The physics of spheromak plasmas is addressed by time-dependent, three-dimensional, resistive magnetohydrodynamic simulations with the NIMROD code [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)]. Included in some detail are the formation of a spheromak driven electrostatically by a coaxial plasma gun with a flux-conserver geometry and power systems that accurately model the sustained spheromak physics experiment [R. D. Wood et al., Nucl. Fusion 45, 1582 (2005)]. The controlled decay of the spheromak plasma over several milliseconds is also modeled as the programmable current and voltage relax, resulting in simulations of entire experimental pulses. Reconnection phenomena and the effects of current profile evolution on the growth of symmetry-breaking toroidal modes are diagnosed; these in turn affect the quality of magnetic surfaces and the energy confinement. The sensitivity of the simulation results addresses variations in both physical and numerical parameters, including spatial resolution. There are significant points of agreement between the simulations and the observed experimental behavior, e.g., in the evolution of the magnetics and the sensitivity of the energy confinement to the presence of symmetry-breaking magnetic fluctuations.
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The amount of data in a mesh of biquartic elements, for example, is 16 times greater than that in the same number of standard elements or in a finite-difference grid. Moreover, for a given amount of data, high-order elements will be far more accurate with respect to MHD and anisotropic thermal conduction (Ref. 10). In addition, and similar to polynomial fitting, maxima need not lie at node locations when using cubic and quartic basis functions. There is additional computational cost in forming and solving matrices with high-order elements, however, because they are less sparse.
