Simulation of spheromak evolution and energy confinement

Abstract

Simulation results are presented that illustrate the formation and decay of a spheromak plasma driven by a coaxial electrostatic plasma gun, and model the plasma energy confinement. The physics of magnetic reconnection during formation is also illuminated. The simulations are performed with the three-dimensional, time-dependent, resistive magnetohydrodynamic NIMROD code ͓C. R. The simulation results are tracking SSPX with increasing fidelity ͑e.g., improved agreement with measured magnetic fields, fluctuation amplitudes, and electron temperature͒ as the simulation has been improved in its representations of the experimental geometry, the magnetic bias coils, and the detailed time dependence of the current source driving the plasma gun, and uses realistic parameters. The simulations confirm that controlling the magnetic fluctuations is influenced by the current drive history and by matching the gun current in sustainment approximately to the value corresponding to the eigenvalue in the flux-conserver for the parallel current in a force-free equilibrium.

Magnetic reconnection during flux conversion in a driven spheromak

“…The density is nearly constant ͑5 ϫ 10 19 m −3 ͒ for the reasons discussed in the Introduction and in Ref. 11. As discussed in the Appendix, a plasma rotation has been imposed at the boundary to approximately match the experimental observations.…”

“…Flux conversion continues at a slower rate after the strong event discussed here, eventually being balanced ͑and then dominated͒ by resistive decay later in the discharge as the mode amplitude decreases. 10,11 Examination of vector plots of the fields generated by NIMROD reveals no magnetic field nulls near the mean-field X point, which have been posited by Lau and Finn as necessary for reconnection in the resistive MHD approximation. [23][24][25] Further, field lines were examined using Poincaré puncture plots.…”

“…This anisotropy is important to modeling temperature profiles accurately, and during reconnection the relatively cold and resistive plasma on short, open field lines is important to accurate magnetic-field modeling. 10,11 Additional physics parameters used in the present calculation are listed in the Appendix.…”

“…10,11 For different SSPX shots and different NIMROD simulations, the following data are compared in Ref. 11: gun voltage and the fluxconserver edge poloidal magnetic field versus time; the peak electron temperature versus time; the relative fluctuation levels in the poloidal magnetic field versus time just inside the edge of the flux-conserver midplane; the electron temperature versus major radius; and the peak electron temperature versus time for a double-pulse experiment. The differences between the experimental data and the simulations are no worse than 25% and typically are much smaller.…”

A model of plasma rotation in the Livermore spheromak for the regimes of large connection lengths

“…The aforementioned transition has been identified both experimentally [3] and in numerical simulations [4,5]. The parallel confinement time for a poor confinement regime was evaluated in Refs.…”