SOME STABILITY PROBLEMS IN MHD

Abstract

In this thesis we have studied some interesting Electromagnetic stability problems which have important applications in science. In chapter I, we have introduced the subject of magnetohydrodynamic. We explained the basic EHD and MHD equations of motion in this field. Also we discussed the concept of stability and the technique followed for solving the problems such as the normal modes analysis to the perturbation equations which we used in this thesis. We have made a survey concerning some previous studies relating to the work in this thesis. In chapter II, we have studied the MHD stability of a streaming liquid jet of radius R, and density p surrounded by two dimensions varying vacuum magnetic field under the influence of self-gravitating force and pervaded by a uniform axial magnetic field. We have deduced the dispersion relation for all kinds of perturbations. Some recent published works are recovered as limiting cases from the present result. The analytical results are confirmed along with numerical methods. The axial magnetic fields inside and outside the jet have always stabilizing effects. The transverse magnetic field has a destabilizing effect. It is found that the largest domain of instability is fastly shrinking as (a> 13) with increasing (Ho/Ho)I values, Ho= (41tGp'R� Iµ), where G is the gravitational constant. The streaming has a strong destabilizing influence. These results have been published in Il-Nuove Cimento (1998) vol. 201), N. 12, pp. 1835. See reference [12}