Low frequency interchanges

A necessary stability criterion is derived for a class of selfconsistent low beta longtime guiding centre equilibria. This class is defined by some restrictions, viz. symmetry, zero electric field, small ratio of guiding centre drift velocities and diamagnetic velocities, and stability on the time scale of the longitudinal guiding centre motion. Open ended as well as toroidal configurations (with or without rotational transform) and arbitrarily anisotropic distribution functions are admitted. The stability condition requires that the drifts of the trapped particles be favourable, this depending on their pitch angles in general. If it is violated, then an electrostatic mode occurs which grows on the slow time scale of the guiding centre drifts, thus conserving the longitudinal adiabatic invariant J. The present theory is an improvement and generalization of previous theories of the collisionless trapping instability in isotropic plasmas. It shows that anisotropy can have a stabilizing effect. It also shows that low frequency interchange stability (J conserved) is a more restrictive requirement than interchange stability (J violated), and thus refutes the widely held opposite opinion.