Stability theory of dissipative trapped-electron and trapped-ion modes

This paper treats topics in the linear theory of dissipative trapped-electron instabilities, and in the nonlinear theory of the dissipative trapped-ion instabilities. Stability criteria are obtained for dissipative trapped-electron modes in a tokamak-type magnetic field with shear. In the important case where the mode is driven by the electron temperature gradient, and neglecting ''ballooning'' effects, shear is found to stabilize the mode if typically r/sub n//L/sub s/ greater than 0.1 (r/2R)/sup 1/2/dlnT/sub e//dlnn, a condition that can be attained. With weak shear, it is shown, however, that the mode-structure along the field can exhibit substantial ''ballooning.'' The dissipative trapped-ion mode, which is not shear-stabilized, is considered in its nonlinear regime. Including nonlinear E x B motions, exact stationary trapped-ion-mode solitary-wave solutions are found, in which the wave energy in longer azimuthal wavelengths passes to shorter-wavelength components that are strongly damped by ion bounce resonances; the amplitudes are sufficiently reduced that a diffusion lower than Kadomtsev's is indicated. As a second nonlinear mechanism, anomalous velocity-space scattering due to the development of an unstable loss-cone-type ion distribution function is considered; this mechanism raises the effective ion collision frequency and increases the stability of the longer azimuthal-wavelength modes. (auth)