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The stability of high-n toroidicity-induced shear Alfvén eigenmodes (TAE) in the presence of fusion alpha particles or energetic ions in tokamaks is investigated. The TAE modes are discrete in nature, and thus can easily tap the free energy associated with energetic particle pressure gradient through wave particle resonant interaction. A quadratic form is derived for the high-n TAE modes using gyrokinetic equation. The kinetic effects of energetic particles are calculated perturbatively using the ideal magnetohydrodynamic (MHD) solution as the lowest-order eigenfunction. The finite Larmor radius (FLR) effects and the finite drift orbit width (FDW) effects are included for both circulating and trapped energetic particles. It is shown that, for circulating particles, FLR and FDW effects have two opposite influences on the stability of the high-n TAE modes. First, they have the usual stabilizing effects by reducing the wave particle interaction strength. Second, they also have destabilizing effects by allowing more particles to resonate with the TAE modes. It is found that the growth rate induced by the circulating alpha particles increases linearly with the toroidal mode number n for small kθρα, and decreases as 1/n for kθρα>1. The maximum growth rate is obtained at kθρα on the order of unity, and is nearly constant for the range of 0.7≤vα/vA≤2.5. On the other hand, the trapped particle response is dominated by the precessional drift resonance. The bounce resonant contribution is negligible. The growth rate peaks sharply at the value of kθρα, such that the precessional drift resonance occurs for the most energetic trapped particles. The maximum growth rate due to the energetic trapped particles is comparable to that of circulating particles. Finally, the effect of the two-dimensional wave structure of TAE modes is considered by using the Wentzel–Kramers–Brillouin... [ABSTRACT FROM AUTHOR]

The terpsichore three-dimensional linear ideal magnetohydrodynamic (MHD) stability code [Theory of Fusion Plasmas, Proceedings of the Joint Varenna–Lausanne International Workshop, Chexbres, Switzerland, 1988 (Editrice Compositori, Bologna, Italy, 1989), p. 93; Controlled Fusion and Plasma Heating, Proceedings of the 17th European Conference, Amsterdam, The Netherlands (European Physical Society, Petit-Lancy, Switzerland, 1990), Vol. 14B, Part II, p. 931; Theory of Fusion Plasmas, Proceedings of the Joint Varenna–Lausanne International Workshop, Valla Monastero, Varenna, Italy, 1990 (Editrice Compositori, Bologna, Italy, 1990), p. 655] has been extended to the full MHD equations. The new code is used to calculate the physical growth rates of nonlocal low-n modes for l=2 torsatron configurations. A comprehensive investigation of the relation between the Mercier modes and the low-n modes has been performed. The unstable localized low-n modes are found to be correlated with the Mercier criterion. Finite growth rates of the low-n modes correspond to finite values of the Mercier criterion parameter. Near the Mercier marginal stability boundary, the low-n modes tend to be weakly unstable with very small growth rates. However, the stability of global-type low-n modes is found to be decorrelated from that of Mercier modes. The low-n modes with global radial structures can be more stable or more unstable than Mercier modes. [ABSTRACT FROM AUTHOR]

The stability of global Alfvén eigenmodes is investigated in the presence of super-Alfvénic energetic particles, such as fusion-product alpha particles in an ignited deuterium–tritium tokamak plasma. Alpha particles tend to destabilize these modes when ω[ATOTHER]@B|[/ATOTHER]α>ωA, where ωA is the shear-Alfvén modal frequency and ω*α is the alpha particle diamagnetic drift frequency. This destabilization due to alpha particles is found to be significantly enhanced when the alpha particles are modeled with a slowing-down distribution function rather than with a Maxwellian distribution. However, previously neglected electron damping due to the magnetic curvature drift is found to be comparable in magnitude to the destabilizing alpha particle term. Furthermore, the effects of toroidicity are also found to be stabilizing, since the intrinsic toroidicity induces poloidal mode coupling, which enhances the parallel electron damping from the sideband shear-Alfvén Landau resonance. In particular, for typical ignition tokamak parameters, global Alfvén eigenmodes are found to be completely stabilized by either the electron damping that enters through the magnetic curvature drift or the damping introduced by finite toroidicity. [ABSTRACT FROM AUTHOR]

The toroidicity-induced shear Alfvén eigenmode is found to be destabilized by fusion alpha particles in an ignited tokamak plasma. [ABSTRACT FROM AUTHOR]