Influence of Mach Number on Structure of Collisional Plasma Shock Waves: Fully Kinetic Simulations

doi:10.19596/j.cnki.1001-246x.8621

Abstract

Abstract:

Fully kinetic Particle-in-cell (PIC) simulations are performed to study the structure of collisional plasma shock waves with different Mach numbers. It is found that for low-Mach shocks, the spatial gradient of physical quantities near the shock front is gentle, corresponding to small Knudsen numbers, and the plasma transport properties (e. g. viscosity, heat flux) are well described by the classical transport theory. The simulated shock structure is consistent with that obtained from the numerical solution of the two-fluid equations. With increasing Mach numbers, the spatial gradient of physical quantities near the shock front becomes steep (i. e. the Knudsen number is increased), and the influence of kinetic effects on plasma transport properties become significant. For high-Mach shocks, kinetics effects come into play mainly in the following two aspects: (1) enhanced ion viscosity and heat flux due to the precursor ions and (2) nonlocal transport effects on the electron heat flux. Kinetic effects can significantly influence the shock wave structure by changing the plasma transport properties.

Key words: plasma shock wave, viscosity and heat flux, kinetic simulation, two-fluid equations

Wenshuai ZHANG, Hongbo CAI, Enhao ZHANG, Bao DU, Shiyang ZOU, Shaoping ZHU. Influence of Mach Number on Structure of Collisional Plasma Shock Waves: Fully Kinetic Simulations[J]. Chinese Journal of Computational Physics, 2023, 40(2): 199-209.

Figures/Tables 6

Fig.1 Schematic presentation of the PIC simulation setup (A uniform plasma flow drifting towards the left boundary is reflected and accumulates near the boundary due to particle collisions, resulting in a right-propagating shock wave.)

Fig.2 (a) Time evolution of plasma temperature and density near the left boundary; Ion and electron phase space distribution in logarithm scale at (b) and (d) 0.1 ps and (c) and (e) 0.6 ps

Fig.3 (a)~(c) Spatial profiles of ion density, electric field and temperature from PIC simulations (solid lines) and two-fluid theory (dashed lines); (d)~(f) Spatial profiles of viscosity and heat flux from simulations (solid lines) and transport theory (dashed lines); (g) Spatial profiles of the Knudsen number (Simulations results averaged over y for Msh = 1.22 at t = 0.3 ps.)

Fig.4 (a)~(c) Spatial profiles of ion density, electric field and temperature from simulations (solid lines) and two-fluid theory (dashed lines); (d)~(f) Spatial profiles of viscosity and heat flux from simulations (solid lines) and transport theory (dashed lines). (g) Spatial profiles of the Knudsen number (Simulations results averaged over y for Msh = 1.87 at t = 0.64 ps.)

Fig.5 (a)~(b) Spatial profiles of ion density, electric field and temperature from simulations; (c)~(e) Spatial profiles of viscosity and heat flux from simulations (solid lines) and transport theory (dashed lines); (f) Spatial profiles of the Knudsen number (Simulations results averaged over y for Msh = 4.2 at t = 1.4 ps.)

Fig.6 (a) Shock Mach number dependence of the maximum Knudsen number from PIC simulations; (b) Ratio of the maximum ion viscous stress and ion heat flux from the PIC simulations to that from the transport theory; (c) Ratio of the full-width-half-maximum of the spatial profiles of the simulated and theoretical ion viscous stress and electron heat flux

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