Omnigenous umbilic stellarators

TL;DR

This paper introduces umbilic stellarators with a unique boundary shape, develops optimization techniques for their magnetic fields, and explores their potential to convert tokamaks into stellarators with improved edge confinement.

Contribution

It defines a new class of stellarators with high-curvature boundaries, develops a simultaneous optimization method for boundary and magnetic properties, and proposes a way to convert tokamaks into stellarators.

Findings

Umbilic stellarators favor piecewise omnigenity over specific helicity.

Optimized coil sets successfully generate the desired magnetic configurations.

A proposed experiment could convert tokamaks into finite-beta stellarators.

Abstract

To better understand the dependence of the magnetic field structure in the plasma edge on the plasma boundary shape, in the context of X-point and island divertor designs, we define and develop a class of stellarators called umbilic stellarators. These equilibria are characterized by a single continuous high-curvature edge on the plasma boundary that goes around multiple times toroidally before meeting itself. We develop a technique that allows us to simultaneously optimize the plasma boundary along with a curve lying on the boundary on which we impose a high curvature while imposing omnigenity -- a property of the magnetic field that ensures trapped particle confinement throughout the plasma volume. We find that umbilic stellarators naturally tend to favor piecewise omnigenity instead of omnigenity with a specific helicity. After generating omnigenous umbilic stellarators, we design coil sets for some of them and explore the field line structure in the edge and its sensitivity to small fluctuations in the plasma. Finally, using single-stage optimization, we simultaneously modify the plasma and coil shape and propose an experiment to modify an existing tokamak to a finite-beta stellarator using this technique and explore a potentially simpler way to convert a limited tokamak into a diverted stellarator.