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Physics of Fluids / Volume 15 / Issue 6

Phys. Fluids 15, 1070 (1972); http://dx.doi.org/10.1063/1.1694032 (12 pages)

Near‐Steady Oblique Shock Waves in a Collisionless Plasma

Lynn M. Olson

The University of Wisconsin, Madison, Wisconsin 53706

(Received 22 May 1970)

Waves of small amplitude ϵ which travel at an oblique angle θ to a magnetic field in a cold collisionless plasma and whose head approaches steadiness are studied. The relevant double limit
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is treated in terms of appropriate sets of single limits. Near‐steady waves which can lead from one equilibrium to another are shown to be possible only at propagation speeds corresponding to Alfvén Mach number 1 or cosθ. In the first case, either the magnetic pressure at the head of the wave decreases monotonically from its initial value and the wave spreads linearly with time, or else the head of the wave consists of a near‐periodic train of cnoidal waves, the first crest of which approaches a soliton. For near‐normal shocks, the magnetic pressure in the near‐periodic wave train always exceeds its initial equilibrium value. But for M cotθ>1, where M  =  (m+/m−)1/2−(m−/m+)1/2, it always falls short of that value. A transition with precursor wave is shown to be impossible for a cold collisionless plasma. At an Alfvén Mach number cosθ, the only near‐steady solution consists of a main wave front followed by an oscillatory tail; on the length scale considered, the electric field transverse to the propagation direction oscillates without bound at the tail.

© 1972 American Institute of Physics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.1694032

PUBLICATION DATA

ISSN

0031-9171 (print)  

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$abstract.society.value is a Member of CrossRef American Institute of Physics

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