The detailed dynamics underlying the self-generation of magnetic flux (‘‘dynamo’’) in reversed-field pinches (RFPs) is investigated with a three-dimensional magnetohydrodynamic code. A novel energy diagnostic is used to identify the path taken in Fourier space by the poloidal magnetic field energy as it is converted to axial magnetic field energy by the dynamo. At high values of the pinch parameter, Θ, and Lundquist number, S, the dynamo can be alternatingly dominated by quasilinear and nonlinear processes in a quasiperiodic fashion. Quasilinearly, the m=1 modes can reverse the axial field by themselves. However, m=0 modes are crucial to produce the nonlinear dynamo that triggers quasiperiodic relaxations. The same causal mechanism is likely to be responsible for the experimentally observed sawteeth.

The effect of a resistive boundary and/or a distant conducting wall on a reversed field pinch is investigated with a three-dimensional magnetohydrodynamics code. Fluctuations rise with increasing distance between the conducting wall and the plasma. The enhanced fluctuation-induced vxb electric field primarily opposes toroidal current; hence loop voltage must increase to sustain the current. This increases the helicity injection rate, which is balanced by an enhanced surface loss.

The effect of aspect ratio on magnetic field fluctuations in reversed-field pinches is investigated using a three-dimensional magnetohydrodynamic code. Configurations with aspect ratios of 1.1, 2.2, and 4.4 are modeled. The results are extrapolated to aspect ratio 8.8 for comparison with the Extrap T1 experiment [Nucl. Fusion 34, 427 (1994)]. It is found that the average modal amplitudes decrease with aspect ratio. However, the spectrum broadens correspondingly, resulting in negligible effect on the magnetic fluctuation level. The computed spectrum dynamics are found to be in good agreement with experimental observations on the T1 experiment. Quantitative evaluations of the field line stochasticity indicate no dependence of the mean magnetic field diffusion rate on aspect ratio.

The linear magnetohydrodynamic stability of current-driven modes is evaluated for a reversed field pinch in which the plasma is bounded by a thin resistive shell surrounded by a vacuum region out to a radius at which a perfectly conducting wall is situated. The effects of variation of the shell resistivity and wall proximity are investigated. Growth rates of tearing modes and kink modes are calculated by analytical solution based on the modified Bessel function model for the equilibrium. Relevance to experiments is discussed.

The nonlinear behavior of the reversed-field pinch bounded by a resistive shell or a distant conducting wall is investigated with a three-dimensional magnetohydrodynamic code. Nonlinear interaction between modes enhances fluctuation levels as the conducting wall is removed. The enhanced fluctuation induced v×b electric field, which produces the dynamo effect, suppresses toroidal current, and enhances surface helicity dissipation. Thus, loop voltage must increase to sustain the current and maintain helicity balance.