A globally conservative finite element MHD code and its application to the study of compact torus formation, levitation and magnetic compression

TL;DR

The paper introduces the DELiTE framework, a globally conservative finite element approach for axisymmetric MHD implemented on an unstructured triangular mesh using mimetic, matrix-represented differential operators. It captures a axisymmetric two-temperature MHD model and demonstrates exact discrete conservation of mass, toroidal flux, angular momentum, and energy under appropriate boundary conditions, even when density diffusion and external coil boundaries are included. The framework is applied to model compact torus formation, levitation, and magnetic compression, coupling plasma dynamics to vacuum/insulating regions and validating against General Fusion experimental diagnostics. The results show qualitative and quantitative agreement with measurements, highlight the impact of coil configurations on plasma-wall interactions, and indicate avenues for future improvements such as higher-order time integration and refined diffusion corrections, expanding the tool's applicability to complex plasma systems.

Abstract

The DELiTE (Differential Equations on Linear Triangular Elements) framework was developed for spatial discretisation of partial differential equations on an unstructured triangular grid in axisymmetric geometry. The framework is based on discrete differential operators in matrix form, which are derived using linear finite elements and mimic some of the properties of their continuous counterparts. A single-fluid two-temperature MHD code is implemented in this framework. The inherent properties of the operators are used in the code to ensure global conservation of energy, particle count, toroidal flux, and angular momentum. The code was applied to study a novel experiment in which a compact torus (CT), produced with a magnetized Marshall gun, is magnetically levitated off an insulating wall and then magnetically compressed through the action of currents in the levitation/compression coils located outside the wall. We present numerical models for CT formation, levitation, and magnetic compression, and comparisons between simulated and experimental diagnostics.

Figures (26)

• Figure 1: Linear basis function depiction for triangular elements
• Figure 2: Node-to-element differential operator mechanism
• Figure 3: Element-to-node differential operator mechanism
• Figure 4: Node-to-node second order differential operator mechanism
• Figure 5: Node-to-node differential operator mechanism