It is well-known that, within the ideal magnetohydrodynamic (MHD) description, there exist two low-frequency Alfvén continuous spectra in toroidal plasma devices, such as tokamaks. The corresponding three accumulation frequencies are the beta-induced Alfvén eigenmode (BAE) frequency, the ion-sound wave (ISW) frequency, and the zero frequency accumulation point at vanishing parallel wave number, k∥= 0. To form localized discrete eigenmodes, the plasma with a normal magnetic shear must be ideal MHD unstable. The zero-frequency branch then corresponds to the ideal MHD unstable discrete mode, while the BAE and ISW discrete eigenmode frequencies could be significantly shifted away from the respective accumulation frequencies. Energetic-particle (EP) effects can be analyzed and understood as an effective potential well via the generalized fishbone linear dispersion relation. In particular, it is demonstrated that, for an ideal MHD stable plasma, EPs could play the roles of both discretization and destabilization, and their effect is generally non-perturbative. The theoretical results further predict that EPs preferentially excite the BAE branch over the ISW branch. The zero-frequency branch, meanwhile, becomes the well-known fishbone dispersion relation, giving rise to energetic-particle modes. Extensions to the case of reversed magnetic shear as well as the kinetic effects will also be discussed.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics