Within the gyrokinetic formalism, we present and analytically study the equations for an explicit treatment of the trapped-electron-modified kinetic ballooning mode (KBM) and the electromagnetic version of the trapped-electron mode, in general geometry. The gradient of the plasma =8 p /B², the ratio of kinetic to magnetic pressure, is taken to be small enough to avoid including perturbations of the magnetic field strength. Trapped-electron-modified KBMs are first described close to ideal magnetohydrodynamic marginality, retaining the explicit resonant contribution of both ions and trapped electrons, and then in a strongly driven fluid limit. We show that maximum- J devices (where J is the second adiabatic invariant) enjoy relatively good stability properties at finite, but the coupling of trapped electron and KBMs might induce modes rotating in the ion direction, thus eluding good maximum- J properties. An eigenvalue equation for the finite - trapped-electron-mode is derived and studied. We highlight the possibility of having an electron-temperature-gradient driven electromagnetic instability in regions of bad magnetic curvature. A mechanism for the destabilisation of the trapped-particle-enabled collisionless microtearing mode also is proposed. Our results are general and provide new theoretical ground for the characterisation of several magnetic confinement concepts, such as tokamaks, quasisymmetric and quasi-isodynamic stellarators.
Zocco et al. (Mon,) studied this question.