Abstract
It is shown that the theoretical predictions and experimental observations of toroidicity-induced Alfvén eigenmodes (TAE’s) are now in good agreement, with particularly detailed agreement in the mode frequencies. Calculations of the driving and damping rates predict the importance of continuum damping for low toroidal mode numbers and this is confirmed experimentally. However, theoretical calculations in finite-β, shaped discharges predict the existence of other global Alfvén modes, in particular the ellipticity-induced Alfvén eigenmode (EAE) and a new mode, the beta-induced Alfvén eigenmode (BAE). The BAE mode is calculated to be in or below the same frequency range as the TAE mode and may contribute to the experimental observations at high β. Experimental evidence and complementary analyses are presented confirming the presence of the EAE mode at higher frequencies.
Highlights
Global Alfvin modes, such as the toroidicity-induced Alfven eigenmode’ (TAE) are of considerable concern to fusion experiments since they can be driven resonantly unstable by energetic a particles provided certain criteria are met.* The first estimates* of the destabilization of TAE modes predicted low thresholds in the a-particle p required to overcome stabilization by electron Landau damping
TAE modes were considered to be more dangerous* and little consideration has since been paid to GAE modes, despite the fact that it is clear that TAE modes are more strongly damped than the original estimates suggested
The results reported in this paper demonstrate a clear convergence between the theory of TAE modes and observations in DIII-D
Summary
Global Alfvin modes, such as the toroidicity-induced Alfven eigenmode’ (TAE) are of considerable concern to fusion experiments since they can be driven resonantly unstable by energetic a particles provided certain criteria are met.* The first estimates* of the destabilization of TAE modes predicted low thresholds in the a-particle p required to overcome stabilization by electron Landau damping. The most important of these appear to be ion Landau damping,‘* including an additional resonance’* at one third the AlfvCn speed, continuum damping,i3P*4 and coupling of the TAE mode to nearby kinetic AlfvCn waves.” Inclusion of these effects has been found to provide much more satisfactory agreement between predicted and observed thresholds.‘6 all the recent theories are essentially restricted to low 0, circular cross section, and large aspect ratio, and can only be expected to provide gross quantitative agreement. Two important new results are described as part of this work: a new global AlfvCn mode, the beta-induced AlfvCn eigenmode (BAE), which exists in the P-induced gap, is exhibited and the first definitive experimental evidence for the EAE in DIII-D is presented The existence of these two modes has important consequences for future beam- and a-heated experiments since extrapolations of fast particle instability thresholds to such devices will need to include these new modes.
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