Finite-beta simulations of HIT-SI and HIT-SI3 using the NIMROD code

Abstract

The Helicity Injected Torus with Steady Inductive helicity injection (HIT-SI) and HIT-SI3 experiments are a pair of devices that form and sustain spheromak plasmas through the use of Steady Inductive Helicity Injection (SIHI). SIHI is accomplished through a set of semi-toroidal injectors that inductively drive oscillating non-axisymmetric helical magnetic fields on the surface of the equilibrium plasma. As magnetic helicity is injected the central plasma will relax towards a minimum energy state while conserving helicity, which is the spheromak state. This non-axisymmetric helicity injection additionally enables the usage of Imposed Dynamo Current Drive (IDCD) to sustain the equilibrium that forms. Numerical studies have been performed based on the extended MagnetoHydroDynamics (eMHD) fluid model using the NIMROD code to study the 3-D dynamics present in the devices. The goal of these simulations is two-fold: increased understanding of the dynamic processes at play and validation of the models for use as a predictive tool. A number of simulations have been performed spanning both the experimental operation space of both devices and predictive studies of similar devices. Studies of the HIT-SI device focused on matching the experimental results that were obtained during a parameter scan of the oscillating frequency of the injectors. It was found that zero-β models, which neglected the role of pressure gradients in the system, were ill-equipped to capture experimental results that were observed at higher frequencies. To improve agreement between the models and the experimental results, a finite-β model was implemented that while showing improvement in qualitative agreement with experimental observations,still fails to exactly capture the observed effects. Further improvements to the fluid model have been explored, though currently the computational limits make them untractable. Studies of the HIT-SI3 device focused on comparisons between different injector drive structures. The three-injector setup allows for a variety of modal spectra of the imposed perturbation, allowing control over the equilibrium plasma profile that is eventually achieved. Simulations were able to capture the appropriate modal spectra of a set of HIT-SI3 discharges and similarly demonstrate that the formation of the spheromak is agnostic to the applied perturbation spectrum. Finally, predictive simulations were performed to examine the possibilities for future devices based on SIHI and IDCD. A high-gain version of HIT-SI showed the spontaneous formation of closed-flux surfaces, beneficial in increasing energy confinement, which has not been seen before in other simulated models of helicity injected plasmas. Additionally, a more generalized set of injectors has been created which provides more flexibility in the perturbation spectrum that is applied, to begin quantifying the key differences observed. Finally, expanding beyond spheromak physics, initial simulations of the HIT-SI3 device with an externally produced toroidal magnetic field show promising results for the use of SIHI in forming a tokamak equilibrium.