To study of hydromagnetic stabilities of magnetically confined plasma

To study the hydromagnetic stability of magnetically confined plasma, the macroscopic fluid equation for an electrically neutral, isotropic, infinite –conductivity plasma are used. Even through these plasma equation are highly reduced description of a plasma, they are difficult to solve in detail, except for simple plasma-confinement schemes but this reduced description of a plasma is useful to illustrate and analyze the feature of most of instabilities that lead to rapid loss of plasma from laboratory confinement experiment. We also study the perturbation equation, to determine the dynamical behavior of a plasma equilibrium or to compute the change in energy that result from a small departure from a plasma equilibrium, the one fluid MHD equation are perturbed about an equilibrium state. We see that all the perturbation quantities can be expressed in term of perturbation velocity. Since these equations are only valid for small values v1, p1, and B1, the instabilities growth rates predicted by them are only valid for initial stages of growth after a short period, the amplitude of the perturbation becomes large enough that the nonlinear term are no longer negligible. For later stages of instability, the nonlinear term must be retained in equations. (author)