Stability of ballooning modes in a rotating plasma

Sheared flow effects on ballooning instabilities in three-dimensional equilibria

“…In particular, flow shear stabilization of ideal MHD ballooning modes in axisymmetric tokamak equilibrium have been addressed by a number of authors. [5][6][7][8][9][10][11][12] The result of the present work generalizes these results to threedimensional equilibrium. Application of the conventional ballooning formalism to stellarator equilibrium with small flow reduces the problem to a partial differential equation in three dimensions.…”

“…[5][6][7][8][9][10][11][12] These calculations rely on using a ballooning mode Wentzel-Kramers-Brillouin ͑WKB͒-like formalism. 13,14 In the static limit ͑no equilibrium flow͒, the ballooning transformation produces a lowest order solution in the form of an ordinary differential equation along the field line.…”

Electromagnetic effects in the stabilization of turbulence by sheared flow

“…The equations (15)(16)(17)(18)(19) describing the linear system can be written clearly in characteristics form. The characteristics represent the five basic waves present.…”

“…In this section we therefore take such reduced versions of equations (15)(16)(17)(18)(19) and look for plane wave solutions of the form exp(−iωt + ik z). The simple convective effect of the perpendicular flow shear, M , may be removed by defining a modified frequency in the laboratory frame…”

“…It is of interest to consider an alternative limit of equations (15)(16)(17)(18)(19), again with only the ω * v drive and M = 0 for clarity, but for large z, which corresponds to conditions far along the field line. The terms in ν k and χ k dominate (16) and (17), representing strong ion dissipation due to the sheared system, so the fields V and T tend to zero.…”