The problem of confinement and stability of a plasma enveloped by the magnetic field of a line multipole is considered. An energy method is used to find the increment in potential energy when the configuration is given a small displacement. The frequency and modes of oscillation are found in a particular example.

It is shown that the concept of subdynamics introduced by Prigogine, George & Henin, and extended by Balescu & Wallenborn, can be generalized nontrivially to systems submitted to time-dependent external fields. The distribution vector of the system is split into two components by means of a time- dependent projection operator. Each of these obeys an independent equation of evolution. The description of the evolution of one of these components (the superkinetic component) can be reduced to a kinetic equation for a one-particle distribution function. It is shown that, when the external field vanishes for all times t ≤ t0, and if the system has reached a (field-free) equilibrium (or a ‘kinetic state’) at time t0, then for t ≥ t0 the kinetic equation derived here provides an exact and complete description of the evolution. A general expression for the nonlinear response of the system to the external field is derived.

The general theory developed in part 1 is illustrated for a plasma described by the weak-coupling (Landau) approximation. The kinetic equation, valid for arbitrarily strong external fields, is written out explicitly.

The dispersion relation for a collisionless moving electron plasma, when the direction of motion is along the magnetic field, and that of the wave propagation normal to the magnetic field, is analysed. It is shown that in small magnetic fields the ordinary wave develops a new band of backward waves below the plasma frequency. When the frequency of the wave is higher than the plasma frequency, the effect of the motion of the plasma is identical to a deviation of the direction of propagation.

The quasi-linear concept of plateau formation along resonant diffusion surfaces is compared with the time evolution of the electron distribution function during a computer simulation experiment of whistler-mode waves in unstable plasmas. It is found that, as the wave intensities grow, plateau formation does indeed occur, with the distribution function becoming constant along diffusion surfaces at the time when wave intensities maximize. Following the formation of the plateaus, both the wave intensities and the slope of the distribution function along diffusion surfaces oscillate in a manner suggesting msh;mode coupling. Tbe slope of the distribution function along diffusion surfaces, which controls the linear wave growth rate, also gives good predictions of the sign of the actual wave growth rate during the experiment.

For a laser-driven fusion plasma dense enough to absorb the fusion particles, the slowing down of the reaction products and of their cascade of recoils is calculated (treating discrete energy loss in a collision correctly). The occurrence of reactions between the slowing-down particles and ambient ions is also calculated. The products of these reactions are in turn followed, through as many iterations as necessary. Illustrations are given.

It is shown that an equilibrium of a magnetoplasma with a small separatrix angle at the magnetic neutral point possesses a greater magnetic energy than its corresponding equilibrium with a large separatrix angle. Hence, it is energetically possible for a configuration with two oppositely directed magnetic fields in contact to proceed to a potential field through the process of field line reconnexion. The excessive magnetic energy would be released into kinetic and thermal energies.

Equilibrium solutions, which represent configurations of a magnetoplasma with the geometry of double-inverse-pinch, are presented.

The theory of scattering by charged particle density fluctuations of a plasma is developed for the case of zero magnetic field. The source current is derived on the basis of, first, a three-wave interaction between the incident and scattered electromagnetic waves and one electrostatic plasma wave (either Langmuir or ion-acoustic), and secondly, a synchronous interaction between the same two electromagnetic waves and the discrete components of the charged particle fluctuations. Previous work is generalized by no longer making the assumption that the frequency of the electromagnetic waves is large compared to the plasma frequency. The general result is then applied to incoherent scatter, and to scatter by strongly driven plasma waves. An expansion is carried out for each of these cases to determine the lower order corrections to the usual high-frequency scattering formulae.

An inhomogeneous plasma column surrounded by a glass wall is described through full first order in temperatures Te and Ti using a complete electromagnetic treatment. We study the response of this system to a purely TE wave with K perpendicular to the axis. Comparison with existing theories and experimental results is made in the electron–wave domain (ions play no role) with zero steady magnetic field, i.e. in the case of temperature (Tonks-Dattner) resonances. Perhaps surprising at first sight, there is poor agreement with experiment at low density, the classic T½e theory (scalar perturbed pressure approximation) giving far better results. Simple arguments concerning the different levels of approximation in the description of the longitudinal k2 enable us to distinguish the crucial difference existing between a scalar pressure and a complete T description and to understand this result. We generalize these findings, demoastrating that a description is always more realistic than a one in the range ωpe<ω.

Electromagnetic waves propagating transverse to an external magnetic field in a high-β (β being the ratio of the kinetic pressure to the magnetic pressure) plasma become unstable through purely growing modes when β∥e, (electron β parallel to the magnetic field) exceeds a certain minimum value β∥*. For J ≦ 2 (J being the distribution index), the region of instability consists of a single band of unstable wavenumbers k, whereas for J ≥ 3 more than one unstable wave number band may exist. The growth rates are largest for J = 0, and tend to decrease as J increases. The presence of hot ions increases the instability region by exciting a low-frequency instability. This instability gets excited at considerably lowered values of β‖e, and has growth rates of the order of ion cyclotron frequency. The effect of T‖i/T‖e and T‖e/T⊥e is destabilizing, whereas that of T⊥i/T⊥e is stabilizing.

The problem is considered of the analytical calculation of the fluctuation level of the collective electric field in the case of a collisionless non-dissipative plasma subject to a reactive marginal instability. The existence of this instability only depends on the negative sign of the real part of the dielectric constant e and is not related to the dispersive or dissipative effects described by the frequency dependence or the imaginary part of c. A typical example is given by the non- resonance two streams instability with a symmetric distribution function. In this situation the methods of the thermodynamics of Vlasov systems can be applied to calculate the fluctuation level connected with the instability, provided the Vlasov system is near enough to the marginally stable state and the effect of mode coupling can be neglected (at least for a certain time). In the linear limit, the unstable equilibrium is associated with a minimum of the entropy. When the instability develops new nonlinear terms appear in the dielectric coefficient c, related to the inhomogeneization of the system associated with the growing collective field. These nonlinear terms counterbalance the negative sign of the linear part of c, leading to a saturation of the instability. A neighbouring inhomogeneous equilibrium with long wavelength is then realized, which corresponds to a maximum of the entropy and is stable (under the assumed approximations). The corresponding electrostatic potential is proportional to u−uc, where u is the velocity corresponding to the maxima of the two-stream distribution and uc is the critical value of u for the onset of the instability. The results of the thermodynamic method for the neighbouring equilibria are compared with those obtained by solving the stationary Vlasov equation with conventional analytical methods or with computer calculations.