Author: Wrick Sengupta
Requested Type: Poster
Submitted: 2018-03-01 13:39:02
Co-authors: Harold Weitzner
Courant Institute of Mathematical Sciences, NYU
251 Mercer St #801
New York, New York ( 100012
Previous analytical and numerical studies have suggested that it is possible for nonsymmetric vacuum magnetic fields to have a dense sets of nested toroidal flux surfaces. In this work we shall analytically investigate the possibility of such vacuum magnetic fields in a low shear stellerator. We obtain an equilibrium expansion near a rational surface by analytically solving the force free MHD equilibrium equations derived in Weitzner 2016. The lowest order flux surface will be shown to determine the structure of the expansion to a large extent. In the absence of any continuous symmetry, we demonstrate that the boundary must be carefully chosen so that resonances near rational surfaces can be suppressed. Interestingly, these resonance conditions require that the field line averaged weighted Schwarzian derivative of certain quantities defined on the lowest order flux surface must vanish. Non-vanishing and negative Schwarzian derivatives are a hallmark of chaotic dynamics. Thus, the necessary conditions can be interpreted as the requirement that the 3D nonsymmeytric field lines be non-volume filling and non-chaotic. We shall present our calculations assuming cartesian coordinates (topological torus), cylindrical and finally toroidal coordinates as choices for the lowest order flux surface. Omnigeneity and quasisymmetry constraints on such equilibrium will also be discussed.
This work was supported by the U.S.Department of Energy Grant No. DE-FG02-86ER53223.