J. B. Taylor

Plasma Diffusion in Two Dimensions

Diffusion of plasma in two dimensions is studied in the guiding center model. It is shown that in this model diffusion always exhibits the anomalous 1/B variation with magnetic field. The velocity correlation function and the diffusion coefficient are calculated in detail using functional probabilities. In addition to the 1/B field dependence, the diffusion coefficient is unusual in that it depends weakly on the size of the system. These theoretical results are compared with those from computer experiments and their significance for real plasma is discussed.

Some Stable Plasma Equilibria in Combined Mirror-Cusp Fields

The problem of equilibrium and stability of plasma confined in certain magnetic fields of combined mirror‐cusp form is discussed. These fields have the properties that they are nowhere zero and everywhere increase toward the periphery. Attention is drawn to the importance of the existence of closed surfaces of constant |B|—the magnetic isobars. The conditions for plasma equilibrium are derived and interpreted; then by exploiting the existence of closed magnetic isobars certain low‐β confined equilibria are constructed. These equilibria are shown to be stable according to the fluid (double adiabatic) energy principle and according to the small Larmor radius limit theory. A direct proof of stability against motions which preserve the magnetic moment is given. These equilibria have the property that there is no current along lines of force so that they are also immune to several drift instabilities.

GRAVITATIONAL RESISTIVE INSTABILITY OF AN INCOMPRESSIBLE PLASMA IN A SHEARED MAGNETIC FIELD

The gravitational resistive instability analysed by Furth, Killeen, and Rosenbluth and subsequent authors is examined from a new point of view, which brings out the connection with ordinary Rayleigh‐Taylor instability and thermal convection. In contrast to the modes found by earlier authors, which are either sharply localized in the vertical direction or require a boundary layer, it is shown that coherent motions of arbitrary vertical extent can occur. These alternative modes are derived by first considering a simpler but related model in which resistivity is concentrated at the ends of a system of finite length. This analysis shows that such systems may be unstable even if they satisfy the Newcomb criterion. The new resistive modes do not have the usual periodic dependence along the horizontal direction of the main field, but have finite length and represent convective rolls which are twisted to conform to the field lines. The relation of these new modes to the original periodic localized modes is examined.

Influence of equilibrium flows on tearing modes

Early investigations of resistive instability assumed that the plasma was at rest. However, recent work showed that the influence of the natural diffusion velocity (v∼η/a) on resistive tearing modes was important even in the limit η→0. Here, the effect of a more general velocity, of the same order as the natural resistive diffusion velocity, but otherwise arbitary, is investigated. It is found that as η→0 the effect on the stability threshold is finite and independent of the velocity except for its sign. Hence, the threshold is discontinuous at v=0. There is an additional effect of velocity on modes of finite growth rate which may be stabilizing or destabilizing according to the sign and magnitude of the velocity. The present calculations of these effects agree well with numerical simulations of tearing modes.

Maximum Plasma Pressure for Stability in Magnetic Fields with Finite Minima

The maximum plasma pressure is discussed for stable containment in magnetic fields that possess a nonzero minimum in field strength, (minimum‐B fields or magnetic wells). The basic limitations are ones on the pressure gradient and are calculated exactly for a special class of equilibria and more generally by an expansion procedure based on a shallow‐well approximation. Transcribed into estimates of the critical pressure itself, these results indicate a maximum pressure equal to the depth of the magnetic well. If B1 is the field strength at the largest closed |B| contour and B2 the field strength at the lowest point of the well, then p⊥max ≃ ½(B12 − B22).

Magnetic Moment Under Short‐Wave Electrostatic Perturbations

In the presence of an electrostatic wave the quantity μ0 = v⊥2/B is no longer an approximate invariant, contrary to the conclusion of earlier authors. The real invariant is calculated and an anomaly in minimum‐B stability theory is thereby removed.

Fluctuations in guiding center plasma in two dimensions

Statistical mechanics is developed for a two‐dimensional guiding center plasma. Because there is no kinetic energy associated with guiding center motion, this development is unconventional. Thermal equilibrium is discussed, and an interesting limiting case is noted. Using the random phase assumption, a kinetic equation for the density fluctuations is obtained, which has thermal equilibrium and its limiting form as the only stationary states. However, despite the phase averaging this kinetic equation is reversible and when disturbed the system oscillates about equilibrium. Similar oscillatory behavior appears in the microscopic correlation function of the fluctuations, and the oscillation frequencies are obtained explicitly; however, these oscillations do not significantly change the macroscopic diffusion coefficient derived earlier by McNamara and Taylor.

PLASMA FLUCTUATIONS AND CONVECTIVE MODES.

The electric field fluctuations in an inhomogeneous plasma are calculated directly, using a test particle method, and the result interpreted in terms of convective modes. This serves to place the usual convective mode picture on a more secure basis.