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Axisymmetric MHD equilibria with isothermal toroidal mass flow by variational steepest descent moments method

W A Cooper, S P Hirshman1987年Plasma Physics and Controlled FusionIF 2.2出版社

An energy principle is constructed for an axisymmetric system such that its variation with respect to an artificial time parameter t is demonstrated to yield the components of the magnetohydrodynamic (MHD) force F=j*B- Del p- rho M(V. Del )V when V is only toroidal. An accelerated steepest descent method is applied to the Fourier moments of these MHD forces in an inverse flux coordinate representation to reach a minimum energy state that corresponds to an MHD equilibrium with isothermal toroidal mass flow. Applications to a JET Tokamak configuration show the outward displacement of the pressure surfaces away from the flux surfaces induced by the plasma rotation. For fixed global and peak values of the total plasma energy content (thermal pressure plus directed flow), however, the position of the magnetic axis does not shift with the rotation.

日本語訳

軸対称系に対してエネルギー原理を構築し、その変分が人工時間パラメータに関して取られることにより、磁気流体力学(MHD)力 F=j*B-∇p-ρM(V・∇)V の各成分が導出されることを示す。ここでVはトロイダル方向のみの成分を持つものとする。逆フラックス座標表現におけるこれらのMHD力のフーリエモーメントに対して加速最急降下法を適用し、等温トロイダル質量流を伴うMHD平衡に対応する最小エネルギー状態へ到達させる。JETトカマク配位への適用結果は、プラズマ回転によって誘起される圧力面のフラックス面からの外向き変位を示す。しかしながら、全プラズマエネルギー含有量(熱圧力+指向性流のエネルギー)の大域値およびピーク値を固定した場合、磁気軸の位置は回転によって変化しないことが示される。

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Magnetohydrodynamics
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