# Magneto-Fluid Dynamics Seminar

#### Pressure effects on the topology of magnetic fields in stellarators

**Speaker:**
Antoine Baillod, Ecole Polytechnique Fédérale de Lausanne, Switzerland

**Location:**
Warren Weaver Hall 905

**Date:**
Tuesday, November 2, 2021, 11 a.m.

**Synopsis:**

Three dimensional magnetic equilibria are in general composed of nested flux surfaces, magnetic islands and chaotic field lines, although it is possible to design stellarator coil configurations that produce vacuum fields with nested flux surfaces. At finite β however, currents self-generated by the plasma, such as diamagnetic, Pfirsch-Schlüter or bootstrap, perturb the magnetic field, thus breaking nested flux surfaces and impairing confinement. To date, there is no theory, nor extensive numerical study that characterizes the maximum achievable β above which magnetic surfaces are destroyed, nor a theory on the dependency of this critical β on other relevant parameters. Using the SPEC code, which can compute 3-dimensional stepped-pressure equilibria with magnetic islands and chaos, we study the effect of finite β on the magnetic topology of stellarators. Recent numerical work significantly improved the speed and robustness of SPEC, which allows large parameter scans in a reasonable amount of time. In addition, SPEC has recently been extended to allow free-boundary calculations with prescribed net toroidal current profiles. Leveraging these new capabilities, we present the first extensive and comprehensive study of the equilibrium β-limit in simple stellarator configurations with bootstrap current. We show that two regimes exist: the first one, at low bootstrap current, is characterized by an edge rotational transform that decreases towards zero with increasing β, at which point a separatrix forms. The second regime, at higher bootstrap current, does not allow a separatrix to form but magnetic field lines become chaotic at sufficiently large β. We provide a theoretical understanding of these β-limits by extending analytical stellarator expansions and identify the main parameters that determine these limits. Finally, it is shown that the magnetic chaos that is present in some equilibria can be reduced via a precise optimization procedure using the SIMSOPT code.