One-dimensional theory and simulations of the dynamic Z-pinch

Angus, J. R.; Link, A. J.; Schmidt, A. W.

doi:10.1063/1.5104340

Title: One-dimensional theory and simulations of the dynamic Z-pinch

Journal Article · 09 January 2020 · Physics of Plasmas

DOI: https://doi.org/10.1063/1.5104340 · OSTI ID:1648405

^[1]; Link, A. J. ^[1]; Schmidt, A. W. ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

The dynamical formation of a Z-pinch in the strong-shock limit is studied in this paper using one-dimensional (1D) simulations of a two-temperature magnetohydrodynamic model. The classic 1D picture consists of three stages: run-in, reflected-shock, and expansion. The special case of a constant current I and uniform gas fill, which are approximate conditions of the pinch-formation stage in a dense plasma focus, is examined in detail. Time-profiles for the shock-front and piston positions during the run-in stage are compared with some of the commonly used 0D models from the literature. Some practical improvements to these models are presented here and it is shown that this model gives the best agreement with results from the simulations. Maximum compression of the plasma is achieved when the reflected shock from the axis meets the incoming current layer. The ratio of the plasma radius at this time with respect to its initial radius is found from the simulations to be r_p/R≈1/8 using 5/3 for the adiabatic coefficient γ. The pressure and temperature of the compressed plasma are found to peak a short time after maximum compression due to the inability of the reflected shock to completely stagnate the incoming plasma driven by the converging current layer. Finally, the variation of the results with a finite dI/dt and for different values of γ is presented.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1648405

Report Number(s):: LLNL-JRNL--772662; 964488

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 1 Vol. 27; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (51)

The relaxation schemes for systems of conservation laws in arbitrary space dimensions Jin, Shi; Xin, Zhouping Communications on Pure and Applied Mathematics, Vol. 48, Issue 3 https://doi.org/10.1002/cpa.3160480303	journal	January 1995
Plasma Focus Radiative Model: Review of the Lee Model Code Lee, S. Journal of Fusion Energy, Vol. 33, Issue 4 https://doi.org/10.1007/s10894-014-9683-8	journal	March 2014
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws Sod, Gary A. Journal of Computational Physics, Vol. 27, Issue 1 https://doi.org/10.1016/0021-9991(78)90023-2	journal	April 1978
An analytic description of converging shock waves Chisnell, R. F. Journal of Fluid Mechanics, Vol. 354 https://doi.org/10.1017/S0022112097007775	journal	January 1998
Sheared flow stabilization experiments in the ZaP flow Z pinch Shumlak, U.; Nelson, B. A.; Golingo, R. P. Physics of Plasmas, Vol. 10, Issue 5 https://doi.org/10.1063/1.1558294	journal	May 2003
Investigation of the High-Energy Acceleration Mode in the Coaxial Gun Mather, J. W. Physics of Fluids, Vol. 7, Issue 11 https://doi.org/10.1063/1.1711086	journal	January 1964
Formation of a High-Density Deuterium Plasma Focus Mather, J. W. Physics of Fluids, Vol. 8, Issue 2 https://doi.org/10.1063/1.1761231	journal	January 1965
Z-pinch plasma neutron sources Velikovich, A. L.; Clark, R. W.; Davis, J. Physics of Plasmas, Vol. 14, Issue 2 https://doi.org/10.1063/1.2435322	journal	February 2007
Neutron production and implosion characteristics of a deuterium gas-puff Z pinch Coverdale, C. A.; Deeney, C.; Velikovich, A. L. Physics of Plasmas, Vol. 14, Issue 2 https://doi.org/10.1063/1.2446177	journal	February 2007
Deuterium gas-puff Z-pinch implosions on the Z accelerator Coverdale, C. A.; Deeney, C.; Velikovich, A. L. Physics of Plasmas, Vol. 14, Issue 5 https://doi.org/10.1063/1.2710207	journal	May 2007
Ionization and radiation dynamics of dense MHD plasmas Duston, Dwight; Duderstadt, James J. Journal of Applied Physics, Vol. 49, Issue 8 https://doi.org/10.1063/1.325482	journal	August 1978
Relaxation model for extended magnetohydrodynamics: Comparison to magnetohydrodynamics for dense Z-pinches Seyler, C. E.; Martin, M. R. Physics of Plasmas, Vol. 18, Issue 1 https://doi.org/10.1063/1.3543799	journal	January 2011
Analytic model for the dynamic Z-pinch Piriz, A. R.; Sun, Y. B.; Tahir, N. A. Physics of Plasmas, Vol. 22, Issue 6 https://doi.org/10.1063/1.4922078	journal	June 2015
Deuterium z-pinch as a powerful source of multi-MeV ions and neutrons for advanced applications Klir, D.; Shishlov, A. V.; Kokshenev, V. A. Physics of Plasmas, Vol. 23, Issue 3 https://doi.org/10.1063/1.4942944	journal	March 2016
Development of the dense plasma focus for short-pulse applications Bennett, N.; Blasco, M.; Breeding, K. Physics of Plasmas, Vol. 24, Issue 1 https://doi.org/10.1063/1.4973227	journal	January 2017
Increasing plasma parameters using sheared flow stabilization of a Z-pinch Shumlak, U.; Nelson, B. A.; Claveau, E. L. Physics of Plasmas, Vol. 24, Issue 5 https://doi.org/10.1063/1.4977468	journal	May 2017
Investigation of the Paschen curve for helium in the 100–1000 kV range Xu, Liang; Khrabrov, Alexander V.; Kaganovich, Igor D. Physics of Plasmas, Vol. 24, Issue 9 https://doi.org/10.1063/1.5000387	journal	September 2017
Drift-ideal magnetohydrodynamic simulations of m = 0 modes in Z-pinch plasmas Angus, J. R.; Dorf, M.; Geyko, V. I. Physics of Plasmas, Vol. 26, Issue 7 https://doi.org/10.1063/1.5093625	journal	July 2019
Numerical study on the dynamics of Z ‐pinch carbon plasma Lee, K. T.; Kim, S. H.; Kim, D. Physics of Plasmas, Vol. 3, Issue 4 https://doi.org/10.1063/1.871787	journal	April 1996
The Guderley problem revisited Ramsey, Scott D.; Kamm, James R.; Bolstad, John H. International Journal of Computational Fluid Dynamics, Vol. 26, Issue 2 https://doi.org/10.1080/10618562.2011.647768	journal	February 2012
An attempt to produce a thermo-nuclear reaction in deuterium by means of a high current spark discharge Reynolds, P.; Craggs, J. D. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 43, Issue 337 https://doi.org/10.1080/14786440208561093	journal	February 1952
A Primer on Eulerian Computational Fluid Dynamics for Astrophysics Trac, Hy; Pen, Ue‐Li Publications of the Astronomical Society of the Pacific, Vol. 115, Issue 805 https://doi.org/10.1086/367747	journal	March 2003
A Free, Fast, Simple, and Efficient Total Variation Diminishing Magnetohydrodynamic Code Pen, Ue‐Li; Arras, Phil; Wong, ShingKwong The Astrophysical Journal Supplement Series, Vol. 149, Issue 2 https://doi.org/10.1086/378771	journal	December 2003
An energy-consistent snow-plough model for pinch design Lee, S. Journal of Physics D: Applied Physics, Vol. 16, Issue 12 https://doi.org/10.1088/0022-3727/16/12/023	journal	December 1983
The formation of high-density z-pinches Potter, D. Nuclear Fusion, Vol. 18, Issue 6 https://doi.org/10.1088/0029-5515/18/6/008	journal	June 1978
Analysis of high-density Z-pinches by a snowplow energy equation Miyamoto, T. Nuclear Fusion, Vol. 24, Issue 3 https://doi.org/10.1088/0029-5515/24/3/008	journal	March 1984
Self-similar motions in Z-pinch dynamics Liberman, M. A.; Velikovich, A. L. Nuclear Fusion, Vol. 26, Issue 6 https://doi.org/10.1088/0029-5515/26/6/002	journal	June 1986
Energy balance and the radius of electromagnetically pinched plasma columns Lee, S. Plasma Physics, Vol. 25, Issue 5 https://doi.org/10.1088/0032-1028/25/5/009	journal	May 1983
An Elementary Theory of the Transient Pinched Discharge Allen, J. E. Proceedings of the Physical Society. Section B, Vol. 70, Issue 1 https://doi.org/10.1088/0370-1301/70/1/305	journal	January 1957
A review of the dense Z -pinch Haines, M. G. Plasma Physics and Controlled Fusion, Vol. 53, Issue 9 https://doi.org/10.1088/0741-3335/53/9/093001	journal	June 2011
Ion acceleration mechanism in mega-ampere gas-puff z-pinches Klir, D.; Shishlov, A. V.; Kokshenev, V. A. New Journal of Physics, Vol. 20, Issue 5 https://doi.org/10.1088/1367-2630/aac545	journal	May 2018
Stability conditions in the numerical treatment of parabolic differential equations Du Fort, E. C.; Frankel, S. P. Mathematics of Computation, Vol. 7, Issue 43 https://doi.org/10.1090/s0025-5718-1953-0059077-7	journal	September 1953
Neutron Production in Linear Deuterium Pinches Anderson, Oscar A.; Baker, William R.; Colgate, Stirling A. Physical Review, Vol. 109, Issue 2 https://doi.org/10.1103/PhysRev.109.612	journal	January 1958
Neutron Production in Linear Deuterium Pinches Anderson, Oscar A.; Baker, William R.; Colgate, Stirling A. Physical Review, Vol. 110, Issue 6 https://doi.org/10.1103/PhysRev.110.1375	journal	June 1958
Electrode contaminant plasma effects in 1 0 7 -A Z pinch accelerators Welch, D. R.; Bennett, N.; Genoni, T. C. Physical Review Accelerators and Beams, Vol. 22, Issue 7 https://doi.org/10.1103/PhysRevAccelBeams.22.070401	journal	July 2019
Measurements of Magneto-Rayleigh-Taylor Instability Growth during the Implosion of Initially Solid Al Tubes Driven by the 20-MA, 100-ns Z Facility Sinars, D. B.; Slutz, S. A.; Herrmann, M. C. Physical Review Letters, Vol. 105, Issue 18 https://doi.org/10.1103/PhysRevLett.105.185001	journal	October 2010
High-Gain Magnetized Inertial Fusion Slutz, Stephen A.; Vesey, Roger A. Physical Review Letters, Vol. 108, Issue 2 https://doi.org/10.1103/PhysRevLett.108.025003	journal	January 2012
Fully Kinetic Simulations of Dense Plasma Focus Z -Pinch Devices Schmidt, A.; Tang, V.; Welch, D. Physical Review Letters, Vol. 109, Issue 20 https://doi.org/10.1103/PhysRevLett.109.205003	journal	November 2012
Pressure and Energy Balance of Stagnating Plasmas in z -Pinch Experiments: Implications to Current Flow at Stagnation Maron, Y.; Starobinets, A.; Fisher, V. I. Physical Review Letters, Vol. 111, Issue 3 https://doi.org/10.1103/PhysRevLett.111.035001	journal	July 2013
Transition from Beam-Target to Thermonuclear Fusion in High-Current Deuterium Z -Pinch Simulations Offermann, Dustin T.; Welch, Dale R.; Rose, Dave V. Physical Review Letters, Vol. 116, Issue 19 https://doi.org/10.1103/PhysRevLett.116.195001	journal	May 2016
Z Pinch of a Gas Jet Shiloh, J.; Fisher, A.; Rostoker, N. Physical Review Letters, Vol. 40, Issue 8 https://doi.org/10.1103/PhysRevLett.40.515	journal	February 1978
Evidence of Stabilization in the Z -Pinch Shumlak, U.; Golingo, R. P.; Nelson, B. A. Physical Review Letters, Vol. 87, Issue 20 https://doi.org/10.1103/PhysRevLett.87.205005	journal	October 2001
Strong Ionizing Shock Waves Gross, Robert A. Reviews of Modern Physics, Vol. 37, Issue 4 https://doi.org/10.1103/RevModPhys.37.724	journal	October 1965
The physics of fast Z pinches Ryutov, D. D.; Derzon, M. S.; Matzen, M. K. Reviews of Modern Physics, Vol. 72, Issue 1 https://doi.org/10.1103/RevModPhys.72.167	journal	January 2000
Dimensions and lifetime of the plasma focus pinch IEEE Transactions on Plasma Science, Vol. 24, Issue 3 https://doi.org/10.1109/27.533118	journal	June 1996
A Review of the Gas-Puff $Z$ -Pinch as an X-Ray and Neutron Source Giuliani, J. L.; Commisso, R. J. IEEE Transactions on Plasma Science, Vol. 43, Issue 8 https://doi.org/10.1109/TPS.2015.2451157	journal	August 2015
Self-Similar Solutions for Converging Shocks and Collapsing Cavities Lazarus, Roger B. SIAM Journal on Numerical Analysis, Vol. 18, Issue 2 https://doi.org/10.1137/0718022	journal	April 1981
Fully Ionized Pinch Collapse Hain, K.; Hain, G.; V., K. Zeitschrift für Naturforschung A, Vol. 15, Issue 12 https://doi.org/10.1515/zna-1960-1203	journal	January 1960
Evidence of Stabilization in the Z-Pinch Den Hartog, D. J.; Golingo, R. P.; Nelson, B. A. The American Physical Society https://doi.org/10.17877/de290r-11380	text	January 2001
Stability Conditions in the Numerical Treatment of Parabolic Differential Equations Fort, E. C. Du; Frankel, S. P. Mathematical Tables and Other Aids to Computation, Vol. 7, Issue 43 https://doi.org/10.2307/2002754	journal	July 1953
Strong ionizing shock waves Gross, R. 2nd Aerospace Sciences Meeting https://doi.org/10.2514/6.1965-123	conference	August 1965

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