Modified Bugers equation for ion reflection at quasi-perpendicular shock

Physics

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2139 Interplanetary Shocks, 7851 Shock Waves (4455)

Scientific paper

Ion reflection at a cross-shock potential is treated in a simple hydrodynamics context. The energization of reflected ions by the motional electric field, at quasi-perpendicular shocks, is modeled by the inclusion of source terms in the fluid equations which inject energy and momentum into the plasma directly at the shock front. A perturbation expansion on the fluid equations, where a weak source model is assumed, results in a Burgers' equation, modified by the addition of a quadratically nonlinear term. Thus, it is shown explicitly that particle reflection at a cross-shock potential is a dissipative process. The effects of the quadratic term are illustrated by numerical solutions of the modified Burgers' equation and include a reduction in wave attenuation, reduced breaking time and tendencies toward exponential divergence which may be associated with non- stationary solutions and shock reformation.

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