The Effect of Energetic Particles on Stability of Mirror and Tokamak Plasmas

The effects of an energetic particle species on high-mode-number, curvature-driven instabilities in magnetic mirror and tokamak plasmas are studied. We will investigate whether or not these hot particles can stabilize the magnetohydrodynamic (MHD) ballooning mode by having magnetic drift velocities large enough that they do not respond on the usual time scale of the instability and consequently allow thermonuclear fusion devices to operate at higher, more efficient plasma pressures. However, the energetic particles themselves are subject to instabilities that limit the effectiveness of this procedure. Using an MHD particle simulation code, the stabilizing effect of a diamagnetic well formed by the energetic particles is demonstrated in an axisymmetric mirror by treating the hot species as a rigid current ring. The results match those predicted by an analytic theory based on the MHD equations. More general aspects of linear stability in mirrors containing energetic particles are examined through analysis of equations derived from the drift kinetic equation. Numerical techniques are used to show that a magnetic compressional instability can arise if the core plasma density is too high or if the hot particle pressure gradient is too large. A similar set of equations is solved numerically in a tokamak geometry to determine whether or not energetic particles will allow access to the desirable second stability region for MHD ballooning modes. An instability with frequency on the order of the energetic particle magnetic curvature drift frequency can appear if the hot pressure gradient is too large. When the energetic species pressure peaks on the outside edge of the tokamak, the thermal energy of the species needs to be in excess of 1 MeV for this scheme to be viable. Alternative distributions with pressure peaking on the inside edge were expected to produce more favorable results. However, new instabilities are found to appear with these distributions, yielding no improvements to the stability picture. Furthermore, a simple analytic treatment predicts the loss of an important stabilizing effect with the switch of the pressure peak to the inside.