Particle and energy conservation relations appropriate to drift and MHD ordering are derived and simplified in the MHD case by exploiting an invariant of guiding-centre motion existing when E. B = 0. An MHD perturbation calculation is made of the local average density and energy rates of change induced by a wave of general transverse-electric type in an inhomogeneous plasma. The resulting expressions, which incorporate the effect of equilibrium electric field on zeroth-order trajectories, are of striking simplicity. In the drift-ordered limit their divergence from other drift results is discussed; particle pump-out in the given heating fields is seen to be much smaller than found previously.

The hydrodynamic theory of surface wave propagation in semi-infinite homogeneous isotropic plasma is considered. Explicit linear surface wave solutions are given for the electric and magnetic fields, charge and current densities. These solutions are used to obtain the well-known dispersion relations and, together with the general energy conservation equation, to find appropriate definitions for the energy and the energy flow densities of surface waves. These densities are associated with the dispersion relation and the group velocity by formulae similar to those for bulk waves in infinite plasmas. Both cases of high-frequency (HF) and low-frequency (LF) surface waves are considered.

A general proof is given that in uniform magnetized plasmas described by generalized loss-cone distribution functions (loss-cone index l, thermal velocity α∥, and perpendicular spread α⊥), electromagnetic, electrostatic, or coupled-mode instabilities are insensitive to the separate values of l and (α⊥/α∥); they depend rather, on the effective thermal anisotropy Aeff ≡ (T⊥/T∥)eff-1, where (T⊥/T∥)eff ≡ (l + 1) (α2⊥/α2∥). In the case of parallel propagation this statement is limited only by the linearization assumption; in the oblique propagation case, the additional condition λ⊥/rL ≫ 1 is required (λ⊥ = 1/k⊥, where k⊥ is the wave vector perpendicular to the external magnetic field, and rL is the Larmor radius). Thus, dispersion relations and their solutions obtained by using simple bi-Maxwellian distribution functions can be used directly for the complex case of generalized loss-cone distribution functions by simply replacing the anisotropy factor, A ≡α2⊥/α2∥-1, by Aeff defined above. This result explains earlier conclusions that the growth rate of the whistler instability is independent of the explicit value of the loss-cone index l, for a given thermal anisotropy.

The ‘bumpy Z-pinch’ is a magnetic configuration with potential usefulness for fusion reactors. A conceptually simple version of the configuration is axisymmetric. It contains regions of closed and open field lines. In the region of closed field lines, the field line topology is much like that of a tokamak; these regions link the region of open field lines around the axis of symmetry. Assuming that the plasma spontaneously maintains an equilibrium as described by J. B. Taylor, it is possible to maintain indefinitely the regions of closed field lines by driving an axial current through the plasma in the region of open field lines. The ratio between the total axial driven current and the total poloidal current in each of the tokamak-like regions can, in principle, be made arbitrarily small, which means that the load impedance can be arbitrarily large. In addition, the configuration has the inherent virtue similar to that of the spheromak that the tokamaklike part of the plasma does not link any material coils.

The relativistic effects on strong Langmuir turbulence which arise from both relativistic plasma temperatures and high-amplitude oscillations (i.e. the oscillatory electron velocity in the wave approaches the speed of light) are considered. When relativistic effects arise primarily from high plasma temperature, a kinetic formalism is employed and a nonlinear Schrüdinger equation is derived from expansion of the Vlasov-Maxwell equations. The analysis is appropriate to either hydrogen or electron-positron plasmas, and the relativistic effect is found to provide a new type of nonlinear phase-amplitude coupling in three dimensions. A fluid treatment is used when the relativistic effects of high wave amplitudes predominate. Here, ion dynamics are ignored and the relativistic electron mass correction results in the same type of three-dimensional phase-amplitude coupling as in the kinetic analysis. A Lagrangian formalism for each limiting case is described which leads to a virial theorem from which thresholds for collapse of arbitrary wave packets can be derived.

The present computer experiment studies an explosive magnetic energy conversion in an antiparallel-fleid system of finite width where sheet current flows in the middle of the system and return current flows on both sides of the system. It is demonstrated that, initiated by local onset of anomalous resistivity, the global plasma flow grows so as to bring about the so-called fast reconnexion process that provides rapid magnetic flux transfer as well as rapid magnetic energy release. In the resulting configuration of fast reconnexion, the plasma flow drastically reverses its direction across the magnetic- field region, and the effective width of the magnetic-field region becomes rapidly reduced with time. It is found that the fast reconnexion suddenly decays when the front tip of the return-current region has just arrived at the field-reversal region.

We show that in the case of generalized loss-cone distribution functions characterized by loss-cone index l, parallel thermal velocity α∥ and perpendicular spread α⊥ sufficiently large anisotropy, (α∥/α⊥), may stabilize the high-frequency electrostatic ion cyclotron instability. The discussion refers to the oblique propagation and includes also a second, cold, ion component (besides warm isotropic electrons). Electromagnetic corrections to the quasi-electrostatic dispersion relation are also considered. Simple analytical expressions for the growth rates are derived and discussed.

We study the possibility of measuring the properties of a non-equilibrium plasma by means of a double-dipole radio-frequency probe, consisting of two small dipoles immersed in the plasma, and separated by a distance one or two orders of magnitude greater than the Debye length. This type of probe can be used either in an active or in a passive mode. The theory of both modes is presented, taking the example of an isotropic plasma in which the electrons have a biMaxwellian distribution function; the first Maxwellian represents the major population of thermal electrons, and the second a minor population of suprathermal electrons. In the active mode, one dipole emits artificial signals which the other receives; thus we study the propagation of electrostatic waves between the two dipoles. In the passive mode both dipoles are used to receive random signals induced by the natural electric microfield in the plasma, and we compute the cross-spectrum of these signals. By combining the active and passive techniques, it is possible to measure the electron density and temperature of the thermal electrons, and also to get some information about the distribution function of the suprathermal electrons.

It has been experimentally observed for some time that certain tearing modes in plasmas may be suppressed if the plasma rotates in a preferred direction. In this paper we treat the m = 0, finite-wavelength tearing mode in cylindrical geometry for a reversed-field plasma equilibrium and show that by generalizing Ohm's law to include Hall current terms, we are able to explain this effect of rotation on tearing modes. Our results agree qualitatively with earlier analysis and numerical simulations. We also show that our results are sensitive to the position of the outer conducting wall, and for wall positions sufficiently close to the plasma-vacuum interface, tearing modes may be quenched when the rotation reaches a critical value. These results follow from a boundary-layer analysis and numerical integration of the boundary-layer equations.

An analysis is presented which describes the stimulated backscattering of an electromagnetic wave with frequency large compared with the electron cyclotron frequency and the electrostacic scatterer wave frequency. The electron and ion susceptibilities provided by kinetic theory are employed in convenient approximations valid at moderate temperatures. Formulae are derived which permit calculation of the growth rate and threshold in bounded and unbounded plasmas. A numerical study of the effects of a static magnetic field on the stimulated backscattering of a carbon dioxide laser beam in a hydrogen plasma is included.

In this paper it is shown that a stationary plasma can be accelerated by a moving neutral gas only if the velocity of the neutral gas exceeds Alfvén's critical velocity. An expression for the terminal velocity of the interaction is given which shows that, in the limit of high incoming neutral gas speeds, the composite plasma is accelerated up to one quarter of the gas speed. We also discuss terminal velocities associated with the inverse problem, namely the deceleration of a magnetized plasma as a result of its motion through, and interaction with, a stationary neutral gas.

Heating of a doublet plasma by driving an axisymmetric mode at low frequency may be an attractive means for auxiliary heating. The attractiveness of the method stems from (1) the low technology required for low-frequency power sources, (2) the fact that the field-shaping coils required for doublets may also be used as the antennae for transmitting the power, (3) the possibility of transmitting the power through a resistive vacuum wall, (4) the insensitivity to the plasma temperature and density and (5) the relative simplicity of the physical model. The utility of the concept depends on the existence of a special axisymmetric eigenmode in the resistive M.HD approximation which is used. This mode has nodes through the elliptic axes of the doublet equilibrium and an antinode at the hyperbolic axis. It is remarkable that the dissipation per cycle of this mode remains large at low plasma resistivity. This paper describes a linear theory for such heating.

A pair of coupled nonlinear Schrödinger equations for transverse and longitudinal waves has been derived. The coupling resulting from equalization of group velocities drives the Langmuir waves modulationally unstable for wavelengths shorter than (mi/me)½ λD and also extends the domain of modulational instability of electromagnetic waves when relativistic effects are taken into account. Instability is found to occur also for the perturbation wavenumber domain in which both the uncoupled Langmuir and electromagnetic waves are modulationally stable. This is shown to be caused by resonant four-wave interaction l + t → l′ + t′. The growth rate of the instability is, in general, of the order of but increases to the extent of a factor (c/vth)2 near the resonance Solitary wave solutions are given. Depending on the relative values of the self-modulation and coupling coefficients, the Langmuir or the transverse or both the waves may be localized in space.

This paper considers temperature drift instabilities, modes which can be driven unstable solely by a temperature gradient perpendicular to a magnetic field. The linear electrostatic dispersion relation for a Vlasov plasma in a uniform magnetic field is used and propagation is assumed to be in the plane perpendicular to the gradient. Three temperature drift instabilities have been found. The ion temperature drift instability arises at frequencies much below the ion cyclotron frequency, the electron temperature drift instability propagates somewhat below that frequency and the lower-hybrid temperature drift instability has frequencies above the lower-hybrid frequency. The first of these modes is driven by an ion temperature gradient and is enhanced by increasing Te/Ti. The latter two modes are driven by an electron temperature gradient and are enhanced by a decreasing Te/Ti. Density gradients are considered as an additional source of free energy, and comparisons of temperature drift with density drift instabilities are made.

It is shown that convective cells can be excited by large-amplitude propagating upper-hybrid waves in a plasma. Using the two-fluid model, we obtain a coupled set of differential equations. A nonlinear dispersion relation for the modulational instability is then derived. This relation is investigated for two parameter regimes and expressions for the growth rates are obtained analytically. The limiting case of a dipole pump field is also considered. The relevance of our work in laser-produced, as well as magnetically confined, plasmas is discussed.

A study is made of a diagnostic procedure which allows one to estimate the plasma boundary shape and location in a tokamak by using numerical values of the poloidal magnetic flux function ψ in the vicinity of the plasma. In the case of the Impurity Study Experiment (ISX-B) tokamak, the magnetic sensor coils located around the periphery of the vacuum chamber provide information on ∂BR/∂t and ∂Bz/∂t, which can be processed to obtain data on ψ (and ∂ψ/∂n) through the relation BR = - R-1∂ψ/∂Z and Bz = R-1∂ψ/∂R. This leads to a Cauchy boundary condition for the Grad-Shafranov equation Δ*ψ = 0 in the region between the contour of the sensor coil locations and the plasma boundary flux surface. Numerical equilibria calculated for the ISX-B with different shapes are used to simulate ψ data along the coil locations. Random errors are added to the data to test the efficacy of two different approaches: global fitting and local fitting. Reasonably accurate results are obtained by the method of global fitting of the boundary values, which is based on the expansion of ψ in terms of eigenfunctions of Δ*ψ = 0 in a toroidal ring co-ordinate system. This approach is found to permit a relatively large random error in poloidal B field values at the sensor coils and appears to have the potential of rapidly displaying the plasma shape and location.

The problem of the penetration of a longitudinal electric field into a bounded plasma layer is considered. The method of solution is based on the representation of the disturbance in the plasma layer as that generated by an appropriate charge source in the complementary regions into which, for the purpose of the representation, the plasma is conceived to extend. The problem is solved for each of the three boundary conditions in common use: these are the specular refiexion, the absorption and the diffuse scattering boundary conditions.

A complete investigation is presented of the theory of finite-amplitude electron and ion holes which are localized BGK solutions moving near the respective thermal velocities. For their existence, the distribution functions are required to have a minimum in the resonant region.