Simulation of the inner electrode geometry effect on the rundown phase characteristics of a coaxial plasma accelerator.

C. Gómez Samaniego, M. Nieto Pérez, G. Ramos López


A 2D computational model, incorporating the Snowplow approximation in the mass balance, is used to simulate the acceleration of an annular current sheath along two coaxial electrodes, with the inner one having either cylindrical or conical shape. The circuit, mass and momentum equations are simultaneously solved in 2D (r, z) considering initial breakdown along the insulator surface, ideal gas mass accretion by the current sheath (snowplow model) and distributed inductance along a coaxial transmission line short-circuited by the current sheath. Plasma density and electron temperature in the current sheath are estimated using standard planar shock theory. Numerical integration of the model’s equations for a given electrode geometry yields the temporal evolution of the current sheath parameters during the axial acceleration phase. In order to see the effect of the inner electrode shape on sheath parameters (i.e. transit time, kinetic energy, total mass, shape, etc.) and/or circuit properties (i.e. circuit inductance, voltage and current evolution, etc.), the portion of the inner electrode beyond the insulator was given a conical shape. By changing the cone slant in a range between ±5°, it was found that the current driven on the plasma sheath varies nonlinearly with the angle. The divergent (positive angle) electrode gives the sheath the highest kinetic energy, being twice the value corresponding to that of the straight inner electrode case, and the transit time is reduced from 1.34 to 1.20 µs. The estimates of plasma density and electron temperature indicate that the achievable ion densities are on the order of 4x1022 m-3, which corresponds to 30 % ionization, and typical temperatures at the end of the rundown phase are on the order of 8 eV. These values are comparable with those measured in experimental devices. The development of this tool will enable us to benchmark its results against an experimental installation currently close to being operational, and a future follow-up paper will be devoted to the comparison between the prediction of the rundown phase behavior and experimental results utilizing conical electrodes.


Plasma simulation; plasma accelerators; snowplow-model.

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Ishii K, Suemitsu H, Fukuda K. Contraction of Plasma in a Linear Z-Pinch Tube. Jpn J Appl Phys. 5 (1966) 1235-1239

Potter D. The formation of high-density z-pinches. Nucl Fusion. 18 (1978) 813-823

Rosenbluth M, Rosenbluth A, Garwin R. Infinite Conductivity Theory of the Pinch. (1854).

Wyld HW. Dynamic Stability of a Self‐Pinched Discharge. J Appl Phys. 29 (1958) 1460-1465

Lovberg RH. The use of magnetic probes in plasma diagnostics. Ann Phys (N Y). 8 (1959) 311-324

Jahoda FC, Sawyer GA. Pickup-Coil Measurement of the Plasma Magnetic Field in the Scylla I Theta Pinch. Phys Fluids. 6 (1963) 1195

Oliphant TA. A mixed snowplow-bounce model for shock heating in a staged theta pinch. Nucl Fusion. 14 (1974) 377-382

Itoh S, Fujisawa N, Yamamoto K. Toroidal Theta Pinch Collapse by the Snowplow Model. Phys Fluids. 12 (1969)

Pert GJ. A simple model of the coaxial plasma gun with positive central electrode. J Phys D Appl Phys. 1 (1968) 1487-1493

Hart PJ. Plasma acceleration with coaxial electrodes. Phys Fluids. 5 (1962) 38-47

Rawat RS. High-energy-density pinch plasma: A unique nonconventional tool for plasma nanotechnology. IEEE Trans Plasma Sci. 41 (2013) 701-715

Kikuchi Y, Sakuma I, Iwamoto D, et al. Surface cracking and melting of different tungsten grades under transient heat and particle loads in a magnetized coaxial plasma gun. J Nucl Mater. 438 (2013) S715-S718

Inestrosa-Izurieta MJ, Jauregui P, Soto L. Deposition of materials using a plasma focus of tens of joules. J Phys Conf Ser. 720 (2016) 9

Brezinsek S, Coenen JW, Schwarz-Selinger T, et al. Plasma–wall interaction studies within the EUROfusion consortium: progress on plasma-facing components development and qualification. Nucl Fusion. 57 (2017) 10

Ramos G, Martinez M, Herrera JJE, Castillo F. The plasma focus as a tool for plasma-wall-interaction studies. J Phys Conf Ser. 591 (2015) 9

Battaglia DJ, Bongard MW, Fonck RJ, Redd AJ, Sontag AC. Tokamak Startup Using Point-Source dc Helicity Injection. Phys Rev Lett. 102 (2009) 4

Shriver E. Analytical and Experimental Investigation of the Coaxial Plasma Gun for Use as a Particle Accelerator. NASA TN D-6687 I (1972).

Cheng DY. Plasma deflagration and the properties of a coaxial plasma deflagration gun. Nucl Fusion. 10 (1970) 305-317

Hawke RS, Susoeff AR, Asay JR, et al. Armature formation and performance in a railgun using a two-stage light-gas gun injector. In: IEEE International Conference on Plasma Science. 17 (1989) 8

Katulka GL, White KJ, Oberle WF, Kaste P, Pesce-Rodriguez R, Leadore M. Experimental characterization of plasma effects on energetic materials for electrothermal-chemical launch applications. IEEE Trans Magn. 35 (1999) 197-200

Mather JW. 15. Dense Plasma Focus Rep. LA-3802-MS 1544 (1971) 187-249.

Rawat RS. Dense Plasma Focus - From Alternative Fusion Source to Versatile High Energy Density Plasma Source for Plasma Nanotechnology. J Phys Conf Ser. 591 (2015) 26

Langhoff M. Disruption Simulation by a Coaxial Plasma Gun M.S. University of New Mexico (1991) Ph.D. Theses

Rabiński M, Zdunek K. Physical model of dynamic phenomena in impulse plasma coaxial accelerator. Vacuum. 48 (1997) 715-718

Moreno C, Casanova F, Correa G, Clausse A. Experimental study and two-dimensional modelling of the plasma dynamics of magnetically driven shock waves in a coaxial tube. Plasma Phys Control Fusion. 45 (2003) 1989-1999

Rabiński M, Zdunek K. Computer simulations and experimental results in studies of plasma dynamics during the impulse plasma deposition process. Surf Coatings Technol. 116-119 (1999) 679-684

Miyamoto T. Analysis of high-density Z-pinches by a snowplow energy equation. Nucl Fusion. 24 (1984) 337-348

Rabiński M, Zdunek K. Snow plow model of IPD discharge. User Model User-adapt Interact. 70 (2003) 303-306

Miyazawa J, Yamada H, Yasui K, et al. Design of spheromak injector using conical accelerator for Large Helical Device. Fusion Eng Des. 54 (2001) 1-12

Casanova F, Moreno C, Clausse A. Finite-elements numerical model of the current-sheet movement and shaping in coaxial discharges. Plasma Phys Control Fusion. 47 (2005) 1239-1250

Kwek KH, Tou TY, Lee S. Current sheath structure of the plasma focus in the run-down phase. IEEE Trans Plasma Sci. 18 (1990) 826-830

Abd Al-Halim MA. Estimation of the plasma sheath thickness and particle number density in the axial phase of plasma coaxial accelerator. Vacuum. 138 (2017) 80-86

Winterhalter D, Kivelson MG, Walker RJ, Russell CT. The MHD Rankine-Hugoniot jump conditions and the terrestrial bow shock: A statistical comparison. Adv Sp Res. 4 (1984) 287-292

Gross RA. Strong Ionizing Shock Waves. Rev Mod Phys. 37 (1965) 724-743

Lee S. Radius Ratios of Argon Pinches. Aust J Phys. 36 (1983) 891

Frignani M. Simulation of gas breakdown and plasma dynamics in plasma focus devices. Dip di Ing Energ Nucl e del Control Ambient. Ph.D. (2007)

Cassibry JT, Thio YCF, Wu ST. Two-dimensional axisymmetric magnetohydrodynamic analysis of blow-by in a coaxial plasma accelerator. Phys Plasmas. 13 (2006) 14

Witherspoon FD, Case A, Messer SJ, et al. A contoured gap coaxial plasma gun with injected plasma armature. Rev Sci Instrum. 80 (2009) 15

Szabo JJ. Fully Kinetic Numerical Modeling of a Plasma Thruster Massachusetts Institute of Technology Ph.D. (2001)



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