The Strauss equations of reduced resistive magnetohydrodynamics are solved pseudo-spectrally, inside a cylinder of square cross-section. Conducting, free-slip, boundary conditions are imposed at the boundaries normal to the direction of the imposed d.c. magnetic field and net current, and periodic boundary conditions are imposed in the third direction. The emphasis is on the development of disruptions. Initial conditions are not analytical equilibria, and are characterized by wide-band noise perturbations in many Fourier modes. Typical spatial resolution is 32 × 32 × 16. At this resolution, the code takes approximately 0·7 seconds per time step on a CRAY-1 computer. Lundquist numbers are limited by the need to resolve the small-scale turbulence which develops. Disruptions are characterized by (i) a burst of kinetic fluid activity which is roughly equipartitioned with the magnetic fluctuations at the small scales, but which involves overall kinetic energies which are much less than the magnetic energies; (ii) a helical ‘m = l, n = 1’ current filament which develops out of the wide-band turbulent noise and wraps itself around the magnetic axis; and (iii) relatively mild disturbances of the magnetic field lines, at least at these low values of Lundquist number (S ≃ 100). The results are compared with those from similar codes which solve the linearized Strauss equations.

We study the influence of a weak quasi-static parallel electric field on the stability of electromagnetic plasma waves. Using an operator calculus to solve the Boltzmann-Maxwell equations we derive a dispersion relation for the electromagnetic waves. Assuming that the electrons have a loss-cone distribution, the real frequency of waves in the whistler band is not changed by the presence of the electric field. Resonant interaction damps the HF waves for propagation parallel to the electric field. In the case of opposite propagation, a new HF excitation is found at frequencies ω ≲ ωce The width of the excitation region depends on the width of the loss cone, field strength and collision frequency. This result is applied to observations of the splitting of VLF emissions under natural conditions in the magnetosphere. It is found that the observed splitting could have been caused by the presence of the weak parallel electric field of a kinetic (shear) Alfvén wave in the emission region, which is quasi-stationary compared with the growth of the observed VLF emission.

A hydrodynamic system of equations, valid in the limit in which the Larmor radius and the electron to ion mass ratio are both zero, and including the thermo-dynamic variables and the energy equation of the electrons, is used to investigate the propagation of small-amplitude waves in a collisionless heat-conducting plasma. The result is compared with that derived from the Chew, Goldberger & Low equations. It is found that for zero heat flux, the inclusion of the electron pressure does not change the number and characteristic of the modes but modifies the mirror stability criterion. In the general case, the phase speed is symmetric with respect to two axes: one parallel to the heat flux vector and the other normal to it. The heat flux generates a new mode and couples strongly the slow and fast magnetosonic modes whose wavenumber vectors have projections in the positive flux vector direction, giving rise to a new overstability whose existence does not depend on the ion anisotropy.

Particle diffusion is investigated in a strictly two-dimensional collisionless guiding-centre model for a strongly magnetized plasma. An analytical expression is presented for the entire time variation of the mean square test-particle displacement in the limit of low-frequency, strongly turbulent, electric field fluctuations. The analysis relies on an explicit integral expression for the Lagrangian autocorrelation function in terms of the Eulerian wavenumber spectrum and a time-varying weight function. Bohm diffusion is discussed by means of a simple model spectrum. The analysis applies for turbulent transport associated with electrostatic convective cells, magnetostatic cells and drift wave turbulence with the assumption of local homogeneity and isotropy in two dimensions.

The dispersion relation for magnetosonic waves in a dissipative plasma, which is penetrated by a high-frequency electromagnetic wave, is derived. Previous results are generalized and discussed.

A Hamiltonian formulation, in terms of a non-canonical Poisson bracket, is presented for a nonlinear fluid system that includes reduced magnetohydro-dynamics and the Hasegawa–Mima equation as limiting cases. The single-helicity and axisymmetric versions possess three nonlinear Casimir invariants, from which a generalized potential can be constructed. Variation of the generalized potential yields a description of exact nonlinear stationary states. The new equilibria, allowing for plasma flow as well as partial electron adiabaticity, are distinct from those found in conventional magnetohydrodynamic theory. They differ from electrostatic stationary states in containing plasma current and magnetic field excitation. One class of steady-state solutions is shown to provide a simple electromagnetic generalization of drift-solitary waves.

Nonlinear saturation effects associated with the generation of electron plasma waves by two high-frequency electromagnetic waves, beating at a frequency nearly equal to the electron plasma frequency, are studied. A fluid model including collisions, frequency mismatch and relativistic mass variation is used. It is shown that for large-amplitude driving waves a transition to chaos can occur, leading to plasma wave breakdown. The results may be relevant to the beat-wave current drive in tokamak devices and to beat-wave particle accelerators.

Through rescaling and obtaining invariant equations, we study the expansion of charged particles immersed in a time-varying magnetic field B(t) = B0(1+Ωt)–β. We develop the theory for a configuration of point particles confined in a plane with an initial cylindrical symmetric configuration. It is found that the system expands according to (1+Ωt)2β/3 for β ≤ 1 and it is conjectured that in a properly rescaled space and time, it reaches asymptotically an inhomogeneous (in space) Brillouin flow with rigid rotation at half the cyclotron frequency (ω = ½ωc). Particular attention is given to the ‘pivot’ case β = 1. It is shown then that the radius of the rescaled configuration is now dependent on the ratio Ω/ωc, and grows indefinitely with time for Ω/> 3.2–3/2;. Numerical experiments are presented which confirm these theoretical predictions and conjectures. Finally, the properties of this system are compared with those of single-particle and ‘rod’ electrostatic models.

A nonlinear model equation describing ballooning modes for β of the order of the inverse aspect ratio and including magnetic shear is derived. For the special case of circular concentric flux surfaces, we obtain an approximate dispersion relation, including finite Larmor radius effects, and show the possibility of explosive instability in the nonlinear regime. The results are shown to remain valid in the presence of a low-density hot-ion constituent.

The theory of particle aspect analysis is extended to the drift wave in the presence of an inhomogeneous magnetic field. The dispersion relation and growth rate of the wave are evaluated and discussed when the magnetic field gradient is directed opposite to the density gradient. The plasma under consideration is assumed to be anisotropic and the effects of temperature anisotropy on the dispersion characteristics and growth rate of the wave are also studied. The dispersion relation and the growth rate are evaluated for the space plasma parameters.