Asymptotic scaling laws for the stagnation conditions of Z-pinch implosions

Ruiz, D. E.; Williams, C. A.; Vesey, R. A.

doi:10.1063/5.0242367

Title: Asymptotic scaling laws for the stagnation conditions of Z-pinch implosions

Journal Article · 23 January 2025 · Physics of Plasmas

DOI: https://doi.org/10.1063/5.0242367 · OSTI ID:2506892

;

Implosions of magnetically driven annular shells (Z pinches) are studied in the laboratory to produce high-energy-density plasmas. Such plasmas have a wide-range of applications including x-ray generation, controlled thermonuclear fusion, and astrophysics studies. In this work, we theoretically investigate the in-flight dynamics of a magnetically driven, imploding cylindrical shell that stagnates onto itself upon collision on axis. The converging flow of the Z-pinch is analyzed by considering the implosion trajectory in the (A, M) parametric plane, where A is the in-flight aspect ratio and M is the implosion Mach number. For an ideal implosion in the absence of instabilities and in the limit of A≫1, we derive asymptotic scaling laws for hydrodynamic quantities evaluated at stagnation (e.g., density, temperature, and pressure) and for performance metrics (e.g., soft x-ray emission, K-shell x-ray emission, and neutron yield) as functions of target-design parameters.

View Journal Article

Cite

Export

Save

Sponsoring Organization:: USDOE

Grant/Contract Number:: NONE; NA0003525

OSTI ID:: 2506892

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 1 Vol. 32; ISSN 1070-664X

Publisher:: American Institute of PhysicsCopyright Statement

Country of Publication:: United States

Language:: English

References (53)

On the mechanism by which the current contracts in fast and intense gas discharge Leontovich, M. A.; Osovets, S. M. The Soviet Journal of Atomic Energy, Vol. 1, Issue 3 https://doi.org/10.1007/BF01514504	journal	May 1956
A higher-than-predicted measurement of iron opacity at solar interior temperatures Bailey, J. E.; Nagayama, T.; Loisel, G. P. Nature, Vol. 517, Issue 7532 https://doi.org/10.1038/nature14048	journal	December 2014
Inertially confined fusion plasmas dominated by alpha-particle self-heating Hurricane, O. A.; Callahan, D. A.; Casey, D. T. Nature Physics, Vol. 12, Issue 8 https://doi.org/10.1038/nphys3720	journal	April 2016
Pulsed-power-driven high energy density physics and inertial confinement fusion research Matzen, M. Keith; Sweeney, M. A.; Adams, R. G. Physics of Plasmas, Vol. 12, Issue 5 https://doi.org/10.1063/1.1891746	journal	May 2005
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
Scaling of (MHD) instabilities in imploding plasma liners Hussey, T. W.; Roderick, N. F.; Kloc, D. A. Journal of Applied Physics, Vol. 51, Issue 3 https://doi.org/10.1063/1.327792	journal	March 1980
Pulsed-power-driven cylindrical liner implosions of laser preheated fuel magnetized with an axial field Slutz, S. A.; Herrmann, M. C.; Vesey, R. A. Physics of Plasmas, Vol. 17, Issue 5 https://doi.org/10.1063/1.3333505	journal	May 2010
X rays from z ‐pinches on relativistic electron‐beam generators Pereira, N. R.; Davis, J. Journal of Applied Physics, Vol. 64, Issue 3 https://doi.org/10.1063/1.341808	journal	August 1988
Stability of a nonlinear magnetic field diffusion wave Oreshkin, V. I.; Chaikovsky, S. A. Physics of Plasmas, Vol. 19, Issue 2 https://doi.org/10.1063/1.3683557	journal	February 2012
Optimization of the parameters of plasma liners with zero-dimensional models Oreshkin, V. I. Physics of Plasmas, Vol. 20, Issue 11 https://doi.org/10.1063/1.4829436	journal	November 2013
Theory of hydro-equivalent ignition for inertial fusion and its applications to OMEGA and the National Ignition Facility Nora, R.; Betti, R.; Anderson, K. S. Physics of Plasmas, Vol. 21, Issue 5 https://doi.org/10.1063/1.4875331	journal	May 2014
Evolution of helical perturbations in a thin-shell model of an imploding liner Ryutov, D. D.; Dorf, M. A. Physics of Plasmas, Vol. 21, Issue 11 https://doi.org/10.1063/1.4901197	journal	November 2014
A semi-analytic model of magnetized liner inertial fusion McBride, Ryan D.; Slutz, Stephen A. Physics of Plasmas, Vol. 22, Issue 5 https://doi.org/10.1063/1.4918953	journal	May 2015
Experimental study of the nonlinear diffusion of a magnetic field and skin explosion of cylindrical conductors Chaikovsky, S. A.; Oreshkin, V. I.; Datsko, I. M. Physics of Plasmas, Vol. 22, Issue 11 https://doi.org/10.1063/1.4935401	journal	November 2015
Technique for fabrication of ultrathin foils in cylindrical geometry for liner-plasma implosion experiments with sub-megaampere currents Yager-Elorriaga, D. A.; Steiner, A. M.; Patel, S. G. Review of Scientific Instruments, Vol. 86, Issue 11 https://doi.org/10.1063/1.4935838	journal	November 2015
Discrete helical modes in imploding and exploding cylindrical, magnetized liners Yager-Elorriaga, D. A.; Zhang, P.; Steiner, A. M. Physics of Plasmas, Vol. 23, Issue 12 https://doi.org/10.1063/1.4969082	journal	December 2016
Evolution of sausage and helical modes in magnetized thin-foil cylindrical liners driven by a Z-pinch Yager-Elorriaga, D. A.; Lau, Y. Y.; Zhang, P. Physics of Plasmas, Vol. 25, Issue 5 https://doi.org/10.1063/1.5017849	journal	May 2018
Fast implosion of foil liners Sorokin, S. A. Physics of Plasmas, Vol. 26, Issue 8 https://doi.org/10.1063/1.5110651	journal	August 2019
A conservative approach to scaling magneto-inertial fusion concepts to larger pulsed-power drivers Schmit, P. F.; Ruiz, D. E. Physics of Plasmas, Vol. 27, Issue 6 https://doi.org/10.1063/1.5135716	journal	June 2020
An analytic asymmetric-piston model for the impact of mode-1 shell asymmetry on ICF implosions Hurricane, O. A.; Casey, D. T.; Landen, O. Physics of Plasmas, Vol. 27, Issue 6 https://doi.org/10.1063/5.0001335	journal	June 2020
Review of pulsed power-driven high energy density physics research on Z at Sandia Sinars, D. B.; Sweeney, M. A.; Alexander, C. S. Physics of Plasmas, Vol. 27, Issue 7 https://doi.org/10.1063/5.0007476	journal	July 2020
Extended magnetohydrodynamics simulations of thin-foil Z-pinch implosions with comparison to experiments Woolstrum, J. M.; Yager-Elorriaga, D. A.; Campbell, P. C. Physics of Plasmas, Vol. 27, Issue 9 https://doi.org/10.1063/5.0012170	journal	September 2020
A model for K-shell x-ray yield from magnetic implosions at Sandia's Z machine Schwarz, J.; Vesey, R. A.; Ampleford, D. J. Physics of Plasmas, Vol. 29, Issue 10 https://doi.org/10.1063/5.0102275	journal	October 2022
Exploring the parameter space of MagLIF implosions using similarity scaling. I. Theoretical framework Ruiz, D. E.; Schmit, P. F.; Yager-Elorriaga, D. A. Physics of Plasmas, Vol. 30, Issue 3 https://doi.org/10.1063/5.0126696	journal	March 2023
Exploring the parameter space of MagLIF implosions using similarity scaling. II. Current scaling Ruiz, D. E.; Schmit, P. F.; Yager-Elorriaga, D. A. Physics of Plasmas, Vol. 30, Issue 3 https://doi.org/10.1063/5.0126699	journal	March 2023
Exploring the parameter space of MagLIF implosions using similarity scaling. III. Rise-time scaling Ruiz, D. E.; Schmit, P. F.; Weis, M. R. Physics of Plasmas, Vol. 30, Issue 3 https://doi.org/10.1063/5.0126700	journal	March 2023
Implosion of heavy metal liners driven by megaampere current pulses Oreshkin, V. I.; Baksht, R. B.; Chaikovsky, S. A. Physics of Plasmas, Vol. 31, Issue 10 https://doi.org/10.1063/5.0226543	journal	October 2024
Degradation of performance in ICF implosions due to Rayleigh–Taylor instabilities: A Hamiltonian perspective Ruiz, D. E. Physics of Plasmas, Vol. 31, Issue 12 https://doi.org/10.1063/5.0233454	journal	December 2024
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
Improved formulas for fusion cross-sections and thermal reactivities Bosch, H. -S; Hale, G. M. Nuclear Fusion, Vol. 32, Issue 4 https://doi.org/10.1088/0029-5515/32/4/I07	journal	April 1992
Fast z-pinches as dense plasma, intense x-ray sources for plasma physics and fusion applications Matzen, M. K.; Deeney, C.; Leeper, R. J. Plasma Physics and Controlled Fusion, Vol. 41, Issue 3A https://doi.org/10.1088/0741-3335/41/3A/011	journal	January 1999
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
Magnetic implosion of thin aluminum foil liners Sorokin, S. A. Plasma Physics and Controlled Fusion, Vol. 64, Issue 6 https://doi.org/10.1088/1361-6587/ac688f	journal	May 2022
An overview of magneto-inertial fusion on the Z machine at Sandia National Laboratories Yager-Elorriaga, D. A.; Gomez, M. R.; Ruiz, D. E. Nuclear Fusion, Vol. 62, Issue 4 https://doi.org/10.1088/1741-4326/ac2dbe	journal	February 2022
Scaling of plasma temperature, density, size, and x-ray emission above 1 keV with array diameter and mass for aluminum imploding-wire plasmas Gersten, M.; Clark, W.; Rauch, J. E. Physical Review A, Vol. 33, Issue 1 https://doi.org/10.1103/PhysRevA.33.477	journal	January 1986
Material effects on dynamics in triple-nozzle gas-puff Z pinches Narkis, J.; Conti, F.; Beg, F. N. Physical Review E, Vol. 105, Issue 4 https://doi.org/10.1103/PhysRevE.105.045205	journal	April 2022
Characteristics and scaling of tungsten-wire-array z -pinch implosion dynamics at 20 MA Cuneo, M. E.; Waisman, E. M.; Lebedev, S. V. Physical Review E, Vol. 71, Issue 4 https://doi.org/10.1103/PhysRevE.71.046406	journal	April 2005
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
Experimental Demonstration of Fusion-Relevant Conditions in Magnetized Liner Inertial Fusion Gomez, M. R.; Slutz, S. A.; Sefkow, A. B. Physical Review Letters, Vol. 113, Issue 15 https://doi.org/10.1103/PhysRevLett.113.155003	journal	October 2014
Systematic Study of L -Shell Opacity at Stellar Interior Temperatures Nagayama, T.; Bailey, J. E.; Loisel, G. P. Physical Review Letters, Vol. 122, Issue 23 https://doi.org/10.1103/PhysRevLett.122.235001	journal	June 2019
Stabilization of Liner Implosions via a Dynamic Screw Pinch Campbell, Paul C.; Jones, T. M.; Woolstrum, J. M. Physical Review Letters, Vol. 125, Issue 3 https://doi.org/10.1103/PhysRevLett.125.035001	journal	July 2020
Performance Scaling in Magnetized Liner Inertial Fusion Experiments Gomez, M. R.; Slutz, S. A.; Jennings, C. A. Physical Review Letters, Vol. 125, Issue 15 https://doi.org/10.1103/PhysRevLett.125.155002	journal	October 2020
Characterization of Quasi-Keplerian, Differentially Rotating, Free-Boundary Laboratory Plasmas Valenzuela-Villaseca, V.; Suttle, L. G.; Suzuki-Vidal, F. Physical Review Letters, Vol. 130, Issue 19 https://doi.org/10.1103/PhysRevLett.130.195101	journal	May 2023
Observation of Fast Current Redistribution in an Imploding Plasma Column Stollberg, C.; Kroupp, E.; Mikitchuk, D. Physical Review Letters, Vol. 130, Issue 20 https://doi.org/10.1103/PhysRevLett.130.205101	journal	May 2023
Asymptotic Scaling Laws for Imploding Thin Fluid Shells Basko, M. M.; Meyer-ter-Vehn, J. Physical Review Letters, Vol. 88, Issue 24 https://doi.org/10.1103/PhysRevLett.88.244502	journal	May 2002
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
A Renewed Capability for Gas Puff Science on Sandia's Z Machine Jones, Brent; Jennings, Christopher A.; Lamppa, Derek C. IEEE Transactions on Plasma Science, Vol. 42, Issue 5 https://doi.org/10.1109/TPS.2013.2287180	journal	May 2014
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
A Primer on Pulsed Power and Linear Transformer Drivers for High Energy Density Physics Applications McBride, R. D.; Stygar, W. A.; Cuneo, M. E. IEEE Transactions on Plasma Science, Vol. 46, Issue 11 https://doi.org/10.1109/TPS.2018.2870099	journal	November 2018
Assessing Stagnation Conditions and Identifying Trends in Magnetized Liner Inertial Fusion Gomez, Matthew R.; Slutz, Stephen A.; Knapp, Patrick F. IEEE Transactions on Plasma Science, Vol. 47, Issue 5 https://doi.org/10.1109/TPS.2019.2893517	journal	May 2019
Specific features of shock wave formation in superstrong magnetic field Krivosheev, S. I.; Pomazov, V. S.; Shneerson, G. A. Technical Physics Letters, Vol. 37, Issue 9 https://doi.org/10.1134/S1063785011090227	journal	September 2011
Why W? Hayes, Brian American Scientist, Vol. 93, Issue 2 https://doi.org/10.1511/2005.52.3448	journal	January 2005

Similar Records

Implosion and stagnation of wire array Z pinches

Journal Article · 2007 · Physics of Plasmas · OSTI ID:20975071

Bland, S N; Lebedev, S V; Chittenden, J P; +7 more

Simulations of the implosion and stagnation of compact wire arrays

Journal Article · 2010 · Physics of Plasmas · OSTI ID:21432282

Jennings, C A; Cuneo, M E; Waisman, E M; +5 more

Effect of the axial magnetic field on a metallic gas-puff pinch implosion

Journal Article · 2016 · Physics of Plasmas · OSTI ID:22600143

Rousskikh, A. G.; Zhigalin, A. S.; Frolova, V.; +4 more

Title: Asymptotic scaling laws for the stagnation conditions of Z-pinch implosions

Citation Formats

References (53)

Similar Records

Related Subjects