MHD Stability in Axisymmetric Multiple Mirror Geometry

The marginal stability of MHD modes is discussed in application for high beta multiple mirror experiments planned at Budker Institute of Nuclear Physics. Flute modes arc dangerous in axisymmetric systems with β < 1. In the case of “wall confined” plasmas, (β ≫ 1), pressure slightly varies along the radius providing less radial gradient and more stability against MHD modes. Effect of ion-ion viscosity becomes important in corrugated magnetic field. It results in the reduction of the growth rate by a factor β^1/2. In the process of start up and plasma heating β < 1. If flute modes are stabilized during this period by the line-tying mechanizm ballooning modes are still unstable when β > β_cr. A very low ballooning margin is predicted in multiple mirror with the large number of cells: β_cr < π² /N². For the number of cells N ≃ 10: β_cr ≃ 5%. Results of the calculations are discussed in the context of old and new multiple mirror experiments.