This paper analyzes several important features of trapped-particle instabilities. For trapped-electron modes, the complete two-dimensional (2D) spatial structure, including the effects of magnetic shear, is numerically calculated within the framework of a differential formulation for long radial wavelength modes. Growth rates obtained for representative cases correlate reasonably well with the usual one-dimensional (1D) estimates of shear stabilization. However, the spatial structure of the mode differs markedly; e.g., it typically extends over several mode-rational surfaces. At the shorter wavelengths, where the maximum growth rates of the modes typically occur, it is necessary to introduce an integral equation formulation for calculating the …
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This paper analyzes several important features of trapped-particle instabilities. For trapped-electron modes, the complete two-dimensional (2D) spatial structure, including the effects of magnetic shear, is numerically calculated within the framework of a differential formulation for long radial wavelength modes. Growth rates obtained for representative cases correlate reasonably well with the usual one-dimensional (1D) estimates of shear stabilization. However, the spatial structure of the mode differs markedly; e.g., it typically extends over several mode-rational surfaces. At the shorter wavelengths, where the maximum growth rates of the modes typically occur, it is necessary to introduce an integral equation formulation for calculating the radial dependence. Growth rates from this 2D analysis are significantly smaller than 1D estimates, and the poloidal mode structure exhibits a pronounced localization at the magnetic field minimum. Specific collisional mechanisms affecting the linear stability of these modes are also studied. Collisional scattering of low energy electrons can reduce the nonadiabatic trapped-electron response, and collisional broadening can strongly modify the resonant response of the untrapped electrons. The saturation of the usual form of the dissipative trapped-ion instability by mode coupling is studied analytically and numerically.
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Tang, W. M.; Adam, J. C. & Cohen, B. I.Linear and nonlinear theory of trapped-particle instabilities,
article,
September 1, 1976;
New Jersey.
(https://digital.library.unt.edu/ark:/67531/metadc1446118/:
accessed May 23, 2024),
University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu;
crediting UNT Libraries Government Documents Department.
