Double-Gap Alfvén Eigenmodes: Revisiting Eigenmode Interaction with the Alfvén Continuum

A new type of global shear Alfvén eigenmode is found in tokamak plasmas where the mode localization is in the region intersecting the Alfvén continuum. The eigenmode is formed by the coupling of two solutions from two adjacent gaps (akin to potential wells) in the shear Alfvén continuum. For tokamak plasmas with reversed magnetic shear, it is shown that the toroidicity-induced solution tunnels through the continuum to match the ellipticity-induced Alfvén eigenmode so that the resulting solution is continuous at the point of resonance with the continuum. The existence of these double-gap Alfvén eigenmodes allows for potentially new ways of coupling edge fields to the plasma core in conditions where the core region is conventionally considered inaccessible. Implications include new approaches to heating and current drive in fusion plasmas as well as its possible use as a core diagnostic in burning plasmas.

Figure 1

Shear Alfvén continuum for $n=8$ in the reversed shear plasma with the safety factor profile shown in Fig. 2. EAE, TAE, and BAE gaps are indicated. The DGAE solution radial extension is shown for the mode frequency ${\Omega }^2=4.8$.

Figure 2

The plasma safety factor, beta, and density profiles used in NOVA simulations.

Figure 3

DGAE poloidal harmonic radial structures for $n=8$ (a). (b) Represents the magnified radial structure of $m=20–22$ harmonics near the resonance with the continuum, $\rho =0.67$. Also shown in (b) is $(A^{-1}C{)}_{m_s}=d{\xi }_m/d\rho$, $m_s=21$.

Figure 4

Diagonal elements of the matrix of the coefficients at the second derivatives in the eigenmode equation, $A_{mm},m=20–22$, (a). (b)  Represents flux vector-function elements, ${\widehat{C}}_m$, for poloidal harmonics $m=20,21,22$.