We use computer simulation experiments to investigate the nonlinear behaviour of plasmas with a mixture of anisotropic protons and isotropie alpha particles, embedded in a static magnetic field. Specifically, we study the linearly predicted ‘stop-band’ for the propagation of the proton-produced electromagnetic ion cyclotron waves in conjunction with the energization of the heavier ions by the same waves. For this, three cases are considered: (1) proton + electron plasma; (2) proton + electron + cold alpha particle plasma, and (3) proton + electron + warm alpha particle plasma. Among the main results obtained we mention the following, (a) In the presence of significant relative He2+ concentrations (either cold or warm) all proton-produced left-polarized waves having frequencies above the alpha-particle gyrofrequency are practically suppressed, during the entire nonlinear evolution of the system, indicating that particle–wave–particle interactions are confined to the low-frequency branch of the waves, (b) The ‘remnant’ wave energy, i.e. that part of the wave energy not transferred to the particles, decreases significantly when going from case 1 to case 3. (c) Nevertheless, in all three cases, the initial proton thermal anisotropy relaxes to the same quasi-equilibrium value (≃ 1·5). (d) The cold alpha particles in case 2 are strongly heated by their non-resonant interaction with the proton-produced ion cyclotron electromagnetic waves, (e) In contrast, the initially warm isotropic alpha particles in case 3 are heated by resonant interaction with the proton-produced waves, resulting in an increase in the perpendicular energy and a decrease in the parallel energy. The physical processes involved in the collisionless interaction of these mixed protons and heavier ions (alpha particles) are discussed.

It is argued that familiar nonlinear instabilities, such as three-wave decay instabilities and scattering off quasi-modes, have reactive and resistive versions. In appropriate limits these versions correspond to fixed-phase parametric instabilities and to random phase growth in weak turbulence theory, respectively. Using a simplified model it is shown that the reactive version passes over into the resistive version when the band-width of the pump is comparable with the growth rate.

A macroscopic interpretation for the problem of Landau damping of longitudinal oscillations in a collisionless plasma is investigated by including macroscopic fluid conservation of mass, momentum, and energy. It is shown that Landau damping may be derived macroscopically by appropriate consideration of the heat flux term for a collisionless plasma. This heat flux is expressed in terms of the perturbed velocity distribution function. A possible form of an equivalent complex thermal conductivity is postulated for a collisionless plasma. Both temporal and spacial damping are discussed.

In part 1, a model problem for collisional relaxation in velocity space was constructed, and a series solution suitable for small times was obtained. In the present paper, a series suitable for large times is obtained, and further properties of both series are investigated.

Nonlinear behaviour of azimuthally symmetric compressional hydromagnetic waves propagating along a cylindrical cold magnetized plasma-filled waveguide is investigated. A nonlinear Schrödinger equation describing the nonlinear evolution of such waves is derived. Numerical evaluation of the dispersive and nonlinear terms reveals that such waves are modulationally stable in the fundamental radial mode of propagation. Calculations are presented for the amplitude dependent frequency and wavenumber shifts.

The cross-field plasma diffusion coefficient is expressed in terms of the perturbed potential energy W by making use of the nonlinearity of orbit diffusion. The thermodynamic bound of the energy W for a current-carrying collisionless plasma has been determined consistently with four constraints: the invariance of averaged Hamiltonian, angular momentum, entropy and density. It is found that with momentum invariance the major contribution from the plasma current cancels, and the lowest upper bound of W is determined by the high-order toroidal effect coupled with the plasma current, which yields the neo-Alcator (TFTR) scaling for the energy confinement time. When neoclassical deformation is allowed in the plasma distribution, the thermodynamic bound has additional terms which come from the neoclassical source of free energy due to the bootstrap current. When the poloidal beta is larger than a certain critical value, the energy confinement time shows the effect of density saturation, and becomes proportional to the plasma current.

The theory of plasma ablation by laser irradiation of a solid target is considered when thermal conduction is weak and the absorption is dominated by inverse bremsstrahlung (the self-regulating model). Analytic solutions are identified to treat both steady and time-dependent flows in limiting cases. The intermediate behaviour is explored by numerical modelling. The models are presented for planar, cylindrical and spherical geometries with both tight and weak focused beams. A brief investigation of the applicability of analytic models to the heating of thin foil systems is also presented.

It is shown that for a plasma with ion temperature greater than electron temperature, an extraordinary electro-magnetic pump wave can parametrically decay into upper-hybrid and electron-acoustic oscillations. The threshold power flux and the growth rate of the instability are obtained. Comparison of our investigation with an earlier work and its possible application to a mirror machine is pointed out.

This paper presents a formulation of the nonlinear coupling of the electron whistler mode radiation with generalized (including higher frequencies than allowed by the magnetohydrodynamic model) magnetosonic fluctuations. A coupled set of nonlinear equations describing the interaction of the whistler wave electric field with the density and the field-aligned magnetic fluctuations of the generalized magnetosonic waves is derived and the problem of modula-tional instability is discussed. Our results have relevance to the non-thermal magnetic field fluctuations which lead to supplementary plasma heating.

The propagation of nonlinear high-frequency TM antisymmetric surface waves on a thin un magnetized plasma slab bounded by vacuum has been studied. It is found that smooth surface wave solitons due to the modulation of finite-amplitude electron surface waves by slow ion-acoustic motion exist. When the high-frequency wave propagation is modified by a purely electronic slow motion, the governing equation is a derivative nonlinear Schröd inger equation with a cusped-soliton solution.

Excitation of electron holes and electron wave pulses is investigated numerically in a single-ended plasma by computer simulation using a particle model. The transverse effects are taken into account by introducing the perpendicular wavenumber in the Poisson equation. Increase in the plasma potential in front of a plasma source, resulting from propagation of the rarefaction pulse from an end boundary, gives rise to the excitation of electron holes, while the rarefaction pulse reflects back as the compression pulse toward the boundary. The qualitative properties are in good agreement with experiment.

Ion-acoustic solitons in a collisionless plasma with adiabatic positive and negative ions with equal ion temperature and isothermal electrons are studied by using the reductive perturbation method. The basic set of fluid equations is reduced for the fast ion-acoustic wave to the Korteweg–de Vries and modified Korteweg–de Vries equation and for the slow ion-acoustic wave to the Korteweg–de Vries equation. Stationary solutions of these equations are obtained and the effect of ion temperature on fast and slow ion-acoustic solitons is investigated.

Several branches of strongly damped electromagnetic hot plasma modes have been found around the first two harmonics of the electron cyclotron frequency. They are right circularly polarized in parallel propagation, and their frequency mismatches and damping rates are linearly proportional to their parallel wavenumber, and almost independent of the plasma density when the density is sufficiently high. Details of the modes are presented.