A two-dimensional numerical study of the magneto-Rayleigh–Taylor instability with FLASH: Application to the staged Z-pinch concept

Tranchant, V.; Hansen, E. C.; Michta, D.; Garcia-Rubio, F.; Rahman, H. U.; Ney, P.; Ruskov, E.; Tzeferacos, P.

doi:10.1063/5.0248761

Title: A two-dimensional numerical study of the magneto-Rayleigh–Taylor instability with FLASH: Application to the staged Z-pinch concept

Journal Article · 04 March 2025 · Physics of Plasmas

DOI: https://doi.org/10.1063/5.0248761 · OSTI ID:2527371

^[1];

^[1]; Garcia-Rubio, F. ^[2];

^[3];

^[4]

Univ. of Rochester, NY (United States)
Pacific Fusion Inc., Fremont, CA (United States)
Magneto-Inertial Fusion Technology Inc., Tustin, CA (United States)
Univ. of Rochester, NY (United States). Lab. for Laser Energetics

Magnetically driven implosions involving a liner collapsing onto a target are inherently vulnerable to the magneto-Rayleigh–Taylor instability (MRTI). Among the various approaches proposed to achieve fusion conditions within the target, the staged Z-pinch (SZP) concept employs a high-Z liner, the advantages of which remain an active area of investigation. Consequently, ongoing design optimization efforts are essential, while critical physical processes such as magnetic field (B-field) diffusion and radiation transport increase the complexity of required simulations. In this study, we utilize the new capabilities of the FLASH code to simulate in 2D, for the first time using this code, staged Z-pinch configurations (designated SZP1 and SZP1*), focusing on their stability. First, a comparison of simulation results with theoretical predictions of MRTI growth provide new insights into the often-overlooked influences of high mesh resolution and initial perturbation seeding on instability dynamics. These findings then lead to a discussion on potential improvements for future SZP experiments. These include the use of an axial B-field stabilization and the optimization of radiation transport processes during the implosion. The results presented herein establish the framework for simulating multi-dimensional Z pinches using the FLASH code and pave the way for the development of innovative experimental configurations leveraging its advanced simulation capabilities.

View Journal Article

Cite

Export

Save

Research Organization:: Univ. of Rochester, NY (United States)

Sponsoring Organization:: USDOE; USDOE Advanced Research Projects Agency - Energy (ARPA-E); USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF)

Grant/Contract Number:: AC02-05CH11231; AR0001272; NA0004144; NA0004147; SC0023246

OSTI ID:: 2527371

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 3 Vol. 32; ISSN 1070-664X; ISSN 1089-7674

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

Country of Publication:: United States

Language:: English

References (65)

Hyperbolic Divergence Cleaning for the MHD Equations Dedner, A.; Kemm, F.; Kröner, D. Journal of Computational Physics, Vol. 175, Issue 2 https://doi.org/10.1006/jcph.2001.6961	journal	January 2002
The Piecewise Parabolic Method (PPM) for gas-dynamical simulations Colella, Phillip; Woodward, Paul R. Journal of Computational Physics, Vol. 54, Issue 1 https://doi.org/10.1016/0021-9991(84)90143-8	journal	April 1984
Theory of the Rayleigh-Taylor instability Kull, H. J. Physics Reports, Vol. 206, Issue 5 https://doi.org/10.1016/0370-1573(91)90153-D	journal	August 1991
Collaborative comparison of simulation codes for high-energy-density physics applications Fatenejad, M.; Fryxell, B.; Wohlbier, J. High Energy Density Physics, Vol. 9, Issue 1 https://doi.org/10.1016/j.hedp.2012.10.004	journal	March 2013
FLASH MHD simulations of experiments that study shock-generated magnetic fields Tzeferacos, P.; Fatenejad, M.; Flocke, N. High Energy Density Physics, Vol. 17 https://doi.org/10.1016/j.hedp.2014.11.003	journal	December 2015
A novel approach of divergence-free reconstruction for adaptive mesh refinement Li, Shengtai; Li, Hui Journal of Computational Physics, Vol. 199, Issue 1 https://doi.org/10.1016/j.jcp.2004.01.027	journal	September 2004
A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics Miyoshi, Takahiro; Kusano, Kanya Journal of Computational Physics, Vol. 208, Issue 1 https://doi.org/10.1016/j.jcp.2005.02.017	journal	September 2005
A solution accurate, efficient and stable unsplit staggered mesh scheme for three dimensional magnetohydrodynamics Lee, Dongwook Journal of Computational Physics, Vol. 243 https://doi.org/10.1016/j.jcp.2013.02.049	journal	June 2013
High yield fusion in a staged Z-pinch Rahman, H. U.; Wessel, F. J.; Rostoker, N. Journal of Plasma Physics, Vol. 75, Issue 6 https://doi.org/10.1017/S002237780900796X	journal	April 2009
Turbulent amplification of magnetic fields in laboratory laser-produced shock waves Meinecke, J.; Doyle, H. W.; Miniati, F. Nature Physics, Vol. 10, Issue 7 https://doi.org/10.1038/nphys2978	journal	June 2014
Laboratory evidence of dynamo amplification of magnetic fields in a turbulent plasma Tzeferacos, P.; Rigby, A.; Bott, A. F. A. Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-02953-2	journal	February 2018
How high energy fluxes may affect Rayleigh–Taylor instability growth in young supernova remnants Kuranz, C. C.; Park, H. -S.; Huntington, C. M. Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-03548-7	journal	April 2018
Fusion and the Z Pinch Yonas, Gerold Scientific American, Vol. 279, Issue 2 https://doi.org/10.1038/scientificamerican0898-40	journal	August 1998
Multigroup radiation hydrodynamics with flux-limited diffusion and adaptive mesh refinement González, M.; Vaytet, N.; Commerçon, B. Astronomy & Astrophysics, Vol. 578 https://doi.org/10.1051/0004-6361/201525971	journal	May 2015
Control of the Rayleigh–Taylor instability in a staged Z pinch Rahman, H. U.; Ney, P.; Rostoker, N. Physics of Plasmas, Vol. 11, Issue 12 https://doi.org/10.1063/1.1814998	journal	December 2004
Modeling fluid instabilities in inertial confinement fusion hydrodynamics codes Zalesak, Steven T.; Schmitt, Andrew J.; Velikovich, A. L. Physics of Plasmas, Vol. 12, Issue 5 https://doi.org/10.1063/1.1885004	journal	May 2005
Nonlinear Rayleigh–Taylor instabilities in fast Z pinches Miles, Aaron R. Physics of Plasmas, Vol. 16, Issue 3 https://doi.org/10.1063/1.3088020	journal	March 2009
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
Magnetic diffusion smoothing with application to the hydromagnetic Rayleigh–Taylor instability Roderick, N. F.; Hussey, T. W. Journal of Applied Physics, Vol. 59, Issue 2 https://doi.org/10.1063/1.336631	journal	January 1986
Closure and transport theory for high-collisionality electron-ion plasmas Ji, Jeong-Young; Held, Eric D. Physics of Plasmas, Vol. 20, Issue 4 https://doi.org/10.1063/1.4801022	journal	April 2013
Classical transport equations for burning gas-metal plasmas Molvig, Kim; Simakov, Andrei N.; Vold, Erik L. Physics of Plasmas, Vol. 21, Issue 9 https://doi.org/10.1063/1.4895666	journal	September 2014
Gas puff Z-pinch implosions with external Bz field on COBRA Qi, N.; de Grouchy, P.; Schrafel, P. C. 9TH INTERNATIONAL CONFERENCE ON DENSE Z PINCHES, AIP Conference Proceedings https://doi.org/10.1063/1.4904775	conference	January 2014
Hydrodynamic description of an unmagnetized plasma with multiple ion species. I. General formulation Simakov, Andrei N.; Molvig, Kim Physics of Plasmas, Vol. 23, Issue 3 https://doi.org/10.1063/1.4943894	journal	March 2016
Numerical modeling of laser-driven experiments aiming to demonstrate magnetic field amplification via turbulent dynamo Tzeferacos, P.; Rigby, A.; Bott, A. Physics of Plasmas, Vol. 24, Issue 4 https://doi.org/10.1063/1.4978628	journal	April 2017
The staged z-pinch as a potential high gain fusion energy source: An independent review, a negative conclusion Lindemuth, Irvin R.; Weis, Matthew R.; Atchison, Walter L. Physics of Plasmas, Vol. 25, Issue 10 https://doi.org/10.1063/1.5045123	journal	October 2018
Study of stability in a liner-on-target gas puff Z-pinch as a function of pre-embedded axial magnetic field Conti, F.; Aybar, N.; Narkis, J. Physics of Plasmas, Vol. 27, Issue 1 https://doi.org/10.1063/1.5131170	journal	January 2020
The staged Z-pinch as a potential fusion energy source Ruskov, E.; Ney, P.; Rahman, H. U. Physics of Plasmas, Vol. 27, Issue 4 https://doi.org/10.1063/1.5131770	journal	April 2020
Stability analysis of dynamic Z pinches and theta pinches Bud’ko, A. B.; Felber, F. S.; Kleev, A. I. Physics of Fluids B: Plasma Physics, Vol. 1, Issue 3 https://doi.org/10.1063/1.859207	journal	March 1989
Unstable normal mode for Rayleigh–Taylor instability in viscous fluids Menikoff, R.; Mjolsness, R. C.; Sharp, D. H. Physics of Fluids, Vol. 20, Issue 12 https://doi.org/10.1063/1.861831	journal	January 1977
Rayleigh–Taylor instability: Comparison of hybrid and nonideal magnetohydrodynamic simulations Huba, J. D.; Winske, D. Physics of Plasmas, Vol. 5, Issue 6 https://doi.org/10.1063/1.872904	journal	June 1998
The past, present, and future of Z pinches Haines, M. G.; Lebedev, S. V.; Chittenden, J. P. Physics of Plasmas, Vol. 7, Issue 5 https://doi.org/10.1063/1.874047	journal	May 2000
Z-pinch fusion Shumlak, U. Journal of Applied Physics, Vol. 127, Issue 20 https://doi.org/10.1063/5.0004228	journal	May 2020
Transport coefficients for magnetic-field evolution in inviscid magnetohydrodynamics Davies, J. R.; Wen, H.; Ji, Jeong-Young Physics of Plasmas, Vol. 28, Issue 1 https://doi.org/10.1063/5.0023445	journal	January 2021
Staged Z-pinch modeling of high and low atomic number liners compressing deuterium targets using parameters of the Z pulsed power facility Ruskov, E.; Ney, P.; Rahman, H. U. Physics of Plasmas, Vol. 28, Issue 11 https://doi.org/10.1063/5.0051028	journal	November 2021
Dynamics and energy coupling of gas puff Z-pinches on a fast linear transformer driver Conti, F.; Narkis, J.; Williams, A. Journal of Applied Physics, Vol. 130, Issue 2 https://doi.org/10.1063/5.0051335	journal	July 2021
Code-to-code comparison and validation of the radiation-hydrodynamics capabilities of the FLASH code using a laboratory astrophysical jet Orban, Chris; Fatenejad, Milad; Lamb, Donald Q. Physics of Plasmas, Vol. 29, Issue 5 https://doi.org/10.1063/5.0079493	journal	May 2022
Self-similar solutions for resistive diffusion, Ohmic heating, and Ettingshausen effects in plasmas of arbitrary β Farrow, G.; Chittenden, J. P.; Kagan, G. Physics of Plasmas, Vol. 29, Issue 3 https://doi.org/10.1063/5.0082435	journal	March 2022
On the importance of three-dimensional modeling for high-energy-density physics experiments Sauppe, J. P.; Lu, Y.; Tzeferacos, P. Physics of Plasmas, Vol. 30, Issue 6 https://doi.org/10.1063/5.0144517	journal	June 2023
Improved analytic modeling of the linear Rayleigh–Taylor instability with plasma transport Keenan, Brett D.; Sauppe, Joshua P. Physics of Plasmas, Vol. 30, Issue 7 https://doi.org/10.1063/5.0155331	journal	July 2023
Feasibility and performance of the staged Z-pinch: A one-dimensional study with FLASH and MACH2 Hansen, E. C.; Garcia-Rubio, F.; Adams, M. B. P. Physics of Plasmas, Vol. 31, Issue 4 https://doi.org/10.1063/5.0187342	journal	April 2024
A fusion-grade 20-MA liner-on-plasma implosion system without preheat and premagnetization Lindemuth, Irvin R. Physics of Plasmas, Vol. 31, Issue 7 https://doi.org/10.1063/5.0215373	journal	July 2024
Code-to-code comparison between FLASH and HYDRA in gas-puff Z-pinch modeling Michta, D.; Tranchant, V.; Narkis, J. Physics of Plasmas, Vol. 31, Issue 12 https://doi.org/10.1063/5.0231394	journal	December 2024
Developed turbulence and nonlinear amplification of magnetic fields in laboratory and astrophysical plasmas Meinecke, Jena; Tzeferacos, Petros; Bell, Anthony Proceedings of the National Academy of Sciences, Vol. 112, Issue 27 https://doi.org/10.1073/pnas.1502079112	journal	June 2015
Time-resolved turbulent dynamo in a laser plasma Bott, Archie F. A.; Tzeferacos, Petros; Chen, Laura Proceedings of the National Academy of Sciences, Vol. 118, Issue 11 https://doi.org/10.1073/pnas.2015729118	journal	March 2021
A flux-limited diffusion theory Levermore, C. D.; Pomraning, G. C. The Astrophysical Journal, Vol. 248 https://doi.org/10.1086/159157	journal	August 1981
FLASH: An Adaptive Mesh Hydrodynamics Code for Modeling Astrophysical Thermonuclear Flashes Fryxell, B.; Olson, K.; Ricker, P. The Astrophysical Journal Supplement Series, Vol. 131, Issue 1 https://doi.org/10.1086/317361	journal	November 2000
Second‐Order–accurate Schemes for Magnetohydrodynamics with Divergence‐free Reconstruction Balsara, Dinshaw S. The Astrophysical Journal Supplement Series, Vol. 151, Issue 1 https://doi.org/10.1086/381377	journal	March 2004
Converging geometry Rayleigh–Taylor instability and central ignition of inertial confinement fusion targets Atzeni, Stefano; Schiavi, Angelo; Temporal, Mauro Plasma Physics and Controlled Fusion, Vol. 46, Issue 12B https://doi.org/10.1088/0741-3335/46/12B/010	journal	November 2004
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
Modeling of capillary discharge plasmas for wakefield acceleration and beam transport Cook, N. M.; Carlsson, J.; Moeller, P. Journal of Physics: Conference Series, Vol. 1596, Issue 1 https://doi.org/10.1088/1742-6596/1596/1/012063	journal	November 2020
MA-class linear transformer driver for Z -pinch research Conti, F.; Valenzuela, J. C.; Fadeev, V. Physical Review Accelerators and Beams, Vol. 23, Issue 9 https://doi.org/10.1103/PhysRevAccelBeams.23.090401	journal	September 2020
Understanding the impact of an applied axial magnetic field on efficient current coupling on the Z machine Zimmer, D.; Gomez, M. R.; Bennett, N. Physical Review Accelerators and Beams, Vol. 27, Issue 10 https://doi.org/10.1103/PhysRevAccelBeams.27.100401	journal	October 2024
Exploring the Atwood-number dependence of the highly nonlinear Rayleigh-Taylor instability regime in high-energy-density conditions Rigon, G.; Albertazzi, B.; Mabey, P. Physical Review E, Vol. 104, Issue 4 https://doi.org/10.1103/PhysRevE.104.045213	journal	October 2021
Mitigation of magneto-Rayleigh-Taylor instability growth in a triple-nozzle, neutron-producing gas-puff Z pinch Narkis, J.; Conti, F.; Velikovich, A. L. Physical Review E, Vol. 104, Issue 2 https://doi.org/10.1103/PhysRevE.104.L023201	journal	August 2021
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
Shock wave formation in radiative plasmas Garcia-Rubio, F.; Tranchant, V.; Hansen, E. C. Physical Review E, Vol. 109, Issue 6 https://doi.org/10.1103/PhysRevE.109.065206	journal	June 2024
Power enhancement by increasing the initial array radius and wire number of tungsten Z pinches Deeney, C.; Nash, T. J.; Spielman, R. B. Physical Review E, Vol. 56, Issue 5 https://doi.org/10.1103/PhysRevE.56.5945	journal	November 1997
Explicit expressions for the evolution of single-mode Rayleigh-Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers Mikaelian, Karnig O. Physical Review E, Vol. 67, Issue 2 https://doi.org/10.1103/PhysRevE.67.026319	journal	February 2003
Study of the Internal Structure and Small-Scale Instabilities in the Dense Z Pinch Ivanov, V. V.; Chittenden, J. P.; Altemara, S. D. Physical Review Letters, Vol. 107, Issue 16 https://doi.org/10.1103/PhysRevLett.107.165002	journal	October 2011
Staged Z Pinch Rahman, H. U.; Wessel, F. J.; Rostoker, N. Physical Review Letters, Vol. 74, Issue 5, p. 714-717 https://doi.org/10.1103/PhysRevLett.74.714	journal	January 1995
Displacement current phenomena in the magnetically insulated transmission lines of the refurbished Z accelerator McBride, R. D.; Jennings, C. A.; Vesey, R. A. Physical Review Special Topics - Accelerators and Beams, Vol. 13, Issue 12 https://doi.org/10.1103/PhysRevSTAB.13.120401	journal	December 2010
Mitigation of Instabilities in a Z-Pinch Plasma by a Preembedded Axial Magnetic Field Mikitchuk, Dimitry; Stollberg, Christine; Doron, Ramy IEEE Transactions on Plasma Science, Vol. 42, Issue 10 https://doi.org/10.1109/TPS.2014.2327094	journal	October 2014
Fusion in a Staged $Z$ -Pinch Wessel, Frank J.; Ur-Rahman, Hafiz; Ney, Paul IEEE Transactions on Plasma Science, Vol. 43, Issue 8 https://doi.org/10.1109/TPS.2015.2433796	journal	August 2015
Strong suppression of heat conduction in a laboratory replica of galaxy-cluster turbulent plasmas Meinecke, Jena; Tzeferacos, Petros; Ross, James S. Science Advances, Vol. 8, Issue 10 https://doi.org/10.1126/sciadv.abj6799	journal	March 2022

Similar Records

Feasibility and performance of the staged Z-pinch: A one-dimensional study with FLASH and MACH2

Journal Article · 2024 · Physics of Plasmas · OSTI ID:2567555

Hansen, E. C.; Garcia-Rubio, F.; Adams, M. B. P.; +8 more

Code-to-code comparison between FLASH and HYDRA in gas-puff Z-pinch modeling

Journal Article · 2024 · Physics of Plasmas · OSTI ID:2484255

Michta, D.; Tranchant, V.; Narkis, J.; +7 more

3D modeling of the Staged Z-pinch with the FLASH code

Technical Report · 2024 · OSTI ID:2337682

Tzeferacos, Petros

Related Subjects

Adaptive mesh refinement
Computational physics
Flow instabilities
Fluid mechanics
Fusion energy
Plasma confinement
Plasma heating

Title: A two-dimensional numerical study of the magneto-Rayleigh–Taylor instability with FLASH: Application to the staged Z-pinch concept

Citation Formats

References (65)

Similar Records

Related Subjects