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Viscous and inertial effects at cosmic-ray shocks
Jokipii, J. R.; Williams, L. L.
AA(Arizona, University, Tucson, AZ), AB(Arizona, University, Tucson, AZ)
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 394, no. 1, July 20, 1992, p. 184-187. (ApJ Homepage)
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NASA/STI Keywords:
Computational Astrophysics, Cosmic Rays, Shock Waves, Viscosity, Collisionless Plasmas, Interstellar Magnetic Fields, Transport Properties, Velocity Distribution
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To illustrate the effect of the viscous and inertial terms on the structure of cosmic-ray-modified shocks, an analysis of a time-independent 1D shock is presented in which the pressure of the background fluid and the magnetic-field energy density are negligible compared with the cosmic-ray pressure. The effect of the magnetic field on cosmic-ray transport coefficients is retained. The diffusion, viscous and inertial terms work to 'thicken' the shock. When the average magnetic field is negligible and the cosmic-ray transport is isotropic, diffusion is the dominant effect unless the parameters are such that the scattering time becomes comparable to the characteristic times for velocity change in the fluid frame. For a perpendicular shock, where the diffusion is strongly reduced by the magnetic field, the relative magnitude of the viscous effect is increased by a factor about (omega tau) exp 2, leading to the conclusion that cosmic-ray viscosity can be important to the structure of collisionless MHD shocks. In both cases considered, the viscous and inertial terms become important for those parameter ranges where the diffusion approximation begins to break down.

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