Abstract
A nonlocal theory for the low-frequency trapped particle instability in toroidal systems has been developed in a model field. The stability of the trapped particle mode is studied by using normal mode analyses with radial boundary conditions. In the absence of magnetic shear, the finite-orbit effect is shown to be incapable of stabilizing the mode; large magnetic shear is needed for stabilization. The ratio of the localization width of the mode to the characteristic density length is of the order of (Λ/r;)1/2ε1/4 (Λ is the charactistic “banana” size, r is the characteristic density length, and ε is the aspect ratio). An estimate of the nonlinear diffusion coefficient for the mode is given.
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