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Annular self-similar solutions in ideal magnetogasdynamics

Published online by Cambridge University Press:  01 August 2008

R. M. LOCK  and
A. J. MESTEL
R. M. LOCK
Affiliation:
AWE, Reading, Berkshire RG7 4PR, UK (r.lock@ic.ac.uk and robert.lock@awe.co.uk)
A. J. MESTEL
Affiliation:
Department of Mathematics, Imperial College, London SW7 2AZ, UK
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Abstract

We consider the possibility of self-similar solutions describing the implosion of hollow cylindrical annuli driven by an azimuthal magnetic field, in essence a self-similar imploding liner z-pinch. We construct such solutions for gasdynamics, for ideal ‘β=0’ plasma and for ideal magnetogasdynamics (MGD). In the latter two cases some quantities are singular at the annular boundaries. Numerical solutions of the full ideal MGD initial value problem indicate that the self-similar solutions are not attractive for arbitrary initial conditions, possibly as a result of flux-freezing.

Type
Papers
Information
Journal of Plasma Physics , Volume 74 , Issue 4 , August 2008 , pp. 531 - 554
Copyright
Copyright © Cambridge University Press 2008

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