zbMATH — the first resource for mathematics

A multispecies, multifluid model for laser-induced counterstreaming plasma simulations. (English) Zbl 07072842
Summary: The interpenetration of counterstreaming plasmas is an important phenomenon in several application areas, such as astrophysical flows, design of controlled fusion devices, and laser-induced plasma experiments. Multispecies “single-fluid” codes are unable to model this phenomenon due to the single velocity representation for all the species/fluids. Kinetic codes, though capable of modeling interpenetration, are computationally prohibitive for at-scale simulations. In this paper, we propose a multifluid model that solves the fluid equations for each ion fluid or stream. This allows distinct flows that interact with each other through electrostatic and collisional forces. We introduce and describe our code, EUCLID, that uses a conservative finite-difference formulation to discretize the governing equations in space. The 5th-order monotonicity-preserving WENO scheme is used for the upwind approximation of the hyperbolic flux, and the explicit 4th-order Runge-Kutta scheme is used for time integration. The code is verified for several benchmark cases and manufactured solutions. We simulate one- and two-dimensional interactions of counterstreaming plasmas in vacuum as well as in the presence of gas fill, where the setups are representative of laser-induced plasma experiments.
Reviewer: Reviewer (Berlin)
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
35L04 Initial-boundary value problems for first-order hyperbolic equations
35L65 Hyperbolic conservation laws
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
Full Text: DOI
[1] Berzak Hopkins, L. F.; Le Pape, S.; Divol, L.; Meezan, N. B.; Mackinnon, A. J.; Ho, D. D., Near-vacuum hohlraums for driving fusion implosions with high density carbon ablators, Phys Plasmas, 22, 5, 056318, (2015)
[2] Le Pape, S.; Berzak Hopkins, L. F.; Divol, L.; Meezan, N.; Turnbull, D.; Mackinnon, A. J., The near vacuum hohlraum campaign at the NIF: a new approach, Phys Plasmas, 23, 5, 056311, (2016)
[3] Bosch, R. A.; Berger, R. L.; Failor, B. H.; Delamater, N. D.; Charatis, G.; Kauffman, R. L., Collision and interpenetration of plasmas created by laser illuminated disks, Physics of Fluids B: Plasma Physics, 4, 4, 979-988, (1992)
[4] Kuramitsu, Y.; Sakawa, Y.; Morita, T.; Gregory, C. D.; Waugh, J. N.; Dono, S., Time evolution of collisionless shock in counterstreaming laser-produced plasmas, Phys Rev Lett, 106, 175002, (2011)
[5] Park, H.-S.; Ryutov, D.; Ross, J.; Kugland, N.; Glenzer, S.; Plechaty, C., Studying astrophysical collisionless shocks with counterstreaming plasmas from high power lasers, High Energy Density Phys, 8, 1, 38-45, (2012)
[6] Ross, J. S.; Glenzer, S. H.; Amendt, P.; Berger, R.; Divol, L.; Kugland, N. L., Characterizing counter-streaming interpenetrating plasmas relevant to astrophysical collisionless shocks, Phys Plasmas, 19, 5, 056501, (2012)
[7] Ryutov, D. D.; Kugland, N. L.; Park, H.-S.; Plechaty, C.; Remington, B. A.; Ross, J. S., Intra-jet shocks in two counter-streaming, weakly collisional plasma jets, Phys Plasmas, 19, 7, 074501, (2012)
[8] Marinak, M. M.; Haan, S. W.; Dittrich, T. R.; Tipton, R. E.; Zimmerman, G. B., A comparison of three-dimensional multimode hydrodynamic instability growth on various national ignition facility capsule designs with HYDRA simulations, Phys Plasmas, 5, 4, 1125-1132, (1998)
[9] Dawson, J. M., Particle simulation of plasmas, Rev Mod Phys, 55, 403-447, (1983)
[10] Larroche, O., Kinetic simulation of a plasma collision experiment, Phys Fluids B, 5, 8, 2816-2840, (1993)
[11] Sonnendrücker, E.; Roche, J.; Bertrand, P.; Ghizzo, A., The semi-lagrangian method for the numerical resolution of the vlasov equation, J Comput Phys, 149, 2, 201-220, (1999) · Zbl 0934.76073
[12] Markidis, S.; Lapenta, G.; Rizwan-uddin, Multi-scale simulations of plasma with iPIC3d, Math Comput Simul, 80, 7, 1509-1519, (2010) · Zbl 1195.82086
[13] Filbet, F.; Sonnendrücker, E., Comparison of Eulerian Vlasov solvers, Comput Phys Commun, 150, 3, 247-266, (2003) · Zbl 1196.82108
[14] Kagan, G.; Tang, X.-Z., Electro-diffusion in a plasma with two ion species, Phys Plasmas, 19, 8, 082709, (2012)
[15] Kagan, G.; Tang, X.-Z., Thermo-diffusion in inertially confined plasmas, Phys Lett A, 378, 21, 1531-1535, (2014)
[16] Braginskii, S. I., Transport processes in a plasma, Rev Plasma Phys, 1, 205, (1965)
[17] Anderson, D., Axisymmetric multifluid simulation of high beta plasmas with anisotropic transport using a moving flux coordinate grid, J Comput Phys, 17, 3, 246-275, (1975)
[18] Loverich, J.; Hakim, A.; Shumlak, U., A discontinuous Galerkin method for ideal two-fluid plasma equations, Commun Comput Phys, 9, 2, 240-268, (2011) · Zbl 1364.35278
[19] Srinivasan, B.; Shumlak, U., Analytical and computational study of the ideal full two-fluid plasma model and asymptotic approximations for Hall-magnetohydrodynamics, Phys Plasmas, 18, 9, 092113, (2011)
[20] Vold, E. L., Multidimensional and multifluid plasma edge modelling: status and new directions, Contrib Plasma Phys, 32, 3â4, 404-421, (1992)
[21] Simonini, R.; Corrigan, G.; Radford, G.; Spence, J.; Taroni, A., Models and numerics in the multi-fluid 2-D edge plasma code EDGE2D/U, Contrib Plasma Phys, 34, 2â3, 368-373, (1994)
[22] Meier, E. T.; Shumlak, U., A general nonlinear fluid model for reacting plasma-neutral mixtures, Phys Plasmas, 19, 7, 072508, (2012)
[23] Laguna, A. A.; Lani, A.; Deconinck, H.; Mansour, N.; Poedts, S., A fully-implicit finite-volume method for multi-fluid reactive and collisional magnetized plasmas on unstructured meshes, J Comput Phys, 318, 252-276, (2016) · Zbl 1349.76299
[24] Cagas, P.; Hakim, A.; Juno, J.; Srinivasan, B., Continuum kinetic and multi-fluid simulations of classical sheaths, Phys Plasmas, 24, 2, 022118, (2017)
[25] Alvarez-Laguna, A.; Ozak, N.; Lani, A.; Mansour, N. N.; Deconinck, H.; Poedts, S., A versatile numerical method for the multi-fluid plasma model in partially- and fully-ionized plasmas, J Phys Conf Ser, 1031, 1, 012015, (2018)
[26] Winglee, R. M., Multi-fluid simulations of the magnetosphere: the identification of the geopause and its variation with IMF, Geophys Res Lett, 25, 24, 4441-4444, (1998)
[27] AlexashovD.; Izmodenov, V., Kinetic vs. multi-fluid models of H-atoms in the heliospheric interface: a comparison, Astron Astrophys, 439, 3, 1171-1181, (2005)
[28] Hakim, A.; Loverich, J.; Shumlak, U., A high resolution wave propagation scheme for ideal two-fluid plasma equations, J Comput Phys, 219, 1, 418-442, (2006) · Zbl 1167.76384
[29] Leake, J. E.; Lukin, V. S.; Linton, M. G.; Meier, E. T., Multi-fluid simulations of chromospheric magnetic reconnection in a weakly ionized reacting plasma, Astrophys J, 760, 2, 109, (2012)
[30] Wang, L.; Hakim, A. H.; Bhattacharjee, A.; Germaschewski, K., Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection, Phys Plasmas, 22, 1, 012108, (2015)
[31] O’Sullivan, S.; Downes, T. P., A three-dimensional numerical method for modelling weakly ionized plasmas, Mon Not R Astron Soc, 376, 4, 1648-1658, (2007)
[32] Jones, A. C.; Downes, T. P., The Kelvin-Helmholtz instability in weakly ionized plasmas - II. multifluid effects in molecular clouds, Mon Not R Astron Soc, 420, 1, 817-828, (2012)
[33] Benilov, M. S., Multifluid equations of a plasma with various species of positive ions and the Bohm criterion, J Phys D Appl Phys, 29, 2, 364, (1996)
[34] Benilov, M. S., Multifluid description of nonequilibrium plasmas, IEEE international conference on plasma science, 163-164, (1996)
[35] Sousa, E.; Shumlak, U., A blended continuous-discontinuous finite element method for solving the multi-fluid plasma model, J Comput Phys, 326, 56-75, (2016) · Zbl 1373.76103
[36] Srinivasan, B.; Kagan, G.; Adams, C. S., Multi-fluid studies of plasma shocks relevant to inertial confinement fusion, J Phys Conf Ser, 717, 1, 012054, (2016)
[37] Polak, S.; Gao, X., A fourth-order finite-volume method with adaptive mesh refinement for the multifluid plasma model, (2018), American Institute of Aeronautics and Astronautics
[38] Shumlak, U.; Loverich, J., Approximate Riemann solver for the two-fluid plasma model, J Comput Phys, 187, 2, 620-638, (2003) · Zbl 1061.76526
[39] Baboolal, S., Finite-difference modeling of solitons induced by a density hump in a plasma multi-fluid, Math Comput Simul, 55, 4, 309-316, (2001) · Zbl 0987.76065
[40] Kumar, H.; Mishra, S., Entropy stable numerical schemes for two-fluid plasma equations, J Sci Comput, 52, 2, 401-425, (2012) · Zbl 1311.76150
[41] Shumlak, U.; Lilly, R.; Reddell, N.; Sousa, E.; Srinivasan, B., Advanced physics calculations using a multi-fluid plasma model, Comput Phys Commun, 182, 9, 1767-1770, (2011)
[42] Berger, R. L.; Albritton, J. R.; Randall, C. J.; Williams, E. A.; Kruer, W. L.; Langdon, A. B., Stopping and thermalization of interpenetrating plasma streams, Phys Fluids B, 3, 1, 3-12, (1991)
[43] Rambo, P. W.; Denavit, J., Interpenetration and ion separation in colliding plasmas, Phys Plasmas, 1, 12, 4050-4060, (1994)
[44] Rambo, P. W.; Procassini, R. J., A comparison of kinetic and multifluid simulations of laser produced colliding plasmas, Phys Plasmas, 2, 8, 3130-3145, (1995)
[45] Shu, C.-W.; Osher, S., Efficient implementation of essentially non-oscillatory shock-capturing schemes, J Comput Phys, 77, 2, 439-471, (1988) · Zbl 0653.65072
[46] Shu, C.-W.; Osher, S., Efficient implementation of essentially non-oscillatory shock-capturing schemes, II, J Comput Phys, 83, 1, 32-78, (1989) · Zbl 0674.65061
[47] Adams, M.; Colella, P.; Graves, D. T.; Johnson, J.; Keen, N.; Ligocki, T. J., Chombo software package for amr applications - design document, Tech. Rep., (2015), Lawrence Berkeley National Laboratory
[48] Jiang, G.-S.; Shu, C.-W., Efficient implementation of weighted ENO schemes, J Comput Phys, 126, 1, 202-228, (1996) · Zbl 0877.65065
[49] Balsara, D. S.; Shu, C.-W., Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy, J Comput Phys, 160, 2, 405-452, (2000) · Zbl 0961.65078
[50] Laney, C. B., Computational gasdynamics, (1998), Cambridge University Press · Zbl 0947.76001
[51] Wolfram Research, Inc. Mathematica, version 11.3, Champaign, IL, 2018.
[52] Sod, G. A., A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, J Comput Phys, 27, 1, 1-31, (1978) · Zbl 0387.76063
[53] Ross, J. S.; Park, H.-S.; Berger, R.; Divol, L.; Kugland, N. L.; Rozmus, W., Collisionless coupling of ion and electron temperatures in counterstreaming plasma flows, Phys Rev Lett, 110, 145005, (2013)
[54] Chen, F. F., Introduction to plasma physics and controlled fusion, (1984), Springer International Publishing: Springer International Publishing Switzerland
[55] Ascher, U. M.; Ruuth, S. J.; Spiteri, R. J., Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations, Appl Numer Math, 25, 2-3, 151-167, (1997) · Zbl 0896.65061
[56] Kennedy, C. A.; Carpenter, M. H., Additive Runge-Kutta schemes for convection-diffusion-reaction equations, Appl Numer Math, 44, 1-2, 139-181, (2003) · Zbl 1013.65103
[57] Pareschi, L.; Russo, G., Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation, J Sci Comput, 25, 1-2, 129-155, (2005) · Zbl 1203.65111
[58] Dimits, A. M.; Banks, J. W.; Berger, R. L.; Brunner, S.; Chapman, T.; Copeland, D., Linearized coulomb collision operator for simulation of interpenetrating plasma streams, IEEE Trans Plasma Sci, 1-7, (2019)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.