# Exact Solov'ev equilibrium with an arbitrary boundary

## TL;DR

This paper presents a method to compute exact Solov'ev plasma equilibria with arbitrary boundaries, allowing high accuracy and flexibility in boundary shape, including X-points, using a constrained least-squares approach.

## Contribution

It introduces a novel constrained least-squares technique for calculating exact plasma equilibria with arbitrary boundaries, enhancing accuracy and boundary shape flexibility.

## Key findings

- Successfully computed highly-shaped equilibria
- Flexible boundary representation with many constraints
- Demonstrated accuracy with arbitrary boundary shapes

## Abstract

Exact Solov'ev equilibria for arbitrary plasma cross-sections are calculated using a constrained least-squares method. The boundary, with or without $X$-points, can be specified with an arbitrarily large number of constraints to ensure an accurate representation. Thus, the order of the polynomial basis functions in the homogeneous solution of the Grad-Shafranov equation becomes an independent parameter determined only by the accuracy requirements of the overall solution. Examples of exact, highly-shaped equilibria are presented.