Abstract
During beam injection in the DIII-D tokamak, modes with lower frequencies than expected for toroidicity induced Alfvén eigenmodes (TAEs) are often observed. The experimental `TAE' frequency is often ≈0.8 of the nominal theoretical frequency of the TAE, fTAE, while the typical frequency of beta induced Alfvén eigenmodes (BAEs) is (0.2-0.4)fTAE. An analysis is presented of an unstable discharge with a high n stability code, HINST, that includes the effect of energetic ions on mode frequency. The analysis shows that the experimental `TAE' and `BAE' could be resonant branches of the TAE and the kinetic ballooning mode, respectively.
Highlights
The toroidicity induced Alfven eigenmode (TAE) [1] has been studied extensively in tokamaks [2]
In Ref. [20], an extensive database of frequency measurements of DIII-D ‘beta induced Alfven eigenmodes (BAEs)’ was compared with four simple analytical frequency scalings: an Alfven eigenmode (f ∝ vA), a kinetic ballooning mode (KBM) (f ∝ ω∗i), a mode that progagates at the ion thermal speed (f ∝ vi) and an energetic particle mode (EPM) (f proportional to the beam ion circulation frequency)
The code predicts that the higher frequency resonant TAE (RTAE) is more unstable than the lower frequency resonant KBM, but, in the experiment, the ‘BAE’ seems to be slightly more unstable than the ‘TAE.’
Summary
The toroidicity induced Alfven eigenmode (TAE) [1] has been studied extensively in tokamaks [2]. [20], an extensive database of frequency measurements of DIII-D ‘BAEs’ was compared with four simple analytical frequency scalings: an Alfven eigenmode (f ∝ vA), a KBM (f ∝ ω∗i), a mode that progagates at the ion thermal speed (f ∝ vi) and an EPM (f proportional to the beam ion circulation frequency). None of these simple scalings fit all of the data. The code predicts that the higher frequency RTAE is more unstable than the lower frequency resonant KBM, but, in the experiment, the ‘BAE’ seems to be slightly more unstable than the ‘TAE.’
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