Effects of temperature and density evolution in MHD simulations of HIT-SI

Abstract

The helicity injected torus-steady inductive (HIT-SI) experiment uses steady inductive helicity injection to form a spheromak equilibrium and sustain the structure against resistive decay. Helicity injection is performed using two half-tori “injectors” connected to the main plasma volume, whose fields are oscillated in an AC manner. The properties of the sustained spheromak equilibrium have been experimentally observed to vary with the frequency of the injector oscillation, producing higher current gains and more-symmetric and outwardly shifted current centroids with higher frequency. A computational scan of injector frequency using the 3D MHD code PSI-Tet, which models the entire HIT-SI plasma volume including the injectors, has been performed, including a comparison of the results using the full Hall MHD model to those obtained using a simplified “zero-beta” (constant temperature and density) model. The results of both PSI-Tet models are also compared with experimental data and with simulations using the NIMROD code, which does not model the injector regions. The results of the PSI-Tet simulations show that the average temperature and current gain increase with injector frequency, in agreement with experimental trends. The simulations also show qualitative changes in the dynamics of several quantities with increasing injector frequency, such as density oscillations and current evolution. However, the outward shift and symmetrizing of the current centroid, observed experimentally, are not observed in these MHD simulations, indicating that unresolved or excluded dynamics may be important.

Advanced modeling for the HIT-SI Experiment

“…The velocity is zero at the boundary except for a constant inward flow at each injector mouth to counter-act density holes that cause numerical issues. These inwards flows are well-motivated by and comparable in magnitude to large flows seen in PSI-Tet simulations [11,19]. The spatial profile of the normal velocity matches the absolute value of the normal magnetic field, and the peak velocity ≈ 19.5 km/s is in approximate agreement with the flow velocity observed on the experiment with ion doppler spectroscopy [12].…”

“…In HIT-SI the ion inertial scale d i ≈ 8 cm is comparable with experimental length scales, such as the diameter of an injector mouth d inj ≈ 14 cm, and the characteristic magnetic scales of the spheromak λ −1 sph ≈ 10 cm, and of the injector λ −1 inj ≈ 5 cm [9,10]. Numerical models with the Hall terms significantly improve agreement with HIT-SI measurements over the resistive MHD models [6], and validate well with many bulk measurements of the experiment [7,11]. However, from measurements of HIT-SI [12] (and a newer device called HIT-SI3) [13] and theory [9,14], ion temperatures are expected to be significantly higher than electron temperatures.…”

“…Experimental trends in injector frequency indicate that higher frequency operations tend to exhibit higher plasma impedance in the injectors, increased volume-averaged β, reduced chord-averaged density fluctuations from interferometry, and, to a lesser extent, larger current gain G = I φ /I inj . Previous work [7,11,17] with the single-temperature models in NIMROD and PSI-Tet has indicated qualitative agreement with all of these trends when the injector frequency is increased from 14.5 kHz to 68.5 kHz; the twotemperature model facilitates further exploration and understanding of these qualitative trends.…”

“…The PSI-Tet and NIMROD models are described in Section 2 and are compared with their singletemperature counterparts. In Section 3, we extend the scans of the injector frequency performed in previous works [11,17] and find a number of interesting and important changes in the plasma dynamics, including: significantly hotter ions than electrons at high frequency operation, new insights into the dynamical power flows, super-linear injector impedance scaling with the injector frequency, and improved understanding of the structure of spheromak formation. When compared to the single-temperature models, the two-temperature models robustly predict larger (or similar magnitude) toroidal currents, increased volume-averaged ion temperatures, lower chordaveraged densities, and an outward radial shift (this is only true for PSI-Tet) and vertical symmetrization of the current centroid.…”

“…Experimental measurements have indicated an outward radial shift and vertical symmetrization of the current centroid at high frequency in HIT-SI [33]. Previous work comparing single-temperature and constant-temperature simulations did not find evidence of robust changes for different injector frequencies [11]. The two-temperature model in PSI-Tet indicates a small but robust outward radial shift and both two-temperature models produce vertical symmetrization of the current centroid compared to single temperature models.…”