Nonlinear magnetohydrodynamics simulation using high-order finite elements

NIMROD is a code development project designed to study long-wavelength, low-frequency, nonlinear phenomena in toroidal plasmas with realistic geometry and dynamics. The numerical challenges of solving the fluid equations for a fusion plasma are discussed and our discretization scheme is presented. Simulations of a resistive tearing mode show that time steps much greater than the Alfven time are possible without loss of accuracy. Validation tests of a resistive interchange mode in a shaped equilibrium, a ballooning mode and nonlinear activity in reversed-field pinches are described.

https://iopscience.iop.org/article/10.1088/0741-3335/41/3A/067/pdf

The NIMROD code: a new approach to numerical plasma physics

The authors study the hypothesis that sawtooth oscillations or internal disruptions are the result of a cyclic process in which the plasma core is resistively heated until the safety factor drops below unity, causing the m = 1 tearing mode to become unstable, to grow with an accelerating growth rate, and ultimately to flatten the electron temperature and safety factor profiles. A model based on this hypothesis compares favourably with experimental data from the Oak Ridge Tokamak (ORMAK) in explaining (1) the rate at which a sawtooth rises, (2) the radial dependence of the precursor and main sawtooth oscillation amplitudes, (3) the accelerating growth of the m = 1 precursor oscillations, and (4) the repetition time of the sawteeth. The heat lost from the central region during the internal disruption is found to transport diffusively through the exterior plasma with a conduction coefficient that agrees within a factor of two with the value inferred from the observed electron power balance.

Internal disruptions in Tokamaks

Five different codes have been used to simulate the identical problem in reversed‐field pinch (RFP) dynamics using the resistive magnetohydrodynamic (MHD) model in three dimensions with the same set of initial and boundary conditions. Three codes are compressible, while two are incompressible. The assumption of incompressibility was made in the spirit of reducing the model so that, for example, the codes would run faster while retaining the relevant physics. The results show that the three compressible codes agree quite well with each other and the two incompressible codes agree with each other also, but the compressible and incompressible models show qualitatively different behavior. Most importantly, for a certain set of boundary and initial conditions, the compressible codes predict field reversal maintenance while the incompressible codes do not. Thus compressibility is an important feature of RFP physics. This is in contrast to tokamak physics where the strong toroidal field enforces incompressibility at low poloidal beta.

Compressibility as a feature of field reversal maintenance in the reversed‐field pinch

An implicit algorithm for compressible three-dimensional magnetohydrodynamic calculations

A pseudospectral algorithm for three-dimensional magnetohydrodynamic simulation

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A pseudospectral algorithm for three-dimensional magnetohydrodynamic simulation