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Author: Omar E. Lopez
Requested Type: Poster
Submitted: 2017-03-17 17:41:12

Co-authors: L. Guazzotto

Contact Info:
Auburn University
206 Allison Laboratory
Auburn,   36849
USA

Abstract Text:
The Grad-Shafranov-Bernoulli system of equations is a single fluid magnetohydrodynamical description of axisymmetric equilibria with mass flows. Using a variational perturbative approach [1], analytic approximations for high-beta equilibria in circular, elliptical, and D-shaped cross sections in the high aspect ratio approximation are found, which include finite toroidal and poloidal flows. Assuming a polynomial dependence of the free functions on the poloidal flux, the equilibrium problem is reduced to an inhomogeneous Helmholtz partial differential equation subject to homogeneous Dirichlet conditions. An application of the Green's function method leads to a closed form for the circular solution and to a series solution in terms of Mathieu functions for the elliptical case, which is valid for arbitrary elongations. To extend the elliptical solution to an up-down symmetric D-shaped scenario, a boundary perturbation in terms of the triangularity is used. Additionally, we explore the possibility of utilizing the boundary perturbation technique to model configurations with diverted boundaries possessing a single or double X-point. A comparison with the code FLOW [2] is presented for relevant scenarios.

[1] E. Hameiri, Phys. Plasmas 20, 024504 (2013)
[2] L. Guazzotto et al., Phys. Plasmas 11(2), 604–614 (2004)

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