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Defining Validation Metrics for Non-linear Resistive MHD Simulations of the MST RFP

Author: Joshua A. Reusch
Requested Type: Poster Only
Submitted: 2012-12-07 16:05:04

Co-authors: J.K. Anderson, D.J. Den Hartog, C.B. Forest, J.S. Sarff, D.D. Schnack

Contact Info:
University of Wisconsin - Madison
1150 University Ave.
Madison, WI   53706
USA

Abstract Text:
In recent years, extensive high-resolution, single fluid, cylindrical, 3D resistive MHD simulations of the Madison Symmetric Torus (MST) reversed-field pinch (RFP) have been performed at experimentally relevant Lundquist numbers (S~4x10^6). The ability to perform these simulations at experimentally relevant parameters provides a good scenario for code validation, or direct comparison of the simulated plasma to the observed plasma. This is significant as the low safety factor in the RFP allows for a large number of resonant magnetic perturbations that non-linearly couple in ways that dramatically alter the time evolution of the magnetic equilibrium and make high Lundquist number simulations challenging. Qualitatively, the simulations, which are primarily zero-beta simulations performed with the DEBS code, now reproduce many of the features of the MST discharge with striking accuracy. In particular, the long timescale evolution of the magnetic equilibrium is well reproduced, including sustainment of the equilibrium against resistive decay via the MHD dynamo as well as the sharp, quasi-periodic bursts of MHD activity known as sawteeth. Sawteeth are a characteristic feature of the standard discharge in MST and have a limit cycle behavior that consists of three distinct phases: a phase of slow growth of the core resonant m=1 tearing modes, a fast rise phase (known as the sawtooth crash) in which all of the internally resonant modes are observed to rapidly increase in amplitude and non-linear coupling of the edge resonant m=0 modes to the core resonant m=1 modes leads to the flatting of the current density, and a recovery phase in which the core resonant modes reach a cycle minimum. This limit cycle has not only been reproduced in simulation, but is now seen with a period and sawtooth crash duration similar to that seen in MST discharges. Furthermore, the simulated magnetic mode spectra are similar in shape and time evolution to the measured values, and the m=1 mode amplitudes are within a factor of two of those seen on MST. While all of this suggests the simulations are doing a “good job” of reproducing the experimental results, no comprehensive quantitative definition of what “good” means has been attempted. To this end, we have begun constructing a validation metric to asses, in a well defined way, how well the simulations are reproducing the MST plasma and what can be done to improve those simulation. A direct comparison of sawtooth ensembled data from high Lundquist number simulations (~20 sawteeth) to experimental data from 400kA MST discharges (~2000 sawteeth) will be presented as well as initial considerations and framework for a quantitative validation metric. This work supported by the U.S. D.O.E. and the CMSO.

Characterization: 2.0

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