A generalized Grad-Shafranov equation with plasma flow under a conformal coordinate transformation

TL;DR

This paper introduces a conformal mapping approach to solve a generalized Grad-Shafranov equation with plasma flow, enabling the construction of asymmetric tokamak equilibria and offering a new quasi-analytic method for elliptic PDEs.

Contribution

It presents a novel conformal transformation technique to solve the generalized Grad-Shafranov equation with plasma flow, facilitating the creation of asymmetric equilibrium configurations.

Findings

Successfully constructed asymmetric D-shaped tokamak equilibria.

Demonstrated the method as an effective quasi-analytic solution for elliptic PDEs.

Extended the applicability of the Grad-Shafranov equation to include plasma flow with arbitrary direction.

Abstract

We employ a conformal mapping transformation to solve a generalized Grad-Shafranov equation with incompressible plasma flow of arbitrary direction and construct particular up-down asymmetric D-shaped and diverted tokamak equilibria. The proposed method can also be employed as an alternative quasi-analytic method to solving two dimensional elliptic partial differential equations.