Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T13:36:48.279Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected] and [email protected])
A. J. MESTEL
Affiliation:
Department of Mathematics, Imperial College, London SW7 2AZ, UK
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Ryutov, D. D., Derzon, M. S. and Matzen, M. K. 2000 The physics of fast z-pinches. Rev. Mod. Phys. 72.CrossRefGoogle Scholar
[2]Hammer, J. H. et al. 1996 Two-dimensional radiation-magnetohydrodynamic simulations of SATURN imploding z-pinches. Phys. Plasmas 3 (5), 2063–2069.CrossRefGoogle Scholar
[3]Marder, B. M., Sanford, T. W. L. and Allshouse, G. O. 1998 Numerical simulations of annular wire-array z-pinches in (x, y), (r, θ) and (r, z) geometries. Phys. Plasmas 5 (8), 2997–3005.CrossRefGoogle Scholar
[4]Peterson, D. L. et al. 1998 Characterisation of energy flow and instability development in two-dimensional simulations of hollow z pinches. Phys. Plasmas 5 (9), 3302–3310.CrossRefGoogle Scholar
[5]Liberman, M. A. and Velikovich, A. L. 1986 Self-similar motions in z-pinch dynamics. Nucl. Fusion 26, 709–728.Google Scholar
[6]Van Guderley, G. 1942 Starke kugelige und zylindrische verdichtungsstöße in der nähe des kugelmittelpunktes bzw. der zylinderachse. Luftfahrtforschung 19, 302–312.Google Scholar
[7]Meyer-ter-Vehn, J. and Schalk, C. 1982 Selfsimilar spherical compression waves in gas dynamics. Z. Naturforsch 37a, 955–969.Google Scholar
[8]Jeffrey, A. 1966 Magnetohydrodynamics. Oliver and Boyd.Google Scholar
[9]Acheson, D. J. 1990 Elementary Fluid Dynamics. Oxford: Oxford University Press.Google Scholar
[10]Kidder, R. E. 1976 Laser-driven compression of hollow shells: power requirements and stability limitations. Nucl. Fusion 16, 3–14.CrossRefGoogle Scholar
[11]Lock, R. M. 2007 Aspects of the magnetohydrodynamic z-pinch. Imperial College, University of London.Google Scholar
[12]Rahman, H. U., Ney, P., Wessel, F. J. and Rostoker, N. 1997 Staged pinch for controlled thermonuclear fusion. J. Plasma Phys. 58, 367–379.Google Scholar
[13]Glasser, A. H. 1989 A moving finite element model of the high density z-pinch. J. Comput. Phys. 85 (1), 159–209.CrossRefGoogle Scholar