Table of contents

For original paper see L. Turner, J. Maths. Phys., vol. 26, p. 991 (1985). A general scheme for Hamiltonian representation of magnetic field flow is applied to the case of helical symmetry.

A recent theoretical analysis of high- beta shots shows that the ballooning unstable region extends from the highly unstable, low shear central region to the moderate shear region of plasma. The authors have developed a simple model which incorporates the effect of general flux shapes into hot particle stabilization of ballooning modes. They have applied their model to the moderate shear region where the hot particle effect seems to be the dominant stabilization mechanism. The analysis shows that the apparent anomaly can be reconciled if a certain amount of the total energy is carried by hot particles, as in plasma, heated by neutral beam injections.

It is shown that Landau damping in space (LDS), occurring for time-periodic electrostatic waves, does not lead to any deposition of energy in plasmas. A steady-state balance and a steady-state transport of energy, momentum and particles take place both for damped and growing waves. Because of the phase interference of coherent free and forced particle oscillations, the oscillatory energy of particles increases in the direction of wave propagation; the time-averaged flow of plasma kinetic energy being constant in space for these waves, the LDS must take place for a Maxwellian plasma in order to compensate for the growth of the particle oscillatory energy in space.

Parametric interactions among three electrostatic waves in a magnetized plasma are investigated taking into account the finite Larmor radius (FLR) effect on the electron quiver velocity, which arises due to the finite wavelength of the electrostatic pump. It is found that the threshold is enhanced and the growth rates diminished. The changes in both quantities caused by the FLR effect compared with the values corresponding to the zero Larmor radius approximation are O(k₀²r_e²). Harmonic waves, the frequencies of which are the pump frequency, are also generated by shifted multiples of the electron gyrofrequency if the FLR effect is included. A higher-order parametric interaction driven by a harmonic wave is also investigated to find the threshold and growth rate for this instability.

Haeffner (1953) discovered that the isotopes of liquid mercury could be separated by an electric field, with the lighter isotopes being preferentially enriched near the anode. The authors consider the analogous problem for a gaseous, fully-ionized, binary isotopic plasma and it is demonstrated that isotopic separation occurs in the same way, i.e. the lighter isotopes are preferentially located near the anode. A previous analysis by Frie (1963) is discussed.

The problem of plasma stability concerning quasi-flute perturbations in a toroidal magnetic trap with shear is investigated. An analysis is based on a small-oscillation equation for the components of the plasma-volume element displacement obtained from the ideal MHD equation system using only the common properties of differential operators in an arbitrary stream-coordinate system and the assumption of small scale for the perturbation components transverse to the magnetic field. It is shown that in the approximation of an incompressible plasma these equations are reduced to an ordinary differential equation of second order, which is transformed to the form of a stationary Schrodinger equation. The discrete eigenvalue spectrum of this equation describes unstable states of an arbitrary toroidal system with shear and the condition of absence of this spectrum coincides with the general geometric Mercier stability criterion. The dispersion relations relating quasi-flute instability growth rate to local plasma parameters are derived. The general geometric stability criterion is generalized to the case of finite ion Larmor radius.

Fast electron acceleration and velocity diffusion are investigated in wavepackets formed by large-amplitude waves with relativistic phase velocities. In tokamaks, such waves are generated, e.g. in current drive by free-electron lasers where large-amplitude electron plasma waves or lower hybrid waves are generated. At small field intensities, the velocity diffusion in wavepackets with Gaussian-like envelopes is found to be well described by the quasilinear approximation. At large field intensities, trapping effects become important, and deviations from quasilinear diffusion are found. It is demonstrated that these deviations may have a significant effect on the velocity distribution of the electrons. A wave-induced runaway-like phenomenon of relativistic electrons is discussed.

Sawtooth activity occurs in ohmically heated tokamak plasmas even at high values of edge safety factor. This is not consistent with the predictions of transport calculations in which the resistivity is classical and the thermal conductivity is uniform. In that case q falls to unity in the centre only if the edge q is less than 3.3. Sawteeth can persist to higher values of edge q if the neoclassical enhancement to resistivity is included or the thermal conductivity increases with radius. In JET, sawteeth persist to higher values of q than would be expected even using neoclassical resistivity demonstrating that the thermal conductivity increases with radius.

The reflection and mode conversion of microwaves are investigated analytically for the case of relatively high field distortion by density and magnetic fluctuations. The polarization ratio of two extraordinary wave components is obtained. A solution of the full-wave equation is derived for the 1D cross-scattering problem. Peculiarities of cross-polarization scattered waves are discussed as well as possible applications to reflectometry of fusion devices.

In order to increase the reactor advantages of the reversed field pinch (RFP) concept, the possibility of limiting the plasma region by means of a magnetic separatrix has been discussed. However, in experiments on this type of configuration a large pressure gradient, and an associated diamagnetic current, is observed in the separatrix region. The present paper investigates the effect of such a pressure gradient on the MHD stability of the plasma. It is shown both analytically and numerically that, due to the low value of B_z near the plasma boundary, such a system is susceptible to a short-wavelength, edge-localized kink instability, driven by the pressure gradient. These instabilities are akin to the edge-localized modes encountered in high-beta, H-mode tokamak plasmas. Furthermore, while the long-wavelength branch of the m=1 mode is effectively stabilized by a close-fitting conducting wall, the edge-localized kink mode is found to be more or less unaffected by the wall, and persists even when the wall distance shrinks to zero.

Allowing for a number of assumptions and using an auxiliary function of the usual poloidal magnetic stream function, it is possible to obtain axisymmetric solutions of the ideal anisotropic magnetohydrodynamic equations for steady rotating plasmas in terms of solutions of the Maschke-Perrin equation for isotropic plasmas with temperature as a surface function.