Two-parameter Radial Equilibrium Models for Field-Reversed Configurations

TL;DR

This paper introduces a two-parameter equilibrium model for field-reversed configurations that simplifies the description of plasma profiles using only two key parameters, enhancing flexibility and fitting accuracy.

Contribution

The paper proposes a new two-parameter equilibrium pressure profile model extending the Rigid-Rotor model, applicable to both inside and outside the separatrix in FRCs.

Findings

The model accurately fits experimental measurements.

It can accommodate narrow SOL width and hollow current profiles.

Analytical and numerical analyses confirm the model's validity.

Abstract

A new equilibrium pressure profile extending the Rigid-Rotor (RR) model with a simple unified expression $P=P(\psi;\beta_{s},\alpha, \sigma)$ for both inside and outside the separatrix is proposed, in which the radial normalized field-reversed configuration (FRC) equilibrium profiles for pressure, magnetic field, and current can be determined by only two dimensionless parameters $\beta_s\equiv P_s/2\mu_0B_e^2$ and $\delta_s\equiv L_{ps}/R_s$, where $P_s$ is the thermal pressure at the separatrix, $B_e$ is the external magnetic field strength, $L_{ps}$ is the pressure profile scale length at the separatrix, and $R_s$ is the separatrix radius. This modified rigid rotor (MRR) model has sufficient flexibility to accommodate the narrow scrape of layer (SOL) width and hollow current density profiles, and can be used to fit experimental measurements satisfactorily. Detailed one-dimensional (1D) characteristics of the new MRR model are investigated analytically and numerically, and the results are also confirmed in two-dimensional (2D) numerical equilibrium solutions.