# Magneto-Fluid Dynamics Seminar

#### Quasisymmetry near axisymmetry

**Speaker:**
Gabriel Plunk, Max Planck Institute for Plasma Physics, Greifswald, Germany

**Location:**
Warren Weaver Hall 905

**Date:**
Monday, October 26, 2020, 10 a.m.

**Synopsis:**

The "direct construction" of optimized stellarator equilibria, i.e. solving the equilibrium problem for optimal solutions using approximate methods, plays an important role in stellarator design, both in the basic theoretical understanding, as well as in guiding general optimizers. In this talk, one method of direct construction, developed in recent years, is described. It is based on the idea of slightly deforming axisymmetric solutions to break axisymmetry while preserving quasi-axisymmetry. For vacuum fields, this problem was found to be equivalent to Poincaré's problem, also known as the "oblique derivative problem", and existence and uniqueness theorems can readily be quoted. The finite-pressure version of the problem brings significant complications, without such a satisfying theoretical conclusion. However, it's successful numerical solution hints at a way towards a fully nonlinear solver.