FINITE ORBIT ENERGETIC PARTICLE LINEAR RESPONSE TO TOROIDAL ALFVEN EIGENMODES

The linear response of energetic particles of the TAE modes is calculated taking into account their finite orbit excursion from the flux surfaces. The general expression reproduces the previously derived theory for small banana width; when the banana width DELTA(b) is much larger than the mode thickness DELTA(m), we obtain a new compact expression for the linear power transfer. When DELTA(m)/DELTA(b) << 1, the banana orbit effect reduces the power transfer by a factor DELTA(m)/DELTA(b) from that predicted by the narrow orbit theory. A comparison is made of the contribution to the TAE growth rate of energetic particles with a slowing-down distribution arising from an isotropic source, and a balanced-injected beam source when the source speed is close to the Alfven speed. For the same stored energy density, the contribution from the principal resonances (\v parallel-to\ = v(A)) is substantially enhanced in the beam case compared to the isotropic case, while the contribution at the higher sidebands (\v parallel-to\ = v(A)/(2l-1) with l greater-than-or-equal-to 2) is substantially reduced.