The paper basically is a review of a number of studies devoted to the theory of nonlinear motions of plasma under conditions where collisions between particles do not play a determining role.The problem is formulated in the introduction. It concerns the evolution in time of an initial perturbation of finite amplitude. The resulting physical picture will depend on these competing processes: nonlinear increase of wave steepness, dispersion, absorption and instability. In a number of cases where adsorption and instability are insignificant, it is possible to obtain an idea of the character of the nonlinear motions by applying the appropriate linear “dispersion law”.The second Section presents certain specific types of nonstationary nonlinear motions permitting exact mathematical solution, namely: nonlinear oscillations of electrons at zero temperature, nonlinear motion of plasma across a strong magnetic field, and ion waves of finite amplitude in non-isothermal plasma where pi ≪ pe. In a number of instances, evolution of the initial perturbation leads to the formation of a multi-component current, some peculiarities of which are discussed in the third Section. In the next Section stationary nonlinear waves are described, i.e. waves not changing their form with time. In a particular case they are the so-called “solitary waves”, similar to waves on the surface of heavy liquid in a channel of finite depth. The possibility of the existence of such waves requires linear laws of dispersion of a specific character. The possibility of “solitary” waves of rarefaction is pointed out.The question of absorption of waves in rarified plasma is then discussed. An approximate “quasi-linear” method is developed which permits the kinetic considerations in the absorption of waves of finite amplitude to be simplified. The method consists in the representation of the distribution function f(r, v, t) as a sum of rapidly and slowly varying terms. In the equation for the slowly varying term a quadratic average effect of fast oscillations is taken into consideration. This method is applied to two particular problems: the absorption of Langmuir electronic oscillations (in the limit of very small amplitude the equation for wave-damping goes over into the well-known formula for the so-called “Landau-damping”), and the cyclotronic absorption of transversely polarized waves which propagate along the constant magnetic field.In the last section some types of instabilities of non-linear motions are shown. In addition to the instabilities associated with the multi-component motion, it is shown that waves in a magnetic field (in particular, solitary waves) are unstable if their amplitude exceeds a certain critical value which decreases as the plasma temperature decreases.

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Alfvén cascade (AC) eigenmodes excited by energetic ions accelerated with ion-cyclotron resonance heating in JET reversed-shear discharges are studied experimentally in high-density plasmas fuelled by neutral beam injection (NBI) and by deuterium pellets. The recently developed O-mode interferometry technique and Mirnov coils are employed for detecting ACs. The spontaneous improvements in plasma confinement (internal transport barrier (ITB) triggering events) and grand ACs are found to correlate within 0.2 s in JET plasmas with densities up to ∼5 × 10 19 m −3 . Measurements with high time resolution show that ITB triggering events happen before 'grand' ACs in the majority of JET discharges, indicating that this improvement in confinement is likely to be associated with the decrease in the density of rational magnetic surfaces just before q min (t) passes an integer value. Experimentally observed ACs excited by sub-Alfvénic NBI-produced ions with parallel velocities as low as V NBI ≈ 0.2 · V A are found to be most likely associated with the geodesic acoustic effect that significantly modifies the shear-Alfvén dispersion relation at low frequency. Experiments were performed with a tritium NBI-blip (short time pulse) into JET plasmas with NBI-driven ACs. Although considerable NBI-driven AC activity was present, good agreement was found both in the radial profile and in the time evolution of DT neutrons between the neutron measurements and the TRANSP code modelling based on the Coulomb collision model, indicating the ACs have at most a small effect on fast particle confinement in this case.

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*) Здесь мы сразу ограничиваемся «газовым» приближением, т. е. считаем шгазму почти идеальным газом, что справедливо, если дебаевский радиус ионов (электронов) значительно превышает среднее расстояние между частицами. Однако ряд результа-тов по устойчивости, относящихся, в особенности, к магнитогидродинамическому приближению, имеет более широкую область применения.