Modified Burgers' equation resulting from a hydrodynamic model of shock waves with reflected particles

Details Modified Burgers' equation resulting from a hydrodynamic model of shock waves with reflected particles Modified Burgers' equation resulting from a hydrodynamic model of shock waves with reflected particles

Dec 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010aipc.1302..142b&link_type=abstract

PICKUP IONS THROUGHOUT THE HELIOSPHERE AND BEYOND: Proceedings of the 9th Annual International Astrophysics Conference. AIP Con

Astronomy and Astrophysics

Astrophysics

Hydrodynamics, Pickups, Wave Equations, Solar Wind, Hydrodynamics, Pickup Ions, Relativistic Wave Equations, Particle Emission, Solar Wind

Scientific paper

Ion reflection at perpendicular, collisionless shock waves is treated in a simple gas dynamical context. The effect of pickup ions reflected by the cross-shock potential and their subsequent energization in the motional electric field is included through the introduction of source terms in the basic inviscid fluid equations. From a weak source description, a Burgers' equation is derived modified by the addition of a quadratically nonlinear term. The construction of Burgers' equation demonstrates explicitly that particle reflection is a dissipation mechanism for collisionless shocks. Numerical solutions for the modified Burgers' equation (MBE) are presented. From these solutions it is implied that the dissipative term of the MBE is associated with the length scale of the shock foot, while the additional term is associated with the shock ramp. The general physical model is discussed in terms of the reflection and energization of pickup ions at outer heliospheric perpendicular shocks.

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