It is shown that an ion loss cone distribution function with m ≥ 1 becomes unstable against electrostatic waves with ω ≫ Ωp and k0 = 0 in the presence of a cold plasma population, in contrast with pure warm systems, which require m ≥ 3 for instability. This result is an extension to high frequencies, ω ≫ Ω of similar conclusions reached by Pearlstein et al. (1966) and Farr & Budwine (1968), for ω-values equal to the first few harmonics of the proton gyrofrequency.

We study five relativistic plane nonlinear waves: circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativistic Alfvén waves, linearly polarized transverse waves propagating in zero magnetic field, and finally the relativistic analogue of the extraordinary mode propagating at an arbitrary angle to the magnetic field. When the ions are driven relativistic, they behave like electrons, and the assumption of an ‘electron–positron’ plasma guides us to equations which have the form of a one dimensional potential well. Our solutions indicate that a large-amplitude super luminous wave determines the average plasma properties, and not vice versa. For example, linearly polarized waves impose a plasma number flux equal to the relativistic addition of Nc/β and NVE, where N is the density, c the speed of light, β (>1) the ratio of the phase speed to c and VE the E × B speed measured in the frame moving with speed c/β with respect to the frame in which the phase speed is measured. The implications for cosmic ray acceleration in pulsar magnetospheres are considered.

The nonlinear development of a plasma-mean system immersed in a static magnetic field B0 is investigated. The beam electrons are assumed to be streaming parallel to the direction of B0 and have a spread in the perpendicular component of the velocity. We restrict our consideration to the P instabilities which result in growing whistler waves aligned in a direction parallel to that of B0. Scaled equations describing the time evolution of these instabilities are derived under the assumptions that the beam density is small and that the resulting whistler wave is nearly sinusoidal. The perturbation of the perpendicular component of the electron velocity during the interaction can be excluded from the equation determining the wave dynamics, and then these scaled equations can be reduced to the simpler ones amenable to numerical solution which depends analytically on all the basic parameters of the problem. This solution shows that the amplitude of an unstable whistler wave first increases at the linear growth rate until the electrons are trapped and then, after overshooting, it approaches a steady state. The time evolution of the amplitude does not show an oscillation with a constant period; this results from the phase mixing enhanced by the spread in perpendicular velocities of the beam electrons.

The nonlinear Landau damping of a broad-band spectrum of electron plasma waves propagating in a plasma column is considered.

Finite geometrical effects inherent to the boundary value problem are taken into account. It is shown that nonlinear Landau damping of such a spectrum can be easily observed on a plasma column with a density of the order of 2 × 108 particles cm−3 and an electron temperature of about 3eV.

A new method using crossed laser and atom beams within a plasma is capable of determining the electron density with a spatial resolution of 1 mm and a time resolution of 2–5 nsec. The measurement is done in the forward direction of the atom beam and is to a first approximation independent of electric and magnetic fields inside and outside the plasma region. A calculation is carried out for a neutral cesium beam probing a fully ionized hydrogen plasma. It is pointed out that a laser beam can also be combined with available ion beam diagnostics.

In a layer of magnetic field aligned current, waves corresonding to the slow mode in the limit of no current are absorbed and/or reflected as soon as they enter the layer, while, under certain conditions, the waves corresponding to the fast mode do propagate through the layer.

The purpose of this paper is to demonstrate the possibility of measuring the drift velocity of a thermal plasma with an H.F. quadrupole probe. The plasma is assumed to be isotropic and collisionless. A hydrodynamic model is used without restrictive assumptions on the magnitude of the drift velocity, which can be made smaller or larger than the thermal velocity. Some curves are presented for velocities parallel or anti-parallel to the emission-reception axis of the probe.

We show how the Hamiltonian description of an ideal fluid can be used for a two fluid plasma. Translation to wave variables leads to a simple rule to obtain coupled-mode equations if the energy is known as a function of wave variables. In this context we discuss the intimate connexion between a particular dynamical model, specified by the interaction Hamiltonian, and the associated invariants of motion. By this method we derive an improved version of Zakharov's equations for Langmuir and ion sound waves with the correct invariants of motion. As a result of these corrections we find a stationary power law k−2 for the plasmon energy.

By introducing field line potentials for the magnetic induction and current line potentials for the current density, it is shown that the equations which describe a static equilibrium system, in the ideally conducting magnetohydrodynamic approximation, may be derived from two equivalent variational principles. The problem of integration is essentially that of finding a transformation of the potentials which changes one of the associated Lagrangian functions into the other. The assumption that the current density has no component in one direction of a rectangular Cartesian coordinate system leads to a new class of fully three dimensional equilibria having a plane symmetry.

Ion cyclotron waves cannot be quasilinearly stabilized in Q-machine experiments because the electron distribution function does not have time to flatten while electrons pass through the plasma volume. We invoke a turbulently dissipative (or ‘resonance broadening’) model to explain the observed steady-state mode saturation. We give a qualitative picture of the important nonlinear features and their implications for plasma heating experiments. We extend the turbulently dissipative model to give nonlinear frequency shifts and a description of the mode linewidths in steady-state experiments. Turbulent resistivity is calculated and found to be unobservably small compared to the classical value. Implications for further experiments are discussed.

This paper is a theoretical and experimental study of the propagation of longitudinal electron waves in a collisionless, homogeneous, isotropic plasma, whose velocity distribution function is a truncated Maxwellian. Using the method of residues and numerical calculation, the behaviour of the electric field is found to be in good agreement with experimental results. The plasma parameters can be deduced from the theoretical dispersion curves matching the experimental points; they are found to agree well with those measured by electrostatic probes. In conclusion, a pragmatic approach to the resolution of the plasma inverse problem is discussed.