The equation ∇×B−λB=0, where B is the magnetic field and λ is constant, is solved analytically in toroidally curved cylindrical coordinates, assuming a large aspect ratio torus.

Edge fluctuations are characterized and their associated transport is determined from Langmuir probe measurements in the ZT-40M reversed field pinch. It is found that the fluctuations have high normalized amplitudes and |ñ|/n = 0.4). There are significant contributions from magnetic perturbations acting on the equilibrium gradients. Compared to the global estimates, the fluctuation driven particle flux is large, whereas the corresponding electron energy flux is not. In the limiter shadow, the equilibrium density and electron temperature scale lengths are shorter and the fluctuation levels are higher. The fluctuation driven particle flux in the limiter shadow is 60% less than that in the plasma edge; most of the reduction is in the low frequency spectral region, which is where global MHD magnetic fluctuations are strongest.

A method for maintaining toroidal current in toroidal plasmas is discussed. The method requires application of suitably phased oscillating toroidal and poloidal voltages to the plasma resulting in a magnetic field configuration with small oscillations around some mean state. In such quasi-steady states the usual v sec limitation on discharge duration is eliminated. The current drive effect is caused by a nonlinear interaction between the toroidal and poloidal circuits that can be understood in general terms from symmetry considerations. Specific calculations of the effect are made using two models: (1) a zero-dimensional relaxation model, relevant to the reversed-field pinch, and (2) a one-dimensional resistive diffusion model (assuming slab geometry). The results for the relaxation model indicate a useful current drive effect that may be of importance for the reversed-field-pinch program.

Steady-state current sustainment by oscillating field current drive (OFCD) utilizes a technique in which the toroidal and poloidal magnetic fields at the plasma surface are modulated at audio frequencies in quadrature. Experiments on the ZT-40M reversed field pinch [Fusion Technol. 8, 1571 (1985)] have examined OFCD over a range of modulation amplitude, frequency, and phase. For all cases examined, the magnitude of the plasma current is dependent on the phase of the modulations as predicted by theory. However, evidence of current drive has only been observed at relatively low levels of injected power. For larger modulation amplitudes, the data suggest that substantial current drive is offset by increased plasma resistance as a result of modulation enhanced plasma–wall interactions. The initial experimental results and supporting theoretical interpretations of OFCD are discussed.

The importance of error magnetic fields is that, if large enough, they cause the destruction of magnetic surfaces. In this paper error fields in a cylindrical plasma are described by nonlinear tearing mode theory, which deals with plasma equilibria having concentrated currents flowing along closed magnetic field lines. Because of the small spatial scale of the current distribution, resistive diffusion is significant even for small resistivity and, in certain cases, causes instability. An energy principle exists and is discussed. This conceptual framework is used in a study of the stability of zero pressure equilibria toward spontaneous generation of error fields, relevant for the reversed field pinch program. Cylindrical Ohmic states are shown to be extremely unstable. Relaxed states (having flattened current profiles) have much better stability. Both completely relaxed states of the Taylor type and partially relaxed Robinson-type states are studied. A new class of metal–liner stabilized profiles is found, which offers one explanation for the apparent stability observed in experiments with distant conducting shells. The possibility that relaxed states have weakly stochastic magnetic field lines is discussed.