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A complete theory of wave-particle interactions is presented whereby both circulating and trapped energetic ions can destabilize kinetic ballooning modes in tokamaks. Four qualitatively different types of resonances, involving wave-precessional drift, wave-transit, wave-bounce, and precessional drift-bounce interactions, are identified, and the destabilization potential of each is assessed. For a characteristic slowing-down distribution function, the dominant interaction is that which taps those resonant ions with the highest energy. Implications of the theory for present and future generation fusion experiments are discussed. 16 refs.
We have analyzed theoretically the resonant excitations of kinetic ballooning modes (KBM) by the energetic ions/alpha particles in tokamaks. Our theory includes finite-size orbit effects of both circulating and trapped particles. With energetic-particle contributions suppressed in the singular inertial layer, an analytic.dispersion relation can then be derived via an asymptotic matching analysis. The dispersion relation, in particular, demonstrates the existence of two types of modes; that is, the magnetohydrodynamic (MHD) gap mode and the energetic-particle continuum mode. Specific expressions for real frequencies, growth rates and threshold conditions are also derived for a model slowing-down beam ion distribution function.
Analytical theories for the excitations in tokamaks of magnetohydrodynamic (MHD) modes with large toroidal mode numbers (n”1) are presented. Specifically, only instability mechanisms due to resonances with energetic ions/alpha particles are considered. It is noted that, while trapped energetic particles contribute to the ideal region, circulating energetic particles contribute mainly to the singular layer dynamics. A unified dispersion relation manifesting both fishbone-like modes and beam transit-resonance modes is then driven. Finally, we also analyze the stability property of toroidicity-induced shear Alfven waves excited via transit resonances with alpha particles in ignited tokamaks. 11 refs.
This is a graduate textbook on tokamak physics, designed to provide a basic introduction to plasma equilibrium, particle orbits, transport, and those ideal and resistive magnetohydrodynamic instabilities which dominate the behavior of a tokamak discharge, and to develop the mathematical methods necessary for their theoretical analysis.
Toroidal Alfven eigenmodes are shown to be resonantly destabilized by both circulating and trapped energetic ions/alpha particles. In particular, the energetic circulating ions are shown to resonate with the mode not only at the Alfven speed ([upsilon]{sub A}), but also one-third of this speed, while resonances exist between trapped energetic ions and the wave when [upsilon] = [upsilon]{sub A}/21[epsilon]{sup {1/2}} (l=integer, [epsilon]=r/R is the local inverse aspect ratio), although the instability becomes weaker for resonances other than the fundamental. The oft-quoted criterion that instability requires super-Alfvenic ion velocities is thus sufficient but not necessary. 14 refs.