Unstable drift-kinetic Alfvén modes with helicity close to the rotational transform

Abstract

An important feature of some modern facilities (such as optimized stellarators) with low shear is that the value of their rotational transform is close to a rational number. If a mode helicity is close to the rotational transform of the background magnetic field, the Alfvén continuum frequency can lie in the range of the diamagnetic frequencies of the background electrons. An analytical analysis shows that if the local electron diamagnetic frequency curve crosses the Alfvén continuum from above as one proceeds from the axis to the plasma edge at a radial location relatively distant from the axis, a family of unstable drift-kinetic Aflvén modes (DKAEs) arises due to the coupling between the drift and Alfvén waves having same poloidal numbers. The coupling is mediated by the parallel electric field and the mode is destabilized due to parallel resonances. The mode growth rate can be relatively large and comparable to the real part of the mode frequency. The growth rate peaks at a small radial number, so that the most unstable mode can appear global and be confused with the magnetohydrodynamic (MHD) modes which can occur in this part of the spectrum. It follows that it is important to consider the diamagnetic effects and finite parallel electric field, which are frequently neglected for such phenomena in tokamaks, when studying Alfvén phenomena in the lowest part of the electromagnetic spectrum in optimized stellarators.