Abstract Details
Abstracts
Author: WRICK SENGUPTA
Requested Type: Poster
Submitted: 2017-03-16 16:03:06
Co-authors: H. WEITZNER
Contact Info:
COURANT INSTITUTE OF MATHEMATICAL SCIENCES, NYU
251 Mercer Street
NEW YORK, NEW YORK 10012
US
Abstract Text:
It is of particular importance to guarantee radial confinement of collisionless deeply trapped particles in a generic stellarator. Quasisymmetry and omnigeneity are key ideas proposed to ensure confinement of such particles. The underlying idea there, is to ensure that the second adiabatic invariant, $ J_parallel = oint v_parallel dl $, is independent of the field line label on a given magnetic surface. Although, these ideas ensure radial localization of all trapped orbits, in practice, these constraints have stringent restrictions on magnetic geometry, some aspects of which are yet to be fully explored. In this work, we propose an analytical approach, to understand the implications of the constraints. We develop a method, based on Abel integral inversion, that enables one to calculate the magnetic field strength, given $ J_parallel$. We then recover all of the standard results available in the literature on omnigneity and quasisymmetry from this formulation. Furthermore, we obtain a local 3D MHD equilibrium expansion by analytically solving the equations derived in [1]. The equilibrium expression, although local, is sufficient to explore the deeply trapped particle physics, since the expansion is carried out around a region of local minima of the magnitude of the magnetic field. Based on this analytical 3D equilibrium solution, we then obtain explicitly, the aforementioned constraints. Our results show that it is far easier to satisfy the omnigeneity condition than the quasisymmetry requirement. This implies, that there exists a large class of equilibrium close to quasisymmetry, which are still omnigeneous but allow inclusion of quasisymmetry breaking error fields.
This work was supported by the U.S.Department of Energy Grant No. DE-FG02-86ER53223.
[1] Weitzner, H. Physics of Plasmas 23.6 (2016): 062512.
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