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Title:
Uniqueness of the shock velocity determined from the magnetohydrodynamic jump conditions
Authors:
Podesta, John J.
Affiliation:
AA(Center for Space Plasma Physics, Space Science Institute, Boulder, CO 80301, USA)
Publication:
Journal of Plasma Physics, Volume 84, Issue 6, article id. 765840601, 15 pp.
Publication Date:
12/2018
Origin:
CUP
Keywords:
astrophysical plasmas, space plasma physics
Abstract Copyright:
(c) 2018: © Cambridge University Press 2018
DOI:
10.1017/S002237781800065X
Bibliographic Code:
2018JPlPh..84f7601P

Abstract

Spacecraft measurements of propagating interplanetary shocks are often interpreted using the ideal magnetohydrodynamic (MHD) model of a planar shock wave travelling with constant velocity \text{sh}$ through a spatially uniform plasma. In particular, measurements of the plasma variables upstream and downstream have long been used in conjunction with the Rankine-Hugoniot conditions, also known as the MHD jump conditions, to determine shock velocities and other physical parameters of interplanetary shocks. This procedure is justified only if the shock velocity determined by the MHD jump conditions is unique. In this study the important property of uniqueness is demonstrated for non-perpendicular shocks in MHD media characterized by an isotropic pressure tensor. The primary conclusion is that the shock velocity is uniquely determined by the jump conditions regardless of the type of shock (slow, intermediate or fast). Several new formulas for the shock speed are also derived including one that is independent of the shock normal . In principle, the solution technique developed here can be applied to estimate \text{sh}$ using solar wind data provided the measurements obey the MHD shock model with sufficient accuracy. That is not its intended purpose, however, and such applications are beyond the scope of this work.
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