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.

A consistent drift-kinetic theory is developed for the interaction of resonant particles in a relativistic magnetized plasma with HF (high-frequency) wave packets for arbitrary ratio of the gyroradius to the wavelength. Gyrokinetic equations for the plasma particles are obtained for Čerenkov and cyclotron resonances as well as for those at the harmonics of the gyrofrequency, the half-integer cyclotron resonances and those with the beats of two wave packets. The periodic parts of the distribution function for the relativistic non-uniform and non-stationary plasma are calculated.

A set of reduced ideal MHD equations is derived to investigate equilibria of plasmas with mass flow in general two-dimensional geometry. These equations provide a means of investigating the effects of flow on self-consistent equilibria in a number of new two-dimensional configurations, such as helically symmetric configurations with helical axis, which are relevant to stellarators, as well as axisymmetric configurations. It is found that, as in the axisymmetric case, general two-dimensional flow equilibria are governed by a second-order quasilinear partial differential equation for a magnetic flux function, which is coupled to a Bernoulli-type equation for the density. The equation for the magnetic flux function becomes hyperbolic at certain critical flow speeds which follow from its characteristic equation. When the equation is hyperbolic, shock phenomena may exist. As a particular example, unidirectional flow along the lines of symmetry is considered. In this case, the equation mentioned above is always elliptic. An exact solution for the case of helically symmetric unidirectional flow is found and studied to determine flow effects on the magnetic topology.

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.

The problem of ion cyclotron wave structure in EBT has been analyzed using the smallness of the inverse aspect ratio ε = a/R0 and of the inverse cavity number ε' = 1/N. The procedure is to expand in these two parameters, reducing the complete toroidal problem to a system of equations to be solved in sequence. To second order in ε and ε', this system contains two ordinary differential equations of second order and one partial differential equation with periodic coefficients in a magnetically adapted system of co-ordinates. The smallness of the mean bumpiness parameter εB reduces the problem to a single second-order differential equation which, for a parabolic density profile, is a Whittaker equation. The EM wave structure corresponds to a simple mode with only a few wavelengths across the plasma radius, permitting multi-harmonic ion cyclotron heating with interesting efficiency, as observed in experiments.

The electron distribution fonction in a particle-beam generated plasma is derived in its low- and medium-energy portion (under the first excitation threshold) from a Boltzmann equation, which contains elastic and inelastic collisional processes and a continuous source term. This equation is analytically solved and we discuss the importance of the non-Maxwellian deviations and their consequences for the determination of macroscopic values such as electron density or ‘temperature’. A numerical discussion is included for the case of an argon plasma created by a high-energy electron beam between 103 and 106 eV.

The equilibrium electron distribution in a general high-energy particle-beam generated plasma is analysed in detail by a Laplace transformation method in the neighbourhood of the first excitation threshold of the target gas, where all collisional processes, elastic and inelastic, must be taken into account concurrently with a continuous source term. Two continuity conditions for the distribution (and.its derivative) calculated below and above the first threshold, enable us to obtain an analytic representation of the macroscopic quantities such as electron temperature and density. A numerical application is made for the case of a high-energy electron beam ionizing atomic argon and the results are compared with those of the Plasma Group of Orsay.

Polarization of whistler-mode waves in a hot anisotropic plasma is considered in the two limiting cases of quasi-longitudinal and quasi-electrostatic propagation. It is pointed out that electron thermal motion never influences the phase of the propagating waves; the polarization of whistler-mode waves propagating along the magnetic field is totally independent of electron thermal motion. The deformation of polarization (in both electric and magnetic fields), of obliquely propagating whistler-mode waves could be, in principle, observed in magnetospheric conditions and thus could be used to estimate electron temperature and anisotropy. This deformation seems to be especially pronounced for the electric field polarization of quasi-electrostatic waves.

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.

Propagation of nonlinear ion-acoustic waves in a multi-component plasma with negative ions is investigated experimentally. At a critical concentration of negative ions, both compressive and rarefactive solitons are observed. The velocities and widths of the solitons are measured and compared with the soliton solutions of the modified Korteweg–de Vries equation and of the pseudopotential method. The modified Korteweg–de Vries equation is solved numerically to investigate overtaking collisions of a positive and a negative soliton. Fluid equations together with Poisson's equation are numerically integrated to simulate their head-on collisions.

MHD theory with the Hall term has been used to analyse the Alfvén resonance heating of cylindrical plasmas using axisymmetric waves excited by an antenna. An analytic expression for the antenna impedance has been derived for a simple plasma model and this is used to help interpret the computational results for small, medium and large plasmas. Compressional wave eigenmodes give large antenna resistances; however, the energy is deposited near the plasma surface. At a frequency just above each eigenfrequency, the Alfvén resonance damping is zero. Below the first eigenfrequency, the energy can be deposited near the plasma centre; however, the antenna resistance is fairly low except for medium size plasmas with a nearly constant central density. Ion cyclotron wave resonances are briefly discussed. Some general concepts relevant to the penetration of wave energy into large plasmas are presented.

Aitken's or Shanks' transformation of the exponent-modified Bessel function produces better approximations. Dispersion relations for the hybrid and Bernstein waves using these provide better thermal and parallel wavenumber corrections. They also predict more closely the evolution and mode-conversion of these waves.

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 systematic and comprehensive study of linear and nonlinear analyses of the propagation of low-frequency modes in two-ion-species plasma has been made. Two new non-propagating modes on different ion time-scales are reported. These modes are excited by nonlinear coupling with the external pump. The threshold field of the pump and the growth rates of the various modes above the threshold are also calculated. A comparison of the results with those of single-ion-species plasma shows that the non-propagating mode on the fast ion time-scale excites the oscillating two-stream instability. In addition, the mode corresponding to ωr = 0 on the slow ion time-scale becomes important nonlinearly and excites a new type of instability. It is interesting to note that the threshold electric fields excitation of these instabilities are the same.

Resistive normal-mode solutions of the MHD equations are found numerically in a smooth, non-uniform, magnetic field. The (α, S) boundary within which normal-mode solutions exist is explicitly computed, where α is the normalized wavenumber and Sthe Lundquist number. As an extension of our previous analytic results (Mok & Einaudi 1985), the damping rate of these modes is computed to a higher accuracy, and is found to have an a + bS−1/3 dependence, where a and b are independent of S.

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.

We derive the coupled-mode equations for the non-resonant interaction of three high-frequency surface waves propagating along a cold plasma column with sharp movable boundary. The plasma is then supposed to be surrounded by vacuum. Our boundary conditions take into account the effects of the presence of surface charges, as well as the movements of the boundary. The coupling coefficients are expressed in explicit forms and compared with previous results.

By numerical simulations, the dynamical behaviour of the electrons in one-dimensional double layers is studied. The simulation results show that at least one third of the electrons emitted at the low-potential boundary of the simulation system are reflected back before passing through the double layers. Such reflexion is due to (i) quasi-linear or nonlinear scattering by plasma oscillations and (ii) ambipolar potentials observed around the potential front of the localized double layer. The whole temporal evolution of the localized double layers are also presented. In particular, we attempt to explain the steepening and collapsing of the localized double layers in terms of the formula for the double-layer thickness.

The linear dispersion relation for electrostatic electron waves is analysed in some detail. A method is described which allows the dispersion equation to be solved and the attenuation rate/growth rate to be derived for waves generated by electrons flowing through a stationary plasma along the field lines of a static magnetic field. The solution is derived from three simple curves (one for each of the real and imaginary parts of the dispersion equation and one for the growth rate) and is applicable for any propagation angle relative to the magnetic field lines (below a limiting value), for any wavelength, any magnetic field intensity, any electron density and temperature and any flow speed of a beam plasma component. The effects of cyclotron resonance start to be significant at an angle from the direction of the magnetostatic field lines that depends on most of the variables mentioned, but only in one specific combination, which is the measure of the ratio between thermal velocity of the electrons and the phase velocity of the wave at the cyclotron frequency. In contrast to numerical methods, the method described here provides a parameterization of the solutions to the dispersion equation and of the growth rate. It gives an overview of the dependencies on the variables in the equation over a large part of parameter space without any other computations than those involved in adjusting scale factors.