Stability of the electron-driven fishbone mode

Electron-driven fishbones provide a good test bed for the linear theory of fast-particle driven instabilities as they exhibit a very high sensitivity to the details of both the equilibrium and the electronic distribution function. Thus, they can help validate the models developed for studying instabilities driven by alpha particles in future fusion reactors such as ITER. The fishbone dispersion relation is extended to properly account for resonance with passing particles by including the contribution of the parallel motion to the resonance condition. Barely passing electrons are found to drive the mode unstable at a lower frequency than barely trapped electrons. Although globally destabilizing, the influence of passing electrons quickly decreases away from the trapped-passing boundary. This is confirmed by an analysis using distributions close to those obtained in electron cyclotron resonance heating experiments. The major effect of this new resonance condition is a reduction of the fast-electron density threshold coupled to a reduction of the frequency of the mode.