Pressure Gradient Effects on Alfven Cascade Modes in Tokamaks

Alfven cascade modes are discrete shear Alfven eigenmodes localized at the radius of minimum of safety factor in tokamak plasmas with reserved shear q profiles [1]. The mode frequency is given by $\omega \sim (n- m/q_{min})V_A/R$ over most parameters, and transforms to the geodesic acoustic mode near rational field lines. The mode is seen in experiments, where the mode frequency sweeps up as q drops. Numerical results indicate that the plasma pressure gradient helps establish the mode [2], in contrast to a previous analytic prediction [3] that the pressure gradient term hinders mode establishment. here a modification of the analysis is developed to include a previously neglected interchange term due to the favorable average curvature of a tokamak. This is the key addition that is needed for the pressure gradient to be favorable for the establishment of a cascade mode, and thereby explain the numerical results. \newline [1] H. L. Berk et al., Phys. Rev. Lett. {\bf 87}, 185002 (2001). \newline [2] G. J. Kramer et al., Plasma Phys. Controlled Fusion {\bf 46}, L23 (2004). \newline [3] B. N. Breizman et al., Phys. Plasmas {\bf 12}, 112506 (2005).