  It is shown that in perfectly quasi-isodynamic stellarators, trapped
particles with a bounce frequency much higher than the frequency of the
instability are stabilizing in the electrostatic and collisionless limit. The
collisionless trapped-particle instability is therefore stable as well as the
ordinary electron-density-gradient-driven trapped-electron mode. This result
follows from the energy balance of electrostatic instabilities and is thus
independent of all other details of the magnetic geometry.
