MHD stability in axisymmetric multiple mirror geometry

The marginal stability of MHD modes is discussed in application for high be ta multiple mirror experiments planned at Budker Institute of Nuclear Physi cs. Flute modes are dangerous in axisymmetric systems with beta < 1. In the case of "wall confined" plasmas, (beta much greater than 1), pressure slig htly varies along the radius providing less radial gradient and more stabil ity against MHD modes. Effect of ion-ion viscosity becomes important in cor rugated magnetic field. It results in the reduction of the growth rate by a factor beta(1/2). Il, the process of start up and plasma heating beta < 1. If flute modes are stabilized during this period by the line-tying mechani sm ballooning modes are still unstable when beta > beta(cr). A. very low ba llooning margin is predicted in multiple mirror with the large number of ce lls: beta(cr) less than or equal to pi(2) /N-2. For the number of cells N s imilar or equal to 10: beta(cr) similar or equal to 5%. Results of the calc ulations are discussed in the context of old and new multiple mirror experi ments.