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AbstractAbstract
[en] A kinetic energy principle for a tokamak allowing for bounce and transit resonances is considered. By passing over to a variable that has the meaning of the normalized time along the particle trajectory, a solution to the drift-kinetic equation is found for an arbitrary ratio of the wave frequency to the characteristic bounce frequency. This solution is used to derive a general expression for the part of the potential energy of perturbations that is related to the compressibility in the form of series in harmonics of the transit frequency of circulating particles and the bounce frequency of trapped particles with allowance for the drift effects. With the help of the Jacobi elliptic functions, it is shown that, in the vicinities of the singular points of perturbations, the coefficients in the above series are expressed in terms of complete elliptic integrals of the fist kind. General relations for renormalization of the plasma inertia due to the compressibility are obtained; these relations are analyzed both analytically (in the limits of low and high frequencies) and numerically (for intermediate frequencies). It is shown that Landau damping of low-frequency modes results mainly from trapped particles, rather than from circulating ones as was supposed in a number of previous papers. It is noted that, for a plasma toroidally rotating with an angular velocity comparable to the characteristic bounce frequency, Landau damping can play an important role in stabilizing the resistive-wall external kink modes
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Translated from Fizika Plazmy, ISSN 0367-2921, 24, 675-689 (August 1998); (c) 1997 MAIK/Interperiodika; Country of input: International Atomic Energy Agency (IAEA)
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