The kinetics of ions in a tokamak is analyzed on the basis of the Balescu – Lenard equation. We show that the injection of a neutral beam (acting through charge exchange with the plasma) produces a population of high energy ions. The global energy increase is evaluated.

We observe radial expansion of an ion beam propagating along a homogeneous guide magnetic field. The beam spreading appears to arise from interactions with beam-excited resonant ion cyclotron waves. Magnitude and scaling of the expansion agree with a theory based on a resonant diffusion process.

We demonstrate that self-consistent large-amplitude longitudinal waves in a cold plasma are unstable to at least transverse perturbations, with an instability growth rate which is roughly of the order of the plasma frequency of the system. The instability statements derived here are conservative, since modes not discussed may be more unstable.

We demonstrate that a self-consistent large-amplitude circularly polarized wave, propagating in a cold plasma in the presence of a large-scale magnetic field, is unstable if the constant bulk streaming speed of the plasma is zero in the frame in which the wave depends oniy on time. The growth rate is of the order of the plasma frequency or the gyrofrequency at short perturbation wavelengths, and is proportional to the perturbation wave vector at long wavelengths. For nonzero but small streaming the instability rate increases for one streaming direction and decreases for the other. We conclude that instability is the rule rather than the exception for large-amplitude waves in a cold plasma.

We consider the nonlinear development of a long-wavelength finite-amplitude Langmuir wave. The wavenumber k0 of the initial Langmuir wave is chosen such that the three-wave decay is forbidden. We then describe the coupling of the initial Langmuir wave to Stokes and anti-Stokes Langmuir perturbations (with wavenumbers k0 ∓ ks) due to the presence of a low-frequency density perturbation of wavenumber ks. We then show that for a wide range of experimental conditions, the Stokes and anti-Stokes Langmuir waves are generated with wavenumbers well separated from k0. In order to describe the nonlinear evolution of these perturbations and the pump wave we make the static approximation for the ions and describe the high-frequency waves by three distinct wave envelopes. These coupled nonlinear differential equations are then solved exactly for a number of special cases. For the temporal evolution, we obtain periodic solutions and, when damping is included, we find a slow exponential decay of the amplitudes with a corresponding increase in the nonlinear period of oscillation. The stationary spatially varying solutions are shown to include four basic types of behaviour: periodic, solitary wave, phase jump and shock-like profiles. These latter solutions are of interest since they are obtained for zero dissipation and for a coherent wave interaction.

Incompressible magnetohydrodynamic turbulence is treated in the presence of cylindrical boundaries which are perfectly conducting and rigidly smooth. The model treated is non-dissipative and two-dimensional, the variation of all quantities in the axial direction beingignored. Equilibrium Gibbs ensemble predictions are explored assuming the constraint of constant axial current (appropriate to tokamak operation). No small-amplitude approximations are made. The expectation value of the turbulent kinetic energy is found to approach zero for the state of maximum mean-square vector potential to energy ratio. These are the only states for which large velocity fluctuations are not expected.

This paper examines the nature of plane, steady, incompressible MHD flow in a purely hyperbolic magnetic field. It is shown that in such a magnetic field the MHD equations can yield exact analytic solutions for the plasma flow. The flow has the following properties. In the far region where the conductivity is assumed to be sufficiently high so that the plasma is effectively ‘ frozen ’ to the magnetic field, the flow pattern is radial. The plasma motion is directed towards the neutral line in the incident ‘ sectors ’ and away from it in the outgoing ‘ sectors ’ with a consequent reversal in direction across the magnetic separatrices where the solution becomes singular. The plasma pressure and density in this flow are calculated and it is shown that the latter remains constant along a streamline. It is further shown that a uniform finite conductivity is not compatible with a stagnation point at the magnetic null point. However, for a parabolic increase of conductivity with increasing distance from that point, plasma flow with uniform density along hyperbolic streamlines is shown to be possible. The relevance of these flows to the magnetic field merging problem is discussed.

The parametric decay of an intense electromagnetic ordinary wave, propagating perpendicular to a uniform static magnetic field, into an extraordinary wave and a backscattered ordinary wave is investigated. Formulae are derived for the growth rate and threshold power associated with the instability in a homogeneous plasma. An analysis of the spatial amplification of the decay waves in an inhomogeneous plasma is presented. The effects of the uniform static magnetic field on the backscattering in both homogeneous and inhomogeneous plasmas are studied numerically.

Following Dungey's original magnetohydrodynamic formulation, a solution is obtained for the nonlinear evolution of a current discharge in the vicinity of a magnetic neutral line. For an ideal gas with constant conductivity and uniform mass density we obtain a particular exact solution in the limit of an initial, nearly sheet-like configuration. This particular solution implies special boundary conditions for the pressure and electric field at the surface of the conductor. If These conditions are not met, then the solution eventually breaks down before the current density becomes infinite. The time required for complete breakdown is determined by the wave propagation times from the surface of the fluid to the neutral line and by the diffusion time for the magnetic field through the fluid. For large conductivity and a small sound speed, the maximum current density achieved at the time of the solution's complete breakdown depends upon the ratio of the characteristic diffusion time to the Alfvén wave propagation time. In the limit of infinite conductivity or infinite extension of the fluid, the current density along the neutral line becomes infinite at π/23/2 times the Alfvénic scale time. At this same time the inflow Alfvenic Mach number approaches 21/2i while the outflow Alfvenic Mach number approaches infinity.

When an electron distribution drifts relative to the ions along a d.c. magnetic field, it is known that, above some critical drift velocity, a nearly field-aligned electromagnetic ion cyclotron instability may be excited. We extend the study of this instability over wide variations in plasma parameters, ion β in particular, and beyond marginal stability.Above threshold the most unstable waves propagate very obliquely to the ambient d.c. magnetic field at wavenumbers of the order of an inverse ion Larmor radius. At low ion β the critical electron drift normalized to the ion thermal velocity scales inversely as β i- ½ while, for β i>10-2, the critical drift scales as the ion thermal velocity. For the Te≈Tielectromagnetic ion cyclotron instabifity begins to have a lower threshold than the corresponding electrostatic instability at β i≈me/Mi. In a moderately high β i, homogeneous, collisionless plasma the electromagnetic ion cyclotron instability appears to have the lowest threshold of any current driven instability.

Following a prescription invoked by Clemmow for cold plasma, we show how the method can be extended for a warm plasma so that self-consistent, large-amplitude, nonlinear waves can be obtained in an otherwise homogeneous, stationary system. Results are given for situations in the presence of an imbedded constant magnetic field. The relationship of phase and amplitude for such waves is more complex than in the cold plasma since the resultsobtained depend to a surprising degree on the form of the distribution functions invoked for the warm plasma, as we demonstrate by specffic example. We have pursued this problem for two reasons: first, Clemmow has noted that the need has arisen for a detailed investigation of the behaviour of large amplitude waves in plasma; secondly, the self- consistent, large-amplitude waves catalogued by Clemmow in the case of a cold plasma, have recently been shown to be highly unstable. The question then arises of a possible stabilizing influence in the case of a warm plasma. In this paper we investigate the first part of this problem: construction of self-consistent waves in warm plasma.

The jump conditions for MHD shock waves in partly ionized gases and for transverse ionizing shock waves in neutral gases are obtained in explicit forms suitable for calculation. The fractional ionization behind the shook front is determined by assuming the plasma reaches Saha ionizational equilibrium. Solutions to the MHD jump equations are calculated for geometries ranging from transverse to switch-on. Switch-on shock jump solutions are compared with experimental observations of switch-on shock waves in partly ionized hydrogen plasmas. Numerical solutions are presented for transverse ionising shock waves in hydrogen, using the pre-shock electric field as a variable parameter, and the modes of propagation of such shook waves are examined in detail. Ionization is found to play a significant role in medium shock speed behaviour, particularly in determining the density jump.

Finite Larmor radius corrections may be significant in plasma stability theory, and the geometry of the cylindrical pinch is appropriate for theoretical development. The study presented here is limited to calculation of the perturbation of the energy of a particle by a normal mode disturbance. This is found to be complicated when terms proportional to the square of the Larmor radius are retained. It is concluded that stability theory becomes identical with drift wave theory in complex geometry.

The cylindrical MHD equilibrium equation is formulated in a manner suitable for numerical computations which require the application of a constraint. In this formulation a uniqueness theorem is proved for a free boundary equilibrium with a specified total current. Uniqueness is independent of the details of the current density and merely requires that the total current is compatible with the current density. Two uniqueness theorems for diffuse plasmas are also presented. Four free boundary examples are studied with a variety of constraints applied.

By Whitham's method of averaged Lagrangian developed by Dysthe, two coupled nonlinear Schrödiriger equations are obtained for the evolution of the amplitude of two plane polarized transverse waves in a cold plasma, both propagating in the same direction. Relativistic corrections are included and amplitude-dependent frequency shifts are derived. It is found that two transverse waves are modulationally unstable. The relativistic terms play an important part in this instability.