The author obtains a general criterion for the stability of a toroidal plasma with respect to g-mode perturbations, which were first considered by Furth, Killeen and Rosenbluth for a plasma of finite conductivity in a magnetic field with shear and gravitational field g. The criterion is used to elucidate the stability of g-mode perturbations in an axially symmetric tokamak of circular cross-section. It is shown that, if aq'/q is positive and not too small, g-mode perturbations are stable for q2 > 1 (where q is the safety factor, a is the radius and the prime denotes a derivative with respect to a). With negative values of aq'/q, instability is possible even if q2 ≫ 1.

The stabilization of the Alfvén wave instability in a two-component tokamak is investigated theoretically. It is assumed that the instability is caused by fast ions which form in the tokamak when fast neutral atoms are injected into it. Dissipation through collisions with trapped electrons is considered to be a stabilizing factor. The method developed by Timofeev for considering initial perturbations is employed. It is shown that the influence of dissipation through collisions with trapped electrons on the “local” growth rate of the instability of an ion beam is insignificant in cases of practical interest. Such collisional dissipation is also insignificant as regards the evolution of initial perturbations if the thermal spread of the beam is not too great. It can, however, play an appreciable role in the case of very diffuse beams. This opens up the possibility of suppressing Alfvén instability by injecting into a tokamak neutral atoms with a broad energy spectrum.

Alfvén wave instability in a tokamak caused by trapped alpha particles with non-monotonic energy distribution is investigated theoretically. It is shown that this kind of instability is associated with perturbations, the transverse wave-length of which is of the order of the banana width of trapped alpha particles. It occurs during resonance between the Alfvén wave frequency and the bounce frequency of trapped alpha particles. The instability growth rate is of the order of the oscillation frequency multiplied by the ratio of the alpha-particle density to the plasma density.