The convection mode in a collisional plasma is investigated, with the inclusion of electromagnetic effects. It is shown that a dissipative instability can occur. The relationship to several well-known modes as well as applications to typical low-temperature plasmas are discussed.

Our study of the relationship between shock structure and evolutionarity is extended to include the effects of dispersion as well as dissipation. We use the derivative nonlinear Schrödinger-Burgers equation (DNLSB), which reduces to the Cohen-Kulsrud-Burgers equation (CKB) when finite ion inertia dispersion can be neglected. As in our previous CKB analysis, the fast shock solution is again unique, and the intermediate shock structure solutions are non-unique. With dispersion, the steady intermediate shock structure solutions continue to be labelled by the integral through the shock of the non-co-planar component of the magnetic field, whose value now depends upon the ratio of the dispersion and dissipation lengths. This integral helps to determine the solution of the Riemann problem. With dispersion, this integral is also non-zero for fast shocks. Thus, even for fast shocks, the solution of the Riemann problem depends upon shock structure.

A one-dimensional model explaining the mechanism of excitation of electrostatic fields by linearly polarized radio-frequency waves in a plasma layer is presented. It is shown that the ponderomotive and driving forces influence this process strongly; however, these forces act at different times when a wave front passes through the plasma. We consider a semi-infinite plasma, and a plasma layer with and without current. It is observed that near to the plasma boundaries, where the electric field is large, there arise amplitude field oscillations, which are slowly exponentially damped in space. It is shown that the physical processes arising near the boundary x = L are similar to those at the boundary x = 0. It is seen that the current in the plasma block excitation at the boundary x = L.

A generalized Lorentzian (kappa) particle distribution function is useful for modelling plasma distributions with a high-energy tail that typically occur in space. The modified plasma dispersion function is employed to study the instability of ion-acoustic waves driven by electron drift in a hot isotropic unmagnetized plasma modelled by a kappa distribution. The real and imaginary parts of the wave frequency ω0 + ιγ are obtained as functions of the normalized wavenumber kλD, where λD is the electron Debye length. Marginal stability conditions for instability are obtained for different ion-to-electron temperature ratios. The results for a kappa distribution are compared with the classical results for a Maxwellian. In all cases studied the ion-acoustic waves are strongly damped at short wavelengths, kλD ≫ 1, but they can be destabilized at long wavelengths. The instability for both the kappa and Maxwellian distributions can be quenched by increasing the ion-electron temperature ratio Ti/Te. However, both the marginally unstable electron drift velocities and the growth rates of unstable waves can differ significantly between a generalized Lorentzian and a Maxwellian plasma; these differences are also influenced by the value of Ti/Te.

Plasma sources are used to control spacecraft potentials and, in general, to improve the electrical contact between a charged body and the space plasma. From this point of view, they have been proposed in connection with conducting tethers in space to increase current capability and to allow the use of such tethers for power generation and/or propulsion. In this paper we address the problem of the interaction of a plasma source with the ambient plasma. The source is supposed to be positively charged with respect to the ambient. A self-consistent fluid model is developed to obtain a description of the interaction in the collisionless case. The interaction, which appears to be mainly characterized by the presence of a double layer, is discussed in terms of the ratio between source density and ambient plasma density and the value of the polarizing potential. The current-voltage characteristics of the system are then determined.

The theory of linear interaction between internal kink modes and fusionproduced high-energy alpha particles in a toroidal plasma is extended by including finite-banana-width corrections to the alpha dynamics. An important implication of the theory for the stability properties of kink modes is that the finite-banana-width effects increase the value of the poloidal alpha beta required to attain the stable domain of operation as well as that required to excite the high-frequency fishbone instability. Furthermore, these effects lead to a reduction in the instability growth rate in both the low- and high-frequency unstable regimes.

We develop an (r, k) phase-space description of waves in plasmas by introducing Gaussian window functions to separate short-scale oscillations from long-scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation in an inhomogeneous and time-varying background plasma, we first discuss the proper form of the current response function. In analogy with the particle distribution function f(v, r, t), we introduce a wave density N(k, r, t) on phase space. This function is proved to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible.

The time scales and efficiency of plasma heating by resonant absorption of Alfvén waves are studied in the framework of linearized compressible and resistive magnetohydrodynamics. The configuration considered consists of a straight cylindrical axisymmetric plasma column surrounded by a vacuum region and a perfectly conducting shell. The plasma is excited periodically by an external source, located in the vacuum region. The temporal evolution of this driven system is simulated numerically. It is shown that the so-called ‘ideal quasi-modes’ (or ‘collective modes’) play a fundamental role in resonant absorption, and affect both the temporal evolution of the driven system and the efficiency of this heating mechanism considerably. The variation of the energetics in periodically driven resistive systems is analysed in detail for three different choices of the driving frequency, viz an arbitrary continuum frequency, the frequency of an ideal ‘quasi-mode’, and a discrete Alfvén wave frequency. The consequences for Alfvén wave heating of both laboratory plasmas and solar coronal loops are discussed.

We study linear wave propagation in the case of equal-mass plasmas. We show that the special symmetry of such plasmas simplifies the problem and causes the disappearance of well-known phenomena such as Faraday rotation and whistler wave modes. We exploit the Symmetry of the problem to derive analytical expressions for wave propagation for various fluid models of the plasma. We also find which distribution functions will retain the symmetry properties of the fluid models.

A representation of the physical fields as functions on (k, ω, r, t) phase space can be based on Gaussian windows and Fourier transforms. Within this representation, we obtain a very general formula for the second-order nonlinear current J(k, ω, r, t) in terms of the vector potential A(k, ω, r, t). This formula is a convenient starting point for studies of coherent as well as turbulent nonlinear processes. We derive kinetic equations for weakly inhomogeneous and turbulent plasmas, including the effects of inhomogeneous turbulence, wave convection and refraction.

The dispersion equation for parallel whistler-mode propagation in a hot anisotropic plasma is analysed numerically in both weakly relativistic and nonrelativistic approximations under the assumption that wave growth or damping does not influence the wave refractive index. The results of this analysis are compared with the results of an asymptotic analysis of the same equation, and the range of applicability of the latter results is specified. It is pointed out that relativistic effects lead to a decrease in the range of frequencies for which instability occurs. For a moderately anisotropic plasma (T⊥/T‖ = 2) relativistic effects lead to an increase in the maximum value of the increment of instability.

The resonant characteristics of an incompressible ideal MHD fluid are highly structured. To help expose this structure, an equivalent electrical analogue of the MHD system is developed. The model, in the form of a transmission line, makes it possible to identify a number of new and important concepts, one of which is the effective impedance. This in turn enables entire regions of MHD fluid to be replaced with equivalent impedances. When fully exploited, the model also provides a more consistent interpretation of the spectrum of ideal MHD. The discrete Alfvén modes are found to be highly degenerate, while the transition to a discontinuous profile is accompanied by a redistribution of an uncountably infinite number of ‘poles’ from the continuous spectrum and onto the Alfvén modes. In addition, the electrical analogue shows that within a continuously structured fluid the characteristic behaviour is not necessarily dominated by the ‘surface mode’ alone. This view is also supported by the results of a numerical simulation of the linear MHD equations. Depending on the initial conditions, the collective behaviour can have any frequency within the range spanned by the transition zone. The energy itself is monitored using a new pair of energy and flux expressions derived from a variational (Lagrangian) description of the MHD system. Again the electrical model is used to provide a physical interpretation of the individual terms within these expressions. In particular, it allows a partition of the total energy into separate kinetic- and potential-energy terms.

A perfectly conducting hot plasma in thermodynamic equilibrium is studied without taking account of the effects of collisions and viscosity. The medium is inhomogeneous, unbounded, axisymmetric and subject to a magnetic field B0 parallel to the axis of symmetry of the cylinder. Plasma equilibrium is investigated using a magnetohydrodynamic model, and the system of equations is closed with an equation of state corresponding to the adiabatic law for an ideal gas. Transformation groups are applied to generate asymptotic selfsimilar solutions for the density, pressure and magnetic field magnitudes on the equilibrium, and thus to obtain the spatial dependence of the invariant solutions since the temporal variable is eliminated. From consideration of the nature of these solutions, necessary conditions for equilibria in finite inhomogeneous media are obtained. Results are given for inhomogeneous media with finite conductivity. The degrees of inhomogeneity for pressure and density and their relations with dimensionless constants, arising from the group parameters, provide information on certain drastic changes in equilibrium temperature profiles.

Stimulated emission of ordinary plane-polarized electromagnetic waves propagating in the axial direction by a relativistic or non-relativistic electron beam is investigated using a new quantum kinetics based on the Dirac equation. The momentum and energy conservation laws and the time-reversal invariance of the transition probability are used explicitly to calculate the gain without expanding the transition rate as a power series in ħ. It is found that electroncyclotron masing occurs when the longitudinal temperature differs greatly from the transverse temperature for any beam energy. This electron-cyclotron masing is an individual-electron effect, which is not related at all to the phase bunching.

The effect of finite spectral width on the modulational instability of Alfvén waves described by the derivative nonlinear Schrodinger equation is investigated using a method developed by Alber to derive a transport equation for the spectral density. The dispersion relation for a monochromatic wave is regained for a delta spectrum. It is shown that the growth rate and domain of modulational instability diminish as the spectral width increases for both the Gaussian and uniform spectrums.