Magnetohydrodynamic Shock Production and Current Sheet Diffusion

Author: Hoffman, Alan Lowell

Year: 1967

Degree: Dissertation (Ph.D.)

Advisor: Liepmann, Hans Wolfgang

Committee Member: Unknown, Unknown

Option: Aeronautics; Applied Mathematics

DOI: 10.7907/4WVH-W290

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

Current sheets in inverse pinch MHD shock tubes exhibit the strange property of forming shocks in the very rear of the sheet when accelerating heavy gases. When accelerating light gases, shocks are formed further to the front in the sheet, but in no case do the shocks separate from the driving current sheet. This "piston dragging shock" effect is explained on the basis of a single-fluid model with variable conductivity. Shocks are shown to always form within current sheets which move at supersonic speeds with respect to the driven gas. The relevant parameters for determining the shock position are the Mach number and the magnetic Reynolds number. Large magnetic Reynolds numbers and small Mach numbers enhance forward shock formation. These conditions are obtained in light gases with high speeds of sound. Similarity methods are developed to estimate gas conductivities, electron temperatures, and degrees of ionization for the experiments which are conducted. In hydrogen typical electron temperatures of 4 ev are produced by the ohmic heating, but twice this value is shown necessary to achieve separation at the current sheet speeds of 2-3 [...] used. Higher current sheet speeds produce shocks in the rear of the current sheet where separation can never occur. The correct method of procedure and the relevant design parameters to achieve separation are given. The success of single-fluid methods in explaining plasma phenomena is especially notable, and these methods can be extended to other similar problems. Based on these methods, multiple-fluid and microscopic effects are easily detectable and can be accounted for.

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