Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-29T20:11:47.295Z Has data issue: false hasContentIssue false
  • English
  • Français

Gas-ionizing shocks in a magnetic field

Published online by Cambridge University Press:  13 March 2009

M. D. Cowley
M. D. Cowley
Affiliation:
Department of Engineering, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

Ionizing shocks for plane flows with the magnetic field lying in the flow plane are considered. The gas is assumed to be electrically conducting downstream, but non-conducting upstream. Shocks whose downstream state has a normal velocity component less than the slow magneto-acoustic-wave speed and whose upstream state is supersonic are found to be non-evolutionary in the face of plane magneto-acoustic disturbances, unless the upstream electric field in a frame of reference where the gas is at rest is arbitrary. Velocity conditions are also determined for shock stability with the electric field not arbitrary.

Shock structures are found for the case of large ohmic diffusion, the initial temperature rise and ionization of the gas being caused by a thin transition having the properties of an ordinary gasdynamic shock. For the case where shocks are evolutionary when the upstream electric field is arbitrary, the shock structure requirements only restrict the electric field by limiting the range of possible values. When shocks are evolutionary with the electric field not arbitrary, they can only have a structure for a particular value of the electric field. Limits to the current carried by ionizing shocks and the effects of precursor ionization are discussed qualitatively.

Type
Articles
Information
Journal of Plasma Physics , Volume 1 , Issue 1 , February 1967 , pp. 37 - 54
Copyright
Copyright © Cambridge University Press 1967

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

Butler, D. S. 1965 J. Fluid Mech. 23, 1.CrossRefGoogle Scholar
Chu, C. K. 1964 Phys. Fluids 7, 1349.CrossRefGoogle Scholar
Cowley, M. D. 1963 J. Fluid Mech. 15, 577.CrossRefGoogle Scholar
Gross, R. A., Levine, L. & Geldon, F. 1966 Phys. Fluids 9, 1033.CrossRefGoogle Scholar
Helliwell, J. B. 1962 J. Fluid Mech. 14, 405.CrossRefGoogle Scholar
Kantrowitz, A. R. & Petschek, H. E. 1957 Magnetohydrodynamics (ed. Landshoff, R. M.), pp. 3–15. Stanford University Press.Google Scholar
Kulikovskii, A. G. & Lioubimov, G. A. 1960 Rev. Mod. Phys. 32, 977.CrossRefGoogle Scholar
Kunkel, W. B. & Gross, R. A. 1962 Plasma Hydromagnetics (ed. Bershader, D.), pp. 58–82. Stanford University Press.Google Scholar
May, R. M. & Tendys, J. 1965 Nuclear Fusion 5, 144.CrossRefGoogle Scholar
Shercliff, J. A. 1958 J. Fluid Mech. 3, 645.CrossRefGoogle Scholar
Shercliff, J. A. 1960 J. Fluid Mech. 9, 481.CrossRefGoogle Scholar
Soubbaramayer, M. 1962 Comptes Rendus 254, 2135.Google Scholar
Soubbaramayer, M. 1964 Comptes Rendus 258, 436.Google Scholar
Taussig, R. T. 1965 Phys. Fluids 8, 1616.CrossRefGoogle Scholar
Todd, L. 1965 J. Fluid Mech. 21, 193.CrossRefGoogle Scholar
Weyl, H. 1949 Comm. Pure Appl. Math. 2, 103.CrossRefGoogle Scholar
Woods, L. C. 1965 J. Fluid Mech. 22, 689.CrossRefGoogle Scholar