A class of high-beta, large-aspect-ratio quasiaxisymmetric Palumbo-like configurations

TL;DR

This paper explores high-beta, large-aspect-ratio quasiaxisymmetric stellarator configurations using an inverse coordinate approach, revealing equilibria with various geometric features and discussing polynomial ansatz limitations.

Contribution

It extends the Palumbo method with a quadratic polynomial ansatz to find new equilibrium configurations in stellarator design.

Findings

Equilibria with positive or negative triangularity identified

Configurations with cusps and current singularities demonstrated

Polynomial degree limitations for flux function ansatz established

Abstract

The space of high-beta, approximately quasiaxisymmetric, large-aspect-ratio stellarator configurations is explored using an inverse coordinate approach and a quadratic polynomial ansatz for the flux function, following the method of Palumbo, extended by Hernandes and Clemente. This approach yields a system of nonlinear ODEs that, when solved, give equilibria exhibiting positive or negative triangularity, cusps, and (in an extreme limit) current singularities. It is shown that a cubic ansatz may also be used, but that polynomials of degree four or higher will lead to overdetermination.