Analytical solutions to the Grad-Shafranov equation

被引：79
作者：
Atanasiu, CV
Günter, S
Lackner, K
Miron, IG
机构：
[1] MEC EURATOM Assoc, Natl Inst Laser Plasma & Radiat Phys, Bucharest, Romania
[2] EURATOM, Max Planck Inst Plasmaphys, Garching, Germany
来源：
PHYSICS OF PLASMAS | 2004年 / 11卷 / 07期
关键词：
D O I：
10.1063/1.1756167
中图分类号：
O35 [流体力学]; O53 [等离子体物理学];
学科分类号：
070204 ; 080103 ; 080704 ;
摘要：
Two families of exact analytical solutions of the Grad-Shafranov equation are presented by specifying the highest polynomial dependence of the plasma current density on the flux function Psi in such a way that the Grad-Shafranov equation becomes a linear inhomogeneous differential equation. Both the pressure profile and the poloidal current profile each have two free parameters. X-points can be represented by superposition of solutions. Examples of the exact equilibrium solution are given for both a D-shaped plasma and a toroidally diverted plasma. (C) 2004 American Institute of Physics.
引用
收藏
页码：3510 / 3518
页数：9
相关论文
共 18 条
[1]  
ABRAMOWITZ M, 1972, HDB MATH FUNCTIONS, P5537
[2]  
ATANASIU CV, 2001, P 28 EPS C CONTR FUS, V25, P1105
[3]   AN ALGORITHM FOR REGULAR AND IRREGULAR COULOMB AND BESSEL-FUNCTIONS OF REAL ORDER TO MACHINE ACCURACY [J].
BARNETT, AR .
COMPUTER PHYSICS COMMUNICATIONS, 1981, 21 (03) :297-314
[4]  
Grad H., 1958, P 2 UN C PEAC US AT, V31, P190, DOI DOI 10.1016/0891-3919(58)90139-6
[5]   AN ANALYTIC, LARGE ASPECT RATIO, HIGH BETA-EQUILIBRIUM [J].
GREENE, JM .
PLASMA PHYSICS AND CONTROLLED FUSION, 1988, 30 (04) :327-338
[6]  
Herrnegger F., 1972, P 5 EUR C CONTR FUS, VI, P26
[7]   EXACT SOLUTIONS OF MHD EQUILIBRIUM EQUATION FOR A TOROIDAL PLASMA [J].
MASCHKE, EK .
PLASMA PHYSICS AND CONTROLLED FUSION, 1973, 15 (06) :535-541
[8]   Analytical solutions to the Grad-Shafranov equation for tokamak equilibrium with dissimilar source functions [J].
Mc Carthy, PJ .
PHYSICS OF PLASMAS, 1999, 6 (09) :3554-3560
[9]   A NUMERICAL EVALUATOR FOR THE GENERALIZED HYPERGEOMETRIC-SERIES [J].
PERGER, WF ;
BHALLA, A ;
NARDIN, M .
COMPUTER PHYSICS COMMUNICATIONS, 1993, 77 (02) :249-254
[10]   ASDEX Upgrade MHD equilibria reconstruction on distributed workstations [J].
Schneider, W ;
McCarthy, PJ ;
Lackner, K ;
Gruber, O ;
Behler, K ;
Martin, P ;
Merkel, R .
FUSION ENGINEERING AND DESIGN, 2000, 48 (1-2) :127-134
12