THE UNIFORM EXPANSION OF A SPHERICAL PLASMA BUBBLE INTO AN IONIZED ATMOSPHERE IN A WEAK MAGNETIC FIELD. Chap. 2 of THEORETICAL STUDY OF HYDROMAGNETIC STABILITY AND TURBULENCE. INVESTIGATIONS AND DETAILED RESULTS. Annual Report, Period: January 1-December 31, 1961

Technical Report · Wed Oct 31 04:00:00 EST 1962

OSTI ID:4825728

Bernstein, I B; Fanucci, J B; Kruskal, M D; Kulsrud, R M; Ness, N

The expansion of a perfectly conducting spherical piston expanding at constant radial speed into an ideal hydromagnetic fluid is investigated. The ideal hydromagnetic fluid is characterized by constant density pressure and magnetic field. The piston starts from a point and drives a nonspherical shock ahead of itself in the ideal hydromagnetic field. The condition of the fluid in the undisturbed region ahead of the shock is related to that behind the shock by the appropriate magnetohydrodynamic shock relations. The situation possesses azimuthal symmetry about an axis through the center of the piston and parallel to the constant external magnetic field. The structure of the ideal hydromagnetic equations admits of a similarity solution appropriate to this expansion. That is, by introducing a new vari able, namely the position vector divided by the time. It is possible to transform the actual time dependent problem irto a static flow in terms of the new variable. The resultant equations are solved in the limit where the magnetic pressure in the surrounding medium is much less than the material pressure. This permits an expansion essentially in powers of the ratio of Alfven speed to sound speed. The expansion procedure leads to equations which decompose such that the perturbation nonmagnetic quantities involve only odd powers of the parameter of smallness and all other quantities involve only even powers. To lowest order one has the Taylor solution to the hydrodynamic spherical expansion. The lowest significant order magnetic field and perturbations in pressure density and velocity can then be computed. The most interesting result of this calculation is the prediction of the occurrence of a boundary layer near the piston. In this boundaiy layer the magnetic field which everywhere else is small rises to a value such that the magnetic pressure is comparable with the material pressure. This conclusion is independent of the magnitude of the magnetic field. (auth)

• Research Organization: Radio Corp. of America. Missile and Surface Radar Div., Moorestown, N.J.
• NSA Number: NSA-16-022712
• OSTI ID: 4825728
• Report Number(s): AFSWC-TDR-62-12(Vol.II)(Chap.2
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ALFVEN SPEED
ALFVEN WAVES
CONFINEMENT
EQUATIONS
EXPANSION
FLUIDS
MAGNETIC COMPRESSION
MAGNETIC FIELDS
MAGNETOHYDRODYNAMICS
PHYSICS
PLASMA
PLASMA WAVES
PRESSURE
SHOCK WAVES
SOUND
STABILITY
SURFACES
TURBULENCE
VECTORS
VELOCITY