Magnetohydrodynamic Shock Structure without Collisions

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Abstract
The internal structure of a magnetohydrodynamic shock is examined under the condition that there are no collisions among the plasma particles. The equations to be solved are the collisionless, steady Boltzmann equations for ions and electrons coupled with Maxwell's equation for the fields (a self-consistent system). There is one space variable x and all quantities are prescribed constant as x = − ∞. Under appropriate conditions at − ∞, e.g., no transverse magnetic field, low ion pressure, and Alfvén-Mach number roughly less than 2, the state at + ∞ has oscillating fields, density, etc. The length scale is a mean phase length. Thus a change of state is possible without collisions. The theory is based on an asymptotic development in the ion-to-electron mass ratio and is valid over distances that are comparable to or even large compared to the wavelength of the oscillation but small compared to the ion Larmor radius. The electrons are adiabatic.

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