Abstract
An analytical theory based on the MHD model is presented for understanding the coupling between the shear Alfvén wave and the slow magnetosonic wave (or the so called slow mode) in the frequency range below the Toroidal Alfvén Eigenmode (TAE) continuum spectrum gap. In tokamak plasmas, coupling of the Alfvén m poloidal harmonic and the slow mode m ± 1 harmonics causes the Alfvén m harmonic continuous spectrum to be uplifted from the uncoupled Alfvén spectrum by an amount related to the plasma pressure and the geodesic magnetic field curvature. However, the frequency of one of the slow mode m ± 1 harmonics is reduced by the same pressure-curvature coupling effect. But the frequency of the other slow mode harmonic is relatively unaffected. As a result, the Alfvén-slow (AS) mode continuous spectrum is broken up into two Alfvén-Slow (AS) gaps below the TAE continuum gap. Coupling of the Alfvén m harmonic with the slow mode m ± 2 harmonics also creates additional AS gaps if their frequencies cross each other. The AS gap widths increase with the plasma pressure. The creation of AS gaps allows the existence of several new types of Alfvén-Slow Eigenmodes (ASEs). The radial structure of these new ASEs does not intersect with the continuous spectrum and thus does not suffer from continuum damping. The Beta-induced Alfvén-Acoustic Eigenmode (BAAE) is one type of ASEs with frequency in the lowest AS frequency gap. However, the BAAE usually interacts with the Alfvén-Slow continuum and suffers from continuum damping. The existence of ASEs is ubiquitous for normal and reserve safety factor profiles, broad range of plasma β values, different plasma shapes, and many different toroidal mode numbers. The newly discovered ASEs provide explanation for the experimentally observed Beta-induced Alfvén Eigenmodes destabilized by fast ions with frequencies below the TAE frequency gap.
Highlights
In nonuniform plasmas, the magnetohydrodynamics (MHD) model predicts two branches of continuous spectra: The shear Alfven wave and the slow magnetosonic wave
The AS gap widths increase with the plasma pressure
We have presented an analytical theory to understand the physics of coupling between the Alfven wave and the slow mode, which results in the breakup of the MHD continuous spectrum to form Alfven-Slow (AS) frequency gaps for frequency below the Toroidal Alfven Eigenmode (TAE) frequency gap
Summary
The magnetohydrodynamics (MHD) model predicts two branches of continuous spectra: The shear Alfven wave and the slow magnetosonic wave (or the so called slow mode). Because of the pressure and geodesic curvature coupling in the slow mode approximation model, the Alfven continuum below the TAE gap shrinks to form a beta induced Alfven gap and the BAE frequency is at the top of the beta-induced Alfven gap just below the Alfven continuum.[14] Another model is the Beta-induced Alfven-Acoustic Eigenmode (BAAE)[16,17] which is obtained numerically from the NOVA code calculation[18,19] with frequency in the BAAE gap. The uplifted Alfven continuous spectrum can interact with the slow mode m 6 2 harmonics to form additional AS gaps and additional ASEs can exist with frequencies in these additional AS frequency gaps.
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