Energetic particle effects as an explanation for the low frequencies of Alfvén modes in the DIII-D tokamak

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, f TAE , while the typical frequency of beta induced Alfvén eigenmodes (BAEs) is (0.2-0.4) f TAE . 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.