STABILITY OF THE SNOWPLOW DIFFERENTIAL EQUATION REPRESENTING THE EXPANSION OF A PLASMA BUBBLE. Chap. 10 of THEORETICAL STUDY OF HYDROMAGNETIC STABILITY AND TURBULENCE. INVESTIGATIONS AND DETAILED RESULTS. Annual Report, Period: January 1-December 31, 1961
A good approximation to the expansion of a radial bubble against constant external pressure is provided by the snowplow model. According to this model, it is assumed that as the free expanding debris strikes the decelerated interface it sticks to it and contributes to the sheath mass. This model leads to a second order non-linear differential equation with the radius of the bubble as a function of time which must be solved subject to the initial conditions that at zero time the radius is zero and the radial velocity equal to that of the free expanding matter. The uniqueness of solutions of the above-mentioned non-linear ordinary differential equation, the location and nature of the singulai- points, and the stability of the solution are analyzed. The resuits of the analysis are that the solution decreases to zero in time with no singularity along the way and that the differential equation is stable. The snowplow model is probably stable against perturbations whose scale length is comparable with the instantaneous bubble radius. (auth)
- Research Organization:
- Radio Corp. of America. Missile and Surface Radar Div., Moorestown, N.J.
- NSA Number:
- NSA-16-022720
- OSTI ID:
- 4825512
- Report Number(s):
- AFSWC-TDR-62-12(Vol.II)(Chap.1
- Resource Relation:
- Other Information: Orig. Receipt Date: 31-DEC-62
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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