New axisymmetric equilibria with flow from an expansion about the generalized Solov'ev solution

TL;DR

This paper develops analytic axisymmetric plasma equilibria with flow by expanding the generalized Solov'ev solution, enabling the modeling of diverse tokamak and spheromak configurations with flow effects.

Contribution

It introduces a novel analytic method to incorporate flow into generalized Grad-Shafranov equilibria based on an expansion of the Solov'ev solution, broadening equilibrium modeling capabilities.

Findings

Constructed various flow-inclusive equilibria for tokamaks and spheromaks.

Demonstrated modifications of equilibrium configurations with parameter variations.

Included D-shaped and diverted configurations with X-points.

Abstract

We construct analytic solutions to the generalized Grad-Shafranov equation, which incorporates both toroidal and poloidal flows. This is achieved by adopting a general linearizing ansatz for the free-function terms of the equation and expanding the generalized Solov'ev solution [Ch. Simintzis, G. N. Throumoulopoulos, G. Pantis and H. Tasso, Phys. Plasmas {\bf 8}, 2641 (2001)]. On the basis of these solutions, we examine how the genaralized Solov'ev configuration is modified as the values of the free parameters associated with the additional pressure, poloidal-current and electric-field terms are changed. Thus, a variety of equilibria of tokamak, spherical tokamak and spheromak pertinence are constructed, including D-shaped configurations with positive and negative triangularity and diverted configurations with either a couple of X-points or a single X-point.