Extended Magnetohydrodynamic Simulations of the Helicity Injected Torus (HIT-SI) Spheromak Experiment with the NIMROD Code
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A comparative study of 3-D pressureless resistive (single-fluid) magnetohydrodynamic (rMHD) and 3-D pressureless two-fluid magnetohydrodynamic (2fl-MHD) models of the Helicity Injected Torus experiment (HIT-SI) is presented. HIT-SI is a spheromak current-drive experiment that uses two geometrically asymmetric helicity injectors to generate and sustain toroidal plasmas. The goal of the experiment is to demonstrate that steady inductive helicity injection (SIHI) is a viable method for driving and sustaining a magnetized plasma for the eventual purpose of electricity production with magnetic fusion power. The experiment has achieved sustainment of nearly 100 kA of plasma current for ∼1~ms. Fusion power plants are expected to sustain a burning plasma for many minutes to hours with more than 10~MA of plasma current. The purpose of project is to determine the validity of the single-fluid and two-fluid MHD models of HIT-SI. The comparable size of the collisionless ion skin depth to the diameter of the injectors and resistive skin depth predicates the importance of two-fluid effects. The simulations are run with NIMROD (non-ideal magnetohydrodynamics code with rotation-open discussion), an initial-value, 3-D extended MHD code. A constant and uniform plasma density and temperature are assumed. The helicity injectors are modeled as oscillating normal magnetic and parallel electric field boundary conditions. The simulations use parameters that closely match those of the experiment. The simulation output is compared to the formation time, plasma current, and internal and surface magnetic fields. Results of the study indicate 2fl-MHD shows quantitative agreement with the experiment while rMHD only captures the qualitative features. The validity of each model is assessed based on how accurately it reproduces the global quantities as well as the temporal and spatial dependence of the measured magnetic fields. 2fl-MHD produces the current amplification and formation time demonstrated by HIT-SI with similar internal magnetic fields. rMHD underestimates the current amplification and exhibits a much longer formation time. Biorthogonal decomposition (BD), a powerful mathematical tool for reducing large data sets, is employed to quantify how well the simulations reproduce the measured surface magnetic fields without resorting to a probe-by-probe comparison. BD shows that 2fl-MHD captures the dominant surface magnetic structures and the temporal behavior of these features better than rMHD. In addition to the comparisons with the experiment, a detailed investigation of the rMHD and 2fl-MHD models is undertaken. lambda (mu0 J.B/B<super>2</super> and current density <bold>J</bold> are used to track the prominent structures. Both lambda and <bold>J</bold> show highly dynamic, periodic patterns with significant toroidal non-uniformities, consistent with the magnetic energy spectrum. A spheromak-like object forms only in the toroidally-averaged sense. This structure never fully detaches itself from the regions directly-driven by injectors. Parameter scans are carried out to determine the dependence of current amplification on the plasma resistivity, viscosity, injector oscillation frequency, and the ratio of injector current to injector flux. An energetics analysis based on the evolution of the MHD and Hall dynamos is presented for both models. Results of this analysis indicates a large surge of energy into the spheromak mean-field (the n=0 component) by both dynamos, followed by a steady energy transfer to the n=0 predominantly by the MHD dynamo.
- Physics