Two-parameter modified rigid rotor radial equilibrium model for field-reversed configurations

Abstract

Abstract A new equilibrium pressure profile is proposed that extends the rigid rotor (RR) model with a simple unified expression P = P(ψ; β s, α, σ) for both inside and outside the separatrix. A new method is described for solving the field-reversed configuration (FRC) one-dimensional (1D) equilibrium with only two parameters. The radial normalized FRC equilibrium profiles for pressure, magnetic field, and current density can be uniquely determined by the dimensionless parameters of β s ≡ P s / B e 2 / 2 μ 0 and δ s ≡ L ps/R s. This modified rigid rotor (MRR) model has sufficient flexibility to accommodate narrow scrape-off layer (SOL) widths and hollow current density profiles, and can be used to fit experimental measurements. A database of 1D plasma equilibria in the (β s, δ s) space is provided for the convenience of real-time approximate FRC equilibrium reconstruction. The detailed one-dimensional (1D) characteristics of the equilibrium models are investigated analytically and numerically. The 1D results from the MRR models are also validated using two-dimensional (2D) Grad–Shafranov (G–S) equilibrium solutions.