Weakly multi-dimensional cosmic-ray-modified MHD shocks

Details Weakly multi-dimensional cosmic-ray-modified MHD shocks Weakly multi-dimensional cosmic-ray-modified MHD shocks

Aug 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990jplph..44...91z&link_type=abstract

Journal of Plasma Physics (ISSN 0022-3778), vol. 44, Aug. 1990, p. 91-101.

Mathematics

3

Cosmic Rays, Energetic Particles, Magnetohydrodynamic Waves, Perturbation Theory, Plasma-Particle Interactions, Shock Waves, Burger Equation, Eigenvectors, Maxwell Equation, Singularity (Mathematics), Time Dependence

Scientific paper

The multi-dimensional structure of weak, energetic-particle-modified shocks is investigated by means of appropriate perturbation techniques. The time-dependent shock-structure equation is found to be a generalized form of the well-known one-dimensional Burgers equation, whose steady state, in the absence of cosmic rays, is shown to be related to an equation modeling steady transonic flow in several dimensions. The time-dependent (1 + 2)- and (1 + 3)-dimensional Burgers equations are integrated exactly by means of Hirota's technique for one-shock solutions. On the basis of the exact solutions, a discussion relating the various length scales associated with the shock is presented.

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