Highbeta analytic equilibria in circular, elliptical, and Dshaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows
Abstract
The GradShafranovBernoulli system of equations is a single fluid magnetohydrodynamical description of axisymmetric equilibria with mass flows. Using a variational perturbative approach [E. Hameiri, Phys. Plasmas 20, 024504 (2013)], analytic approximations for highbeta equilibria in circular, elliptical, and Dshaped 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 (PDE) 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. In order to extend the elliptical solution to a Dshaped domain, a boundary perturbation in terms of the triangularity is used. A comparison with the code FLOW [L. Guazzotto et al., Phys. Plasmas 11(2), 604614 (2004)] is presented for relevant scenarios.
 Authors:

 Auburn Univ., AL (United States). Physics Dept.
 Publication Date:
 Research Org.:
 Auburn Univ., AL (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1465663
 Alternate Identifier(s):
 OSTI ID: 1348948
 Grant/Contract Number:
 FG0293ER54215
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 24; Journal Issue: 3; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 22 GENERAL STUDIES OF NUCLEAR REACTORS; plasma flows; Bernoulli's principle; Lagrangian mechanics; tokamaks; magnetohydrodynamics; toroidal plasma confinement; boundary value problems; Green's function methods; numerical solutions
Citation Formats
López, O. E., and Guazzotto, L. Highbeta analytic equilibria in circular, elliptical, and Dshaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows. United States: N. p., 2017.
Web. doi:10.1063/1.4976837.
López, O. E., & Guazzotto, L. Highbeta analytic equilibria in circular, elliptical, and Dshaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows. United States. doi:10.1063/1.4976837.
López, O. E., and Guazzotto, L. Wed .
"Highbeta analytic equilibria in circular, elliptical, and Dshaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows". United States. doi:10.1063/1.4976837. https://www.osti.gov/servlets/purl/1465663.
@article{osti_1465663,
title = {Highbeta analytic equilibria in circular, elliptical, and Dshaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows},
author = {López, O. E. and Guazzotto, L.},
abstractNote = {The GradShafranovBernoulli system of equations is a single fluid magnetohydrodynamical description of axisymmetric equilibria with mass flows. Using a variational perturbative approach [E. Hameiri, Phys. Plasmas 20, 024504 (2013)], analytic approximations for highbeta equilibria in circular, elliptical, and Dshaped 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 (PDE) 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. In order to extend the elliptical solution to a Dshaped domain, a boundary perturbation in terms of the triangularity is used. A comparison with the code FLOW [L. Guazzotto et al., Phys. Plasmas 11(2), 604614 (2004)] is presented for relevant scenarios.},
doi = {10.1063/1.4976837},
journal = {Physics of Plasmas},
issn = {1070664X},
number = 3,
volume = 24,
place = {United States},
year = {2017},
month = {3}
}