The Korteweg–de Vries equation which describes cylindrical or spherical converging ion-acoustic waves is solved numerically. Soliton-like structures are shown to be generated not only from compressive but also from rarefactive and mixed initial pulses. The velocity of the soliton-like structures is dependent on the initial pulse shape.

An incompressible, dissipative numerical code of the spectral type is used to follow the nonlinear evolution of a magnetohydrodynamic sheet pinch in two spatial dimensions. The evolution involves considerable turbulent activity in the electric current field, with the excited spatial scales ranging from the size of the containing volume down to the dissipation lengths of the magnetic and velocity fields. Strong current filamentation near magnetic X-points is observed, as is lsquo;jetting’, or expulsion of magnetofluid from the vicinity of the X-point parallel to the current sheet.

The transport properties of a turbulent plasma are investigated in the vicinity of a self-similar turbulent state (SSTS). This state plays the same role of reference as the local equilibrium for a collisional plasma. The stability of the SSTS against velocity gradients is proved. Under certain well-defined conditions a plasma- dynamical regime is established, in which the initial conditions are forgotten and the macroscopic plasmadynamical quantities obey closed differential equations. The anomalous viscosity arising in this regime is investigated in detail. This quantity is time-dependent (a feature impressed by the self-similar character of the reference state). A number of additional typically turbulent terms appear in the equation of motion: they arise from interference between flow and collisions or magnetic field.

The instability of surface wave modes in a semi infinite magnetoactive plasma with a non-homogeneous particle stream is studied. The existence of two possible mechanisms for the development of the instability: induced anomalous Doppler effect and induced Cherenkov effect is demonstrated. Related growth-rates and stability criteria are calculated.

A nonlinear dispersion relation is derived for a homogeneous, magnetized plasma by the conventional ‘ponderomotive force’ method. By using this dispersion relation, various parametric instabilities (stimulated anomalous absorptions and scatterings) are discussed. The results are compared in detail with those obtained by other authors. In the validity region of this model the results derived by previous authors can be recovered. In addition to obtaining a few instabilities which have not been published in the literature, we also find that in general (i) the ‘dipole approximation’ can give the right results for the stimulated anomalous absorption problems and (ii) the ambient magnetic field may enhance the plasma stability.

The modulation instability of small-amplitude ion-acoustic waves is investigated in three dimensions for Ti<0 (ion temperature non-zero). Relevance of results to an experiment of Watanabe is discussed. Instabilities present in this experiment are seen to be due to three-dimensional rather than thermal effects and would also appear for Ti = 0.

The present paper numerically studies a nonlinear development of the Petschek mode in a sheared magnetic field where there is a field component Bz along an X line. It is found that finite-amplitude intermediate waves, adjacent to the slow shock, may eventually stand in the quasi-steady configuration; on the other hand, the fundamental characteristics of the Petschek-mode development are scarcely influenced, either qualitatively or quantitatively, by the Bz field.

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.

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.

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.

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.

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.

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.