Effect of insulator end cap thickness on time-dependent Hartmann flow in a rotating mirror

TL;DR

This paper develops a simplified analytical and numerical framework to study plasma flow in a rotating mirror, focusing on how insulator end cap thickness influences flow dynamics and providing a benchmark for future fusion device simulations.

Contribution

It introduces a reduced one-dimensional MHD model for plasma flow in a rotating mirror and analyzes the impact of insulator end cap thickness on flow behavior.

Findings

Flow overshoot is proportional to insulator thickness and electric field.

Steady-state flow depends weakly on magnetic field strength.

Model serves as a benchmark for more complex future simulations.

Abstract

We present a framework for analyzing plasma flow in a rotating mirror. By making a series of physical assumptions, we reduce the magnetohydrodynamic (MHD) equations in a three-dimensional cylindrical system to a one-dimensional system in a shallow, cuboidal channel within a transverse magnetic field, similar to the Hartmann flow in the ducts. We then solve the system both numerically and analytically for a range of values of the Hartmann number and calculate the dependence of the plasma flow speed on the thickness of the insulating end cap. We observe that the mean flow overshoots and decelerates before achieving a steady-state value, a phenomenon that the analytical model cannot capture. This overshoot is directly proportional to the thickness of the insulating end cap and the external electric field, with a weak dependence on the external magnetic field. Our simplified model can act as a benchmark for future simulations of the supersonic mirror device Compact Magnetic Fusion Experiment (CMFX), which will employ more sophisticated physics and realistic magnetic field geometries.