Astronomy and Astrophysics – Astrophysics
Scientific paper
Jan 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988ap%26ss.140..301z&link_type=abstract
Astrophysics and Space Science (ISSN 0004-640X), vol. 140, no. 2, Jan. 1988, p. 301-324.
Astronomy and Astrophysics
Astrophysics
7
Cosmic Rays, Magnetohydrodynamic Flow, Shock Waves, Two Fluid Models, Korteweg-Devries Equation, Particle Acceleration
Scientific paper
A multiple scales analysis is used to derive a mixed Burger-Korteweg-de Vries (BKdV) equation in the long wavelength regime for a two-fluid MHD model used to describe cosmic-ray acceleration by the first-order Fermi process in astrophysical shocks. The BKdV equation describes the time evaluation of weak shocks in the theory of diffusive shock acceleration for all possible cosmic-ray pressures. Previous work on weak shocks in the cosmic-ray MHD model has assumed that dissipation alone is sufficient to balance nonlinearity, but, as cosmic-ray pressures become small, the weak shock becomes discontinuous. By including Hall current effects into the MHD model, the low cosmic-ray pressure limit leads smoothly into solitary wave behavior. For low cosmic-ray pressure, the shock has a downstream oscillatory precursor which is smoothed into the standard Taylor shock profile with increasing cosmic-ray pressure. As a by-product of the perturbation analysis, a dissipative KdV equation is derived. In conclusion, dispersive effects on Alfven waves are discussed and a modulational stability analysis is presented.
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