Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983a%26a...124..163w&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 124, no. 2, Aug. 1983, p. 163-171.
Astronomy and Astrophysics
Astrophysics
21
Boundary Conditions, Boundary Value Problems, Cosmic Rays, Energetic Particles, Oblique Shock Waves, Particle Acceleration, Diffusion Theory, Electric Fields, Magnetohydrodynamic Waves
Scientific paper
In the case of oblique shocks for which there is a frame of reference in which the electric field E = zero both upstream and downstream of the shock, particle number density and current boundary conditions are derived for scatter-free propagation and convective-diffusive transport. The boundary conditions are initially obtained in the E = zero frame, where approximate conservation of particle adiabatic moment is used to determine the transmission characteristics of the shock. Perturbation solutions are given of the cosmic ray transport equations with the new boundary conditions, and it is shown that the momentum spectrum of particles accelerated at the shock may be harder than that expected from first-order Fermi acceleration between 'scattering centers' in the upstream and downstream regions.
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