Variational method for drift waves - saturation of the trapped-ion mode

A variational method which permits the systematic improvement of the test function is applied to the problem of non-collisional drift waves in toroidal geometry. The strength of the toroidal mode coupling is described by a parameter E proportional to the inverse-aspect ratio. On comparison with the case E=0 (slab limit), it is found that modes which balloon on the inner side of the torus do not become unstable when E not equal to 0. For modes which balloon on the outer side of the torus and which are obtained from the slab limit by continuously increasing E, the effect of the coupling is stabilizing. However, a second branch exists, which is found unstable for realistic parameters. Also given is a simple criterion for quasi-suppression of shear damping by toroidal coupling. Non-linear processes allowing saturation of trapped-ion instabilities are investigated. When the ion temperature gradient is larger than the density gradient (α ln N/(α ln T)<3/2), the modes are driven by resonance with the average magnetic curvature drift of trapped ions. In this case, it is shown that effective saturation occurs through a new mechanism: electrostatic trapping of resonant ions in the 2-D potential of the wave rather than through mode coupling. The radial structure is shown to strongly enhance trapping. Ion collisions partly restore the Maxwellian distribution. Asymptotic equilibrium is reached when this is balanced by electron collisional damping. Radial structure effects are shown to yield very low amplitudes at saturation. (author)