Statistics – Computation
Scientific paper
Jan 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988a%26a...189..338z&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 189, no. 1-2, Jan. 1988, p. 338-348. Research supported by the Council for Sci
Statistics
Computation
12
Burger Equation, Computational Astrophysics, Cosmic Rays, Radiation Distribution, Relativistic Plasmas, Asymptotic Methods, Hydrodynamic Equations, Two Fluid Models
Scientific paper
A reductive perturbation scheme is used to derive a generalized non-linear Burgers' equation, which includes the effects of dispersion, in the long wavelength regime for the two-fluid hydrodynamical model used to describe cosmic ray acceleration by the first-order Fermi process in astrophysical shocks. The generalized Burger's equation is derived for both relativistic and non-relativistic cosmic ray shocks, and describes the time evolution of weak shocks in the theory of diffusive shock acceleration. The inclusion of dispersive effects modifies the phase velocity of the shock obtained from the lower order non-linear Burger's equation through the introduction of higher order terms from the long wavelength dispersion equation. The travelling wave solution of the generalized Burgers' equation for a single shock shows that larger cosmic ray pressures result in broader shock transitions. The results for relativistic shocks show a steepening of the shock as the shock speed approaches the relativistic cosmic ray sound speed. The dependence of the shock speed on the cosmic ray pressure is also discussed.
McKenzie James F.
Webb Gary M.
Zank Gary P.
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