The effects of sloshing energetic particles on ballooning modes in tokamaks

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Abstract
Distributions that give rise to energetic trapped particle pressures peaked in the ‘‘good curvature’’ region of a tokamak (sloshing distributions) are examined in an attempt to find stable regimes for both the magnetohydrodynamic (MHD) and precessional modes. It is the precessional drift destabilization of ballooning modes that inhibits bridging the unstable gap to second stability by the use of deeply trapped energetic particles unless the hot particles have an extremely large energy (∼0.35 MeV for a tokamak like PDX [Phys. Rev. Lett. 49, 326 (1982)]). Unfortunately, our calculations indicate that the sloshing particles do not have a significant stabilizing effect. An analytic treatment shows that stability for the precessional mode can be found only if the sign of the energetic particle magnetic drift frequency can be reversed from its value in vacuum bad curvature without hot species diamagnetism. This is difficult to do in a tokamak because of the destabilizing contribution of the geodesic curvature to the drift frequency. Furthermore, for each of the two sloshing distributions employed (one contains only trapped particles; the other includes trapped and passing particles), a new ‘‘continuum instability’’ (where asymptotically along the field line the mode is a propagating plane wave) is found to be driven by geodesic curvature. These results indicate that energetic sloshing particles are not able to bridge the unstable gap to second stability.