[Paper Review] Advanced modeling for the HIT-SI Experiment

Alan A. Kaptanoglu, Thomas Benedett+3 more|arXiv (Cornell University)|Mar 1, 2020

Magnetic confinement fusion research51 references10 citations

TL;DR

This paper introduces a two-temperature magnetohydrodynamic (MHD) model in the PSI-Tet and NIMROD codes to improve simulation accuracy for the HIT-SI spheromak experiment. By separately evolving electron and ion temperatures, the model achieves better agreement with experimental data—particularly in toroidal current, density profiles, and current centroid symmetry—while revealing significant viscous and compressive heating at high injector frequencies. The key contribution is enhanced predictive capability for low-density, high-performance regimes with gains ≈5.

ABSTRACT

A two-temperature magnetohydrodynamic (MHD) model, which evolves the electron and ion temperatures separately, is implemented in the PSI-Tet code and used to model plasma dynamics in the HIT-SI experiment. When compared with single-temperature Hall-MHD, the two-temperature Hall-MHD model demonstrates improved qualitative agreement with experimental measurements, including: far-infrared interferometry, ion Doppler spectroscopy, Thomson scattering, and magnetic probe measurements. The two-temperature model is utilized for HIT-SI simulations in both the PSI-Tet and NIMROD codes at a number of different injector frequencies in the 14.5-68.5 kHz range. At all frequencies the two-temperature models result in increased toroidal current, lower chord-averaged density, and symmetrization of the current centroid, relative to single-temperature simulations. Both codes produce higher average temperatures and toroidal currents as the injector frequency is increased. Power balance and heat fluxes to the wall are calculated for the two-temperature PSI-Tet model and indicate considerable viscous and compressive heating, particularly at high injector frequency. Parameter scans are also presented for the artificial diffusivity, and Dirichlet wall temperature and density. Artificial diffusivity and the density boundary condition both significantly modify the plasma density profiles, leading to larger average temperatures, higher toroidal current, and increased relative density fluctuations at low diffusivity and low wall density. High power, low density simulations at 14.5 kHz achieve sufficiently high gain (G = 5) to generate significant volumes of closed flux lasting 1-2 injector periods.

Motivation & Objective

• Improve simulation fidelity of the HIT-SI spheromak experiment by incorporating separate evolution of electron and ion temperatures.
• Address limitations of single-temperature Hall-MHD models in capturing energy partitioning and plasma dynamics.
• Validate the two-temperature model against multiple experimental diagnostics: interferometry, Doppler spectroscopy, Thomson scattering, and magnetic probes.
• Investigate the impact of injector frequency, artificial diffusivity, and wall boundary conditions on plasma performance and stability.
• Enable future validation by integrating a circuit model of the injectors and improving heat transport closures.

Proposed method

• Implement a two-temperature Hall-MHD model in the PSI-Tet code, solving separate energy equations for electrons and ions.
• Use the NIMROD code for cross-validation, applying the same two-temperature formulation to assess consistency across codes.
• Perform parameter scans over injector frequency (14.5–68.5 kHz), artificial diffusivity (50–1000 m²/s²), and Dirichlet boundary conditions for wall temperature and density.
• Calculate power balance and heat fluxes to quantify viscous and compressive heating, especially at high frequencies.
• Apply hyper-diffusivity (Dh∇⁴n) in NIMROD to stabilize simulations and compare with PSI-Tet’s explicit diffusivity.
• Use experimental waveforms and injector geometry in PSI-Tet to assess impact on current centroid asymmetry and waveform response.

Experimental results

Research questions

• RQ1 How does separating electron and ion temperature evolution improve agreement with experimental measurements in HIT-SI simulations?
• RQ2 What is the effect of injector frequency on toroidal current, temperature, and density profiles in two-temperature MHD models?
• RQ3 How do artificial diffusivity and wall boundary conditions (temperature and density) influence plasma density profiles, temperature, and current centroid position?
• RQ4 Can low-density, high-power simulations with injector frequency at 14.5 kHz achieve performance gains ≈5 and sustain closed flux for 1–2 injector periods?
• RQ5 Why does PSI-Tet reproduce injector-induced current centroid asymmetry while NIMROD does not, and how does injector geometry affect this?

Key findings

• The two-temperature model produces higher volume-averaged ion temperatures and lower chord-averaged densities compared to single-temperature models, with ⟨Ti⟩ > ⟨Te⟩ at high injector frequencies.
• Both PSI-Tet and NIMROD simulations show increased toroidal current and symmetrized current centroid with two-temperature modeling, especially in PSI-Tet where injector geometry is resolved.
• At 14.5 kHz, low-density, high-power simulations achieve a performance gain G ≈ 5 and sustain closed flux for 50–100 µs (1–2 injector periods), indicating a transition to a high-performance regime.
• Reducing artificial diffusivity from 1000 to 50 m²/s² in PSI-Tet decreases chord-averaged density by ~20%, increases average temperatures and toroidal current, and amplifies relative density fluctuations.
• Wall temperature scans show an inward shift of the current centroid and reduced ⟨β⟩ due to stronger thermal pressure near the wall, consistent with pressure balance effects.
• The two-temperature model reveals super-linear scaling of injector impedance and volume-averaged temperature with injector frequency, indicating enhanced energy coupling at higher frequencies.