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.

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 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.

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.

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.

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.

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.

An analysis of profile modifications in laser-plasma interactions in the presence of an externally applied constant d.c. magnetic field is presented. By considering the case of circular polarization for the incident laser light, the flow velocities and the shelf densities in the incident as well as the evanescent regions are calculated. For left-handed circular polarization, the flow velocity in the incident region is enhanced by the magnetic field, whereas the opposite occurs for right-handed circular polarization. On the other hand, the shelf density in the evanescent region is always supercritical for the former case, and for the latter case it can be either subcriticai or supercritical, depending on the strengths of the incident laser intensity as well as the external magnetic field.

Theoretical analysis for the stability of a diffusion dominated positive column between coaxial cylinders in the presence of an axial magnetic field is carried out under the assumptions of quasi-neutrality of charges and no sheath at the walls. Self-consistent infinitesimal perturbations of plasma density and electric potential, which satisfy the linearized governing equations to the same degree of approximation are used to derive the dispersion relation. The perturbations associated with aximuthal modes m ≤ 0 are stable for any gap size and plasma parameters. The stability of non-axisymmetric perturbations is studied for different gaps. It is found that the presence of inner cylinders increases the stability of a magnetized positive column and m = 2 defines the region of stability when the ratio of the radii of the inner and outer cylinders is less than 0·5. In the case of narrow gaps, higher and higher modes are excited. The minimum non-dimensional axial electric field at which the magnetized positive column between coaxial cylinders becomes unstable for different gaps is also determined.

A diffusion equation for magnetic field lines of force in a turbulent magnetic field, which describes both the random walk of a single field line and how two nearby lines separate from each other, has been obtained using standard statistical techniques. Starting from such an equation, a closed set of equations for the moments may be obtained, in general, with suitable assumptions. From such a set of equations the Kolmogorov entropy may be explicitly calculated. The results have been applied to the most interesting examples of magnetic field geometries.

The investigation of the kinetic cross-field streaming instability, motivated by the research of collisionless shock waves and previously studied by Wu et al., is discussed more fully in the present work. Since, in the ramp region of a quasi-perpendicular shock, electrons can be preferentially heated in the direction transverse to the ambient magnetic field, it is both desirable and necessary to include the effect of the thermal anisotropy on the instability associated with a shock. The present study has found that Te⊥ > Te‖ can significantly enhance the peak growth rate of the cross-field streaming instability when the electron beta is sufficiently high. Furthermore, the present analysis also improves the analytical and numerical solutions previously obtained.