Bi-directional Alfvén cyclotron instabilities in the mega-amp spherical tokamak

Abstract

Alfvén cyclotron instabilities excited by velocity gradients of energetic beam ions were investigated in MAST experiments with super-Alfvénic NBI over a wide range of toroidal magnetic fields from ~0.34 T to ~0.585 T. In MAST discharges with high magnetic field, a discrete spectrum of modes in the sub-cyclotron frequency range is excited toroidally propagating counter to the beam and plasma current (toroidal mode numbers n < 0). At lower magnetic field ≤ 0.45 T, a discrete spectrum of Compressional Alfvén Eigenmodes (CAEs) with n > 0 arises, in addition to the modes with n < 0. At lowest magnetic fields, the CAEs with n > 0 become dominant, they are observed in frequency range from ~250 kHz for 1 = n to ~3.5 MHz for 15 = n , well above the onaxis ion cyclotron frequency (~2.5 MHz). The data is interpreted in terms of normal and anomalous Doppler resonances modified by magnetic drift terms due to inhomogeneity and curvature of the magnetic field. A Hall MHD model is applied for computing the eigenfrequencies and the spatial mode structure of CAEs and a good agreement with the experimental frequencies is found.

Compressional Alfvén eigenmodes in rotating spherical tokamak plasmas

“…To investigate this, the code used in [19], called the CAE code, has been modified to solve a simplified version of the CAE3B equations (21). It does not include the terms stemming from v 1 · ∇v 0 in (11) and B 1 · ∇v 0 in (17), and the effective rotation frequency can thus be expected to be higher (see figure 5). The Hall term and the terms related to J 0 are also neglected, so that the equation becomes…”

“…Neither of the codes used in this work is able to perform both these tasks at the same time. Furthermore, it would be preferable if the v 2 A /(ω 2 B 2 )(B · ∇) 2 ≪ 1 approximation, which prevents shear waves, could be removed, as is done in the WHALES code [17]. Figure 10.…”

“…The CAE3B code (which was presented in [13] but not given a name there), on the other hand, includes the Hall term but excludes shear Alfvén waves by assuming that v 2 A /(ω 2 B 2 )(B · ∇) 2 ≪ 1 when operating on components of the perturbed magnetic field perpendicular to the background field. This restriction is lifted in the WHALES code [17], which is based on finite elements instead of finite differences as in CAE3B. Moreover, nonlinear effects due to the presence of the fast ion population can influence the eigenmode structure [18], but such effects are not considered here.…”

Ion cyclotron emission studies: Retrospects and prospects

“…Furthermore, recent theoretical investigations resulted in the prescription for how to decouple CAE baseline eigenmode equations from the shear Alfvén oscillations, allowing for a focus on CAE properties only [32]. A similar approach, but with a slightly reduced model for the eigenmode equations, was further developed and applied to the MAST plasma [35], where the modes co-and counter-propagating in the direction of the plasma current were reported. As an illustration of those studies, we show the computed CAE radial mode structures in Fig.…”

“…Shown are the real and imaginary values (as indicated) of variable representing the normal to the magnetic surface component of the mode displacement. The depicted mode corresponds towith the mode frequency MHz[35].…”