The possibility of using the Vlasov fluid model to describe large ion Larmor radius effects in a Z pinch is discussed. It is shown that the Vlasov fluid formulation can be applied to the m = 0 mode, but the comparison theorem which states that systems which are MHD stable are also Vlasov fluid stable, is shown to be inapplicable in this case.

The ideal MHD equilibrium, stability, classical diffusion, effective thermal conductivity, and Ohmic heating of a zero-shear toroidal plasma configuration with a single non-planar magnetic axis of variable torsion and curvature are investigated. The plasma has a circular cross-section through which a longitudinal current density with arbitrary profile flows. In this type of magnetic configuration, the magnetic surfaces arbitrarily rotate around the magnetic axis. This magnetic toroidal configuration is of a stellarator type with a non-planar magnetic axis. The present work also covers as special cases tokamak and a magnetic toroidal plasma configuration with a magnetic axis of arbitrarily modulated curvature.

Spontaneous generation of an axial magnetic field is predicted when the usually neglected centripetal acceleration term is properly taken into account in the two-fluid equations of motion for a cylindrically symmetric imploding plasma. An order-of-magnitude calculation is presented to illustrate spontaneous generation of a reversed-field configuration in a plasma imploded by a metallic liner.

In this paper, we consider the effect of stochastic pumps on the parametric instabilities, including the pump band-width effect, the effect of the frequency mismatch and of the plasma temperature fluctuations that are induced by the fluctuations in the pump itself. Contrary to what is found in the literature, the threshold for instability can initially decrease with increasing pump band-width and reach a minimum when these effects are included. We propose a physical explanation of this minimum and point out the relationship between the thresholds for the instability of the mean energy and mean amplitude of the wave. The pump amplitude and the resulting plasma temperature fluctuations compete with the pump band-width and decrease the threshold for instability. Even for large pump band-widths, the threshold for instability for a pump with fluctuating amplitude is always lower than for the coherent one. Our general conclusion is that, in studying the effect of stochastic pumps on parametric instabilities more realistically, one has to include, in addition to the pump band-width, a number of other phenomena like imperfect frequency matching, the fluctuations induced in plasma parameters and the amplitude fluctuations of the pump itself.

The spectra and the instability criteria for the two electromagnetic wave modes previously found to exist in weakly ionized plasmas placed in an external d.c. electric field are analysed here for neon plasma for a wide range of the parameter Eo/nn. The presence of electron-atom inelastic collisions is taken into account, assuming that the electron temperature is in the range where these collisions dominantly result in atomic excitations. The linearized kinetic equations are used in combination with a previously evaluated non-Maxwellian electron steady-state distribution function appropriate for the situation in which collisional excitations are significant. For any given ratio of electron drift to thermal velocity, the wavelengths and the angles of propagation at which the instabilities are predicted to set in are determined.

An exact solution for a temporally damped sinusoidal electric field which obeys the nonlinear, one-dimensional Vlasov-Maxwell equations is given. The electric field is a generalization of the O'Neil model electric field for Landau damping of plasma oscillations. The electric field is a special case of the form found from the invariance of the one-dimensional Vlasov equation under infinitesimal Lie group transformations. The time dependences of the damping decrement, of the wave-number and of the angular frequency are derived. Use of a time-dependent BGK one-particle distribution function is justified for weak damping where, in general, it is necessary to carry out a numerical calculation of the invariant of which the distribution function is a functional.

The Chew, Goldberger & Low equations are a one-fluid system for the thermodynamic variables of the ions that are coupled to the electrons only through the electromagnetic variables. The magnitude of these variables in a collisionless plasma is re-examined in the present paper and it is found that, in the limit in which the Larmor radius and the electron-to-ion mass ratio are both zero, the current, in the plane normal to the magnetic field, is entirely transported by the electrons in the reference frame that moves with the bulk velocity. The first-order electric field contributes to the ion equation of motion with a zero-order term that couples the thermodynamic variables of both species. So the energy equation of the electrons must now be included in the equation set; to close this equation, a simple mathematical representation of the measured quasi-stationary velocity distribution function of this species is used. A two-fluid equation system in the limit in which the Larmor radius and the electron-to-ion mass ratio are both zero is then found.

A numerical study of the normal modes of a compressible resistive MHD fluid in cylindrical geometry is presented. Resistivity resolves the shear Alfvén and slow magnetosonic continua of ideal MHD into discrete spectra and gives rise to heavily damped modes whose frequencies lie on specific lines in the complex plane. Fast magnetosonic waves are less affected but are also damped. Overstable modes arise from the shear Alfvén spectrum. The stabilizing effect of favourable average curvature is shown. Eigenfunctions illustrating the nature of typical normal modes are displayed.

This paper deals with degenerate Fermi–Dirac plasmas in which transport is by quasi-particles that form a dilute gas described by the Boltzmann equation. The off-equilibrium part of the distribution function of each species is estimated by expanding it in terms of the fluid velocity of the species, relative to the plasma, and its relative heat flux vector. Expressions for the frictional forces acting between the species, consisting of a relaxation-model force and a thermal force, are obtained. These are used in a plasma dissipation formalism, yielding, for ternary partially ionized plasmas, a generalized Ohm law and an ambipolar diffusion law. The results are applied to neutron star matter, consisting of thermally ultra-relativistic electrons and non-relativistic protons and neutrons, with the mass density dominated by the neutrons. The dissipation formalism is used to obtain an expression for the magnetic force on this material.

A dispersion relation for electrostatic waves in a current-carrying, resistive, magnetized, two-ion plasma has been solved numerically for a range of parameter values. The behaviour of the resistive ion-ion hybrid instability is described and in addition a two-stream ion-ion hybrid instability is identified.

The equilibrium high-energy electron distribution in a particle beam generated plasma is calculated. The tail of the distribution, above the first excited state, is derived from a Boltzmann equation which contains inelastic collisional processes and a continuous source term. This equation is analytically solved by a Laplace transformation method and, in a numerical application for the case of an argon plasma created by a high-energy electron beam between 103 and 106eV, the branching ratios for energy deposition in ionization and excitation states are calculated. We compare the results with those of the laser group of Orsay.

It is pointed out that ambiguities arise in taking the resonant parts of nonlinear response tensors. A prescription is proposed and used to evaluate the resonant parts explicitly in terms of a covariant and gauge invariant formalism. Symmetry properties of the resonant parts are identified. The prescription used can be justified by analogy with a calculation based on QED where no ambiguity arises; it is also justified directly by classical arguments. In some standard treatments of nonlinear damping processes a necessary symmetry is not imposed. When this symmetry is imposed, the relations derived here imply that turbulent bremsstrahlung, as defined by Tsytovich et al., does not exist.

Electromagnetic cyclotron instabilities of a relativistic electron beam propagating in an external magnetic field are studied by considering electron motion inside a self-consistent electromagnetic field. When the number of electrons in a subgroup is greater than two, or when the phases are random, the linear dispersion relation obtained agrees with that of Chu et al. for a gyrotron in a ring model. When the number of electrons in a subgroup is limited to two only, the linear dispersion relation is different in that it has an instability threshold. Completely nonlinear motion is also studied using the method of Poincaré's return map, or by considering the departure rate of nearby trajectories. Stochasticity is observed in the nonlinear oscillation of the wave-particle system when a critical energy is exceeded. Physical implications for gyrotron operation are also discussed.

The problem of controlling the position and cross-sectional shape of plasmas is addressed for circumstances relevant to large tokamaks. A principle for, as well as a practical method of analysis of, this control problem is presented. The relevant elements of the tokamak system included in the analysis are the plasma, a resistive wall (vacuum chamber wall) surrounding the plasma, toroidally wound coils which also surround the plasma, as well as their associated external circuitry and a number of monitors of properties of the magnetic field in the vicinity of the plasma; the signals obtained from these monitors are used for control of power supplies which are part of the external circuits.

Electron-acoustic (EA) and ion-ion-hybrid resonance (IIHR) waves, in a multi-ion-species magnetoplasma with density gradients perpendicular to the magnetic field and the direction of wave propagation are found to be drift unstable provided the inhomogeneities exceed a certain threshold. The possibility of mode conversion between the EA and the IIHR waves is examined.

A unified approach to the kinetic theory of correlations in a plasma is presented, based on the BBKGY hierarchy. The theory is applied to a one-component plasma with the Coulomb interaction modified to include effects of the background. Closed integro-differential equations in space, momentum and time are obtained for the two-particle correlation function in both the strong and weak coupling limits. To corroborate the theory, the formalism is applied in the equilibrium limit. In the weak-coupling domain, γ ≪ 1, the time-independent analysis returns the well-known linearized Debye-Hückel result, where γ is the plasma parameter. In the strong-coupling domain with γ ≥ 1, the resulting two-particle ‘total’ correlation function exhibits decaying oscillatory behaviour for particle separation of the order of the effective interparticle range. Exponential behaviour of the correlation function found for small values of particle separation agrees with previous results of statistical mechanics.

A general KdV-type equation which covers most of the known model equations for weakly dispersive waves is investigated. First, the possible stationary localized states are discussed. When perturbed longitudinally, the perturbations can be finite and complex but should be small. In the main (second) part of the paper a necessary and sufficient stability criterion for the stationary states is derived. This is performed in two steps: A variational formulation leads to an instability region, whereas the sufficient stability criterion follows from a Liapunov functional. The stability theorem is evaluated for various models including ion-acoustic waves in plasmas and lower-hybrid cones.

A start-up method for producing a plasma in the bi-cusp field configuration of a toroidal magnetic cusp (TORMAC) is described. The method uses the radial injection and trapping of a toroidal gun plasma. Measurements of an injected plasma with a velocity of 17 μsec–1 and 4·5 × 1018 particles is presented. The plasma was observed to be stopped and trapped in an equilibrium position. A well-defined outer boundary remained stationary for 20 μsec. Particle flux distribution emanating from the cusp field lines defined a sheath having a width of 1–1·5 ion gyroradii in the poloidial field. This translates to a narrow outer boundary and a broad inner boundary based on the gradient of the poloidial field at the two radial positions. Measurements of Thomson scattering and interferometry give a Te of 15eV, a 15μsec density decay time, and a 5μsec energy decay time. These results show that this injection and trapping method is successful, and thus a higher gun plasma energy combined with a flux conserving barrier may lead to higher temperatures for testing containment in TORMAC.

To calculate the equilibrium and stability of finite aspect ratio tokamaks, even for circular and elliptical plasma cross-sections, intricate numerical methods must usually be employed, which require a fast and large computer. So far, these calculations have been carried out analytically only for infinite aspect ratio. In fact certain analytical equilibrium solutions at finite aspect ratio are known, but these do not include such important cases as elliptical cross-sections. In this paper, finite aspect ratio equilibrium solutions are derived for circular, prolate and oblate elliptical cross-sections and for a flat current profile. In addition, the problem of axisymmetric stability is studied for prolate elliptical cross-sections, the approach being almost entirely analytical.

The application of RF heating (ICRH or LHH) to a fusion plasma creates high-energy tails on the distribution function of the heated particle species. In the presence of loss regions in velocity space, e. g. due to particle drifts in the toroidal magnetic field ripple of a tokamak, the collisional pitch-angle scattering losses may be significantly enhanced. The present work assesses the importance of such RF-enhanced losses and explicit expressions are derived for the evolution of the loss fraction. In particular, for parameters typical of PLT we find that the loss fraction could rapidly reach high values.