Some mathematical problems arising in the study of magnetohydrodynamics with the Hall effect
Abstract
The equations of ideal magnetohydrodynamics (MHD) are singularly perturbed when the Hall effect is included in the Ohm's law of a plasma. Characteristics and the associated jump conditions are computed. It is found, in contrast to ideal MHD, that the equations are not hyperbolic. A hyperbolic system is obtained from the linearized equations in the case where the equilibrium depends only on the variable x and the equations are Fourier transformed in y and z. When the linearized equations are also transformed in t, a fourth order system of ordinary differential equations is obtained. This system is regular at points where the ideal MHD system is singular. It is singular at certain points where the ideal system is regular. Behavior of solutions of the fourth order system near the ideal MHD singularities is obtained using the method of matched asymptotic expansions.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- December 1976
- Bibcode:
- 1976PhDT........85C
- Keywords:
-
- Hall Effect;
- Magnetohydrodynamics;
- Plasmas (Physics);
- Ohms Law;
- Plasma Conductivity;
- Plasma Oscillations;
- Plasma Physics