Nonlinear dynamics of field maintenance and quasiperiodic relaxation in reversed-field pinches

Abstract

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.

Magnetohydrodynamic simulations of direct current helicity injection for current drive in tokamaks

“…This represents a MHD dynamo that is driving interior current at the expense of exterior current. It is comparable to the MHD dynamo in the reversed-field pinch, 10 but the E f -͗J͘ distribution is flipped. Here, the electromagnetic energy transport from the resonant modes is inward.…”

Numerical Studies of Magnetohydrodynamic Activity Resulting from Inductive Transients Final Report

“…However, the n=6-8 modes typically supply the nonlinear cascading channels [6]. To verify that the profile change is then the stabilization mechanism, we have computed the evolution of the rate of energy transferred from the equilibrium to the core modes [7], plus dissipation,…”

“…The evolution displays familiar characteristics of large core-resonant m=1 tearing modes interacting through m=0 fluctuations [6]. Relaxation results from correlated fluctuations of flow velocity and magnetic field that produce the dynamo electric field b v E× − = f which suppresses parallel current density in the plasma core and drives it near the edge [7]. The simplest PPCD-like effect is modeled by applying a purely poloidal electric field at an arbitrary time after saturation in a standard RFP simulation.…”

Thermal transport dynamics in the quasi-single helicity state

“…While this model is extracted from reduced MHD, it should be stressed that it is a heuristic model -useful for characterizing qualitative behavior -but is neither quantitatively accurate nor rigorous. Apart from the obvious shortcoming of reducing the spectrum to two modes, its mode coupling description is heuristic, it does not explicitly address any role played by the m ¼ 0 coupling intermediary, 19 it does not account for mode structure beyond the boundary layer effect of the shear suppression theory, 11 and does not account for 3D effects or toroidal geometry. Despite its shortcomings, it falls within the performance norms of predator-prey models used for characterizing H-mode transitions 20,21 and internal transport barrier dynamics.…”

“…(19) and (20) on the plasma current, or equivalently the poloidal component of the equilibrium magnetic field B h . This dependence has been described previously, 11,13 but those accounts did not address all sources of B h dependence.…”