass of 10-25 mg. The radial-view vanesprovide diagnostic access to the load. The axial-viewvanes at the bottom provide diagnostic access and serve
Manuscript received May 18, 1987; revised August 7, 1987. This workwas supported by the Air Force Weapons Laboratory.
The authors are with Mission Research Corporation, Albuquerque, NM87106.
IEEE Log Number 8717832.
/-/ SHIVA
/ T-FSTAR,/ /--- BANK
/s/'
__' CURRENT_ | FEED
Fig. 1. Sketch of plasma flow switch/imploding liner system. (Dashed areanot to scale.)
as a current path after switching. Typical positions ofmagnetic current probes are also shown. The switch de-sign is based on that of Turchi and coworkers [4]-[7].At the beginning of a shot, energy from the SHIVA Star
capacitor bank is transferred to the vacuum inductor at thecurrent-carrying annular plasma is accelerated to 7-10cm/its down the gun. When the plasma runs off the cor-ner of the gun, current is switched into the cylindrical foilload causing it to implode radially on axis. In order toproduce a high-quality efficient implosion, a large frac-tion of the total current must be delivered to the implosionfoil during a short time interval.The next section gives a brief description of the com-
puter code, our assumptions, and the input parameters se-lected. Section III gives an overview of the results of in-terest to the experimenter-the results are interpreted interms of current probes. Section IV gives results that areof interest to the theorist-the results of two sample sim-ulations are described in some detail. Section V describesthe simulation for improved current delivery. The finalsection is discussion.
II. CODE, AssUMPTIONS, AND SELECTION OFPARAMETERS
The simulations are performed with MACH2, which isa new two-dimensional MHD computer code for prob-
lems with complex geometry. The code is described indetail elsewhere [8], [91. Briefly, it is an implicit contin-uous Eulerian arbitrary Lagrangian Eulerian (ICE-ALE)magnetohydrodynamics code with physics, geometry, andboundary conditions controlled by input. Real equationsof state are used via the SESAME tables at the Los Ala-mos National Laboratory.The best fractional current delivery in a low-mass im-
plosion occurred in the fifth (QF5) of the QUICK-FIREseries of shots. For this reason, the parameters for thisshot were used in simulations reported here. The initiationof the wire array and the interaction of the wire array withthe barrier foil is a complex three-dimensional process,which we cannot model in detail at the present time; thus,the first 1.9 jus of the experiment were modeled with aone-dimensional slug model. All MACH2 simulationsdiscussed here begin when the centers of mass of the wirearray and the precursor foil overlap. The initial calcula-tion mesh for simulations is shown in Fig. 2. The switchplasma is located in the block at the upper right and isassumed to be 1.8 cm thick. The density of the switchplasma does not vary in a direction parallel to the axis ofsymmetry but is graded in the radial direction to approx-imate the actual density profile of the wire array and bar-rier foil. The actual density profile is approximately in-versely proportional to the radius squared so that themagnetic force per unit area is proportional to the massper unit area. The switch plasma is given an initial uniform velocity of 1.28 cm/4s, as predicted by the slugmodel, and a uniform temperature of 1.5 eV which is con-sistent with one-dimensional simulations of explodingwires under these experimental conditions. The switchingplasma is taken to be pure aluminum. At the beginning ofthe simulations, the current is assumed to flow along thetop edge of the switch plasma.The initial thickness of the plasma and the initial cur-
rent distribution are assumptions, and one might worrythat changing these assumptions would alter our results.We ran a series of two-dimensional simulations in whichwe varied the initial thickness from 0.4 to 3.0 cm. Wealso ran a series of one-dimensional simulations in whichdifferent assumptions about the current distribution weremade. In all cases, we found that there was little effect onthe calculations by the time the switching to the load oc-curred. We did however, find that there was a precursor(some small amount of plasma carrying a small amountof current) whose character was determined largely bythese initial assumptions.The implosion foil for QF5 was 315 jig/cm2 aluminum-
plated Formvar which we approximate as a pure alumi-num foil in our simulations. The foil has a 1-mm bowover its 2-cm length, as illustrated in Fig. 2. The initialradius is 5 cm. The foil is assumed to have an initial thick-ness of 3 mm and is held stationary until current beginsto be switched to the foil. Time-step considerations dur-ing the run-down phase of the switch plasma have pre-cluded using a solid density liner in the simulations. This
7.62 cm
...................
-t--~~1\Q\1111111iFig. 2. Initial calculation mesh for simulationsl-4.
limitation could be removed with minor modifications inthe most recent version of MACH2.The void regions are initially filled with 10-6 gm/cm3
aluminum plasma at a temperature of 1.5 eV. During thefirst 1.2 fts of the MACH2 simulation, the grid followsthe switch plasma in a "Lagrangian-like" fashion. Afterthat time, the upper right portion of the grid is fixed andthe switch plasma moves through the grid and out of thecomputation mesh. Low-density plasma is pulled inthrough the top of the coaxial gun at some specified den-sity. In the experiment, this material is ablated from thewalls of the vacuum power feed by ultraviolet radiationemanating from the switch plasma. The density of this fillplasma is uncertain but, as we shall see, is a critical pa-rameter in understanding the behavior of the plasma flowswitch. Anomalous resistivity is included in the low-den-sity plasma.The model used for the anomalous resistivity is generic
with the resistivity effects due to microturbulence givenin terms of an anomalous collision frequency v [10]:
1 mev7 ar* e2Ne (1)
Here 77* is the resistivity, a* the anomalous conductivity,and Ne the electron density. For the simulations presentedhere, the anomalous collision frequency is taken to be theion plasma frequency, which is a few percent of the elec-tron plasma frequency. As discussed in [10], this modelis in good agreement with particle-in-cell simulations forplasma parameters typical of SHIVA implosions. Theanomalous resistivity is added to the classical resistivityto give a total plasma resistivity.An interesting issue is the choice of proper boundary
conditions that should be applied at the vanes. The vanesare designed so that the spacing between vanes is largeenough to allow plasma to flow through them, and so thatthe spacing is small enough for the magnetic field to bestripped from the plasma. In the absence of detailed sim-
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. PS15, NO. 6, DECEMBER 1987
ulations, we have decided to treat the vanes in the follow-ing way. There is assumed to be a perfect conductor atthe position of the vanes. The plasma is either allowed toflow freely through the vanes, or the axial velocity is lim-ited to that of the switch plasma (7 cm/its) as it exits thegun. In the latter case, the switch mass plugs the vanes,thereby limiting the velocity of the low-density flow. Weshall see that limiting or not limiting the flow velocity iscritically important in the operation of the plasma flowswitch.
If the vanes could be included in our simulations, thenthe hydrodynamics would limit the outflow velocity of thelow-density plasma when it meets the switch plasma clog-ging the vanes. It is almost certain that the switch plasmaclogs some of the outer portion of the axial-view vanes.The inner portion may or may not be clogged. Detailedsimulations and possibly experiments would be needed toresolve these issues. Simulations 1-4 demonstrate thecritical nature of the operation of the vanes. In simulation5, it is not important whether the flow is limited or not.The inner portion of the vanes is closed, and the calcu-lation grid is recessed to the actual vane location.
III. OVERVIEW OF IDEAL SIMULATIONS-EXPERIMENTALVIEWPOINT
In this section we present the results of our simulationsas they would be of interest to the experimenter. In theexperiment, the path of current flow and the location ofthe switch plasma and load plasma are inferred from cur-rent probes. Locations of the current probes are shown inFig. 1. Data from shot QF5 are shown in [1] and [2].
In simulation 1, material was pulled in through the topof the coaxial gun at 10-6 gm/cm3 and allowed to flowfreely through the vanes. The MACH2 simulation starts1.9 [is after the bank is fired. This simulation gives goodagreement with the experiment. Current traces at the ex-perimental probe locations are shown in Fig. 3. The curvelabeled B is that determined by the circuit solver andshould correspond to the current measured at probe 2. Theother curves are labeled with the appropriate probe num-bers as in Fig. 1.The total current is about 12 MA near the time when
switching begins at 3.6 As. Almost all the current arrivesat the end of the gun, as shown by probes 5 and 8. Some20 percent of the current is lost at the probe 11 location.Probe 7 shows that only 60 percent of the current is ini-tially delivered to the liner. As the liner starts to move,more current is lost. Probe 15 shows a maximum currentof only 4.2 MA, and probe 17 shows that only a littlemore than 1 MA is flowing through the liner as it passesthat probe location.
In the current traces of probes 7, 8, and 11, one canclearly see a precursor. This results from gas being thrownahead of the major portion of the current sheath, and a
precursor is also observed in the experimental data. How-ever, the size and shape of the precursor is determined bythe assumptions made at the beginning of the simulation,
0.9
E-~~~~~~~~~~~~~~~~~~~~~~~~~
W 0.688 1
o ~~~~~~~~~~~~~~70.3 -15
0.02.0 3.0 4.0
TIME (p5)
Fig. 3. Current traces for simulation 1. Unlimited exit velocity and an in-jection density of 10 -6 gm/cm3. The curve labeled B is from the circuitsolver.
so one should not attach too much significance to it otherthan to note that it is d'ifficult to make it go away.The current traces from the simulation are in good
agreement with the experimental data from shot QF5. Theexperiment shows a little better current delivery than thesimulation; this could be brought into closer agreementby lowering the density of the gas that is pulled in at thetop of the gun.
Since the experiment and the simulation both show poorcurrent delivery to the load, the next problem is to find away to get more current to the load. One might expectthat lowering the background plasma density would help.Also, in simulation 1, the low-density gas is ejected outthe end of the gun at high velocity (almost 80 cm/As) bythe current that flows there. One might expect that thevelocity of this low-density gas should be limited to theejection velocity of switch mass (7 cm/ps) as it exits thevanes. The switch mass plugs the vanes therefore limitingthe velocity of the low-density flow.
In simulation 2, the density at which plasma is pulledin through the top of the gun is reduced to 10-7 gm/cm3,and the outflow velocity through the vanes is limited soas to be no greater than 7 cm/ALs. The current traces forthis simulation are shown in Fig. 4. Almost all the currentis delivered to the load. This is the kind of performancethat one would like to achieve experimentally.The question of whether lowering the background den-
sity or limiting the outflow velocity is more important re-mains. In simulation 3, the density at which plasma ispulled in is 10-7 gm/cm3, but the outflow is unlimited asin simulation 1. The current traces are shown in Fig. 5.While the current delivery to the load is improved overthat of simulation 1, it is far from perfect. The maximumcurrent delivery at probe 15 is only 57 percent, for ex-ample.
In simulation 4, the density at which plasma is pulledin is 10-6 gm/cm3 as in simulation 17 but the outflowvelocity is limited to 7 cm/As as in simulation 2. The
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BUFF et al.: SIMULATIONS OF A PLASMA FLOW SWITCH
1.5
1.2
0
.t.- 0.9
z
04
70.3 ~~~ ~~~~~~~~~~~1617
0.02.0 3.0 4.0
TIME p9)
Fig. 4. Current traces for simulation 2. Exit velocity limited to 7 cm/' sand injection density of 10-7 gm/cm3.
1.5-
e~~~~~~~~~~~~
1.2-
0~~~~~~~~~~~~~~~~
..0.9z
06
0.3
0.02.0 3.0 4.0
TIME (u8)
Fig. 5. Current traces for simulation 3. Unlimited exit velocity and an in-jection density of 10 7 gm/cm3.
current traces are shown in Fig. 6. We note that the cur-rent delivery to the load is quite good. About 90 percentof the current is delivered to the load as it passes the lo-cation of probe 15. The load is carrying 8 MA as it passesthe location of probe 17. One would be happy to achievethis performnance experimentally.
It is fortunate that limiting the outflow velocity is moreimportant because this is easier to achieve than reducingthe background density. One can reduce the outflow ve-locity in the experiment by closing the radial-view vanescompletely and closing the axial-view vanes partially. Re-ducing the background plasma density, which is presum-ably created by ablation powered by the ultraviolet radia-tion from the switch plasma, is likely to be much moredifficult.
IV. Two-SAMPLE CALCULATIONS-THEORETICALVIEWPOINT
Fig. 7 shows density contours, velocity vectors, mag-netic field contours, and current-density vectots for sim-ulation 1 near the time of switching. As the switch plasma
1.5XX_
1.2
0.3
0.0
2.0 3.0 4.0
TIME (pa)
Fig. 6. Current traces for simulation 4. Exit velocity limited to 7 cm/usand an injection density of 10 6 gm/cm3.
DENSITY VELOCITY
V-PC 1 W
I , 1- U pl,#lllli
nIEIlL g
11 -I_;1 # ,,
MAGNETICFIELD
1l <
IEI '1<
U_-
CURRENTDENSITY
I :1,S::g
Ir u
1~t:..HI.. 1 .
Fig. 7. Density contours, velocity vectors, magnetic field contours, andcurrent-density vectors in simulation 1. Contour levels and lengths ofvectors are rescaled in each plot. The times are from 3.6 As (top) to 3.85,us (bottom) in 0.5-ps intervals.
moves down past the corner, the switch opens and mag-netoplasma flows toward the liner. As the magnetoplasmastrikes the liner, the field is compressed and the current isswitched to the liner. The picture presented here is in gen-eral agreement with that presented by Turchi [6].The switch plasma is tilted as it flows out through both
the radial- and axial-view vanes. Thus, the radial-viewvanes are clogged with switch plasma, explaining why thediagnostics that were looking through the radial-viewvanes were unsuccessful. The velocity vectors in theswitch region in the upper figure are due to a precursorplasma and are of little interest. As switching proceeds,the switching plasma moves in at much higher velocity.A vortex pattern is evident in the lower figure. This pat-tern becomes more pronounced as the foil implodes. Notethe rapid outflow through the bottom.The magnetic field and current plots show that the cur-
rent is first switched to the top of the liner and then sweeps
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7EEE TRANSACTIONS ON PLASMA SCIENCE. VOL. PS-15, NO. 6, DECEMBER 1987
MAGNETIC CURRENTFIELD DENSITY
Fig. 8. Magnetic field contours and current-density vectors in simulation2. Contour levels and lengths of vectors are rescaled in each plot. Thetimes are from 3.6 As (top) to 3.85 jis (bottom) in 0.5-,ts intervals.
down the liner. The switch time is about 100 ns. Thisintroduces a substantial perturbation to the liner, whichcan result in poor implosion quality. This is discussed inmore detail in Peterkin et al. [I]. There is severe currentleakage throughout the gun, resulting in poor current de-livery to the load. As the implosion proceeds, plasma isejected out the bottom of the gun at high velocity. Theswitch, unfortunately, acts as a great particle accelerator.
Fig. 8 shows magnetic field contours and current-den-sity vectors for simulation 2 where the background den-sity is lower by a factor 10 from simulation 1 and theoutflow velocity is limited to 7 cm/its as described above.Qualitatively, the picture is the same as in simulation 1,but the current delivery is much better. As the implosionproceeds, there is almost no cufrent leakage in simulation2.The physical difference between simulations 1 and 2
can be understood by calculating the magnetic Reynoldsnumber, R = vL/k where v and L are the local speed andlength-scale, respectively, and k is the diffusivity. If R ismuch larger than unity, magnetic diffusion is negligibleand the field is frozen in the plasma. Such is the case insimulation 1 where the diffusivity is a few 11 c /s inthe low-density but highly conducting plasma that freelystreams through the gap at tens of centimeters per micro-second. In simulation 2, the velocity is much lower anddiffusivity is somewhat larger. Thus, the flow is some-what diffusive; the field is not well coupled to the flow.Our model includes the effects of anomalous resistivity,which is important, but cancels out to first order sinceboth the Alfvhn velocity and the diffusivity scale in-versely with the square root of density.
V. A SIMULATION WITH IMPROVED ELECTRICALPERFORMANCE
Based on the simulations described above, we sug-gested the following modification to the QUICK-FIRE
4
KI
ie If 4
VANESWALL
Fig. 9. Initial calculation mesh for simulation 5.
geometry. The inner portion of the axial-view vane struc-ture should be sealed and the radial-view vanes should bereplaced with a solid electrode. Fig. 9 shows the initialcalculation grid for simulation 5. The locations where theoriginal vanes are changed to a metal wall are noted. Theaxial-view vanes are recessed 0.6 cm from the edge of theimplosion foil. The reasoning is as follows. The switchplasma almost certainly clogs the outer portion of the ax-ial-view vanes, but it almost certainly does not clog theinner portion of the vanes. Thus, the low-density gas willflow through the inner portion of the vanes unless they areclosed. The radial-view vanes are probably clogged, butthey should be replaced by a solid electrode since they arenot useful for diagnostic purposes.We performed simulations with the vanes removed from
the lower portion before the experiments reported by Deg-nan et al. [3] were performed. However, since some ofthe parameters were changed for the experiments, we arereporting on a simulation performed after these shots sothat qualitative comparisons between experiment and sim-ulation can be made. The following parameters werechanged for simulation 5. The charge voltage was 90 kV,the initial inductance was 19 nH, and the implosion foildensity was 200 ytg/cm2. The inflow density was chosento be 3 x 10 7 gm/cm3. The current traces from the sim-ulation are shown in Fig. 10, and they can be directlycompared to the corresponding figure from the experi-mental data in Degnan et al. [3]. Qualitatively, the agree-ment is excellent. The currents in the simulation are a bitlower than the experiment. The currents at the implosionprobe locations could be raised by lowering the assumedbackground density. The implosion in the experiment oc-
curs earlier in the experiment than in the simulation. Webelieve that the actual wire array mass was less than orig-inally thought and less than the mass used in simulation5. Actually, the current delivery is somewhat less thanone might have hoped for based on simulations 1-4. Wesuspect that this is due to some switch plasma that strikesthe edge of the wall and stays in the corner near the orig-
770
771BUFF et al.: SIMULATIONS OF A PLASMA FLOW SWITCH
<E 0.90
1-z
A0.604:4:)
0.0
3.0 f
1-34rA
P:
04
2.0
1.0
0.0
2.0 3.0 4.0
TIME (p s)
Fig. 10. Current traces for simulation 5.
TIME (p8)
Fig. 11. Radiation power output in simulation 5.
inal foil position providing some additional mass to carrycurrent.
Fig. 11 shows the predicted radiation output from sim-ulation 5. The agreement with experiment is good with a
predicted peak power of 2.5 TW.
VI. DIscuSSIONWe have performed simulations to understand how the
plasma flow switch works, and we have suggested changesto improve the current delivery to the load. This has re-
sulted in better experimental results. Since the MACH2
code is fast and versatile, we are presently running a num-
ber of simulations with the goal of improving the radia-tion output of the imploding foil. We are consideringchanges to the geometry of the system, shaping of theelectrodes, mass grading of the foil, and snowplow sta-
bilization.
ACKNOWLEDGMENTThe authors would like to thank W. Baker, J. Degnan,
K. Hackett, C. Clouse, and W. McCullough for helpfuldiscussions and useful comments on our work. W.McCullough and S. Payne performed the slug-model cal-culations that determined the starting point for theMACH2 calculations. Special thanks are due to R. Rei-novsky for his scientific contributions and for his supportof our development of MACH2. Lastly, we would like tothank P. Turchi for many hours of enlightening discus-sions concerning the plasma flow switch. He first pointedout the importance of limiting the outflow velocity.
REFERENCES
[1] W. L. Baker et al., "QUICK-FIRE plasma flow driven implosionexperiments," in Proc. 5th IEEE Pulsed Power Conf (Arlington,VA), 1985, pp. 728-731.
[21 W. L. Baker et al., "Multi-megampere plasma flow switch drivenliner implosions," in Proc. MegaGauss III Conf. (Santa Fe, NM),1986, in press.
[3] J. H. Degnan et al., "Experimental results from SHIVA Star vacuuminductive store/plasma-flow-switch-driven implosions," IEEE Trans.Plasma Sci., this issue, pp. 760-765.
[41 P. J. Turchi et al., "Development of coaxial plasma guns for powermultiplication at high energy," in Proc. 3rd IEEE Pulsed Power Conf.(Albuquerque, NM), 1981, pp. 455-462.
[51 S. Seiler et al., "High current coaxial plasma gun discharges throughstructured foils," in Proc. 4th IEEE Pulsed Power Conf. (Albuquer-que, NM), 1983, pp. 346-349.
[6] P. J. Turchi, "Magnetoacoustic model for plasma flow switching,"in Proc. 4th IEEE Pulsed Power Conf. (Albuquerque, NM), 1983,pp. 342-345.
[7] P. F. Ottinger, P. J. Turchi, D. Conte, and J. D. Shipman, ji.,"Transmission line code modeling of the plasma flow switch," inProc. 5th IEEE Pulsed Power Conf. (Arlington, VA), 1985, pp. 736-739.
[8] M. H. Frese, "MACH2: A two-dimensional magnetohydrodynamicsimulation code for complex experimental configuration," MissionResearch Corp., Albuquerque, NM, Tech. Rep. AMRC-R-874.
[9] R. E. Peterkin, Jr., J. Buff, M. H. Frese, and A. J. Giancola,"MACH2: A reference manual," Mission Research Corp., Albu-querque, NM, Tech. Rep., AMRC-R-764.
[101 N. F. Roderick et al., "Theoretical modeling of electromagneticallyimploded plasma liners," in Laser and Particle Beams, vol. 1, 1983,pp. 181-206.
[11] R. E. Peterkin, Jr., J. Buff, M. H. Frese, N. F. Roderick, and S. S.Payne, "MACH2 simulations of plasma flow switches with shapedelectrodes," in Proc. MegaGauss lIII Conf. (Santa Fe, NM), 1986,in press.
