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On the role of the Hartmann number in magnetohydrodynamic activity

X Shan, D Montgomery1993年Plasma Physics and Controlled FusionIF 2.2出版社

Magnetohydrodynamic activity near the threshold of instability is studied numerically for resistive equilibria in periodic cylinders. Attention focuses on the role of the viscosity (and its reflection in the Hartmann number) in determining the existence and nonlinear evolution of instabilities. Three identical axisymmetric resistive equilibria without flow are investigated, with three viscosities. The highest viscosity leads to stability of the axisymmetric state. The intermediate value leads to a helically deformed equilibrium with flow, with an (m,n)=(2,1) deformation. The lowest viscosity leads to a 'mixed' helically deformed, final, approximately steady state with flow, with (m,n)=(2,1) and (3,2) deformations and their harmonics, plus other, adjacent, modes near m=2n. It is concluded that it is likely that the numerical value of the viscosity, and possibly the form of the viscous stress tensor, must never be ignored in discussions of near-threshold incompressible MHD activity in driven, dissipative MHD plasmas.

日本語訳

周期的な円筒における抵抗性平衡状態に対して、不安定性の閾値近傍での磁気流体力学活動を数値的に研究した。粘性(およびそのハルトマン数への反映)が、不安定性の存在と非線形発展を決定する上で果たす役割に焦点を当てる。流れのない3つの同一の軸対称抵抗性平衡状態を、3つの異なる粘性値に対して調査した。最も高い粘性は軸対称状態の安定性をもたらす。中間の値は、(m,n)=(2,1)の変形を伴う螺旋状に変形した平衡状態と流れをもたらす。最も低い粘性は、(m,n)=(2,1)および(3,2)の変形とそれらの高調波、さらにm=2nに近い他の隣接モードを伴う「混合した」螺旋状に変形した最終的なほぼ定常状態と流れをもたらす。駆動され散逸を伴うMHDプラズマにおける閾値近傍の非圧縮性MHD活動の議論においては、粘性の数値、おそらくは粘性応力テンソルの形式も、決して無視すべきではないと結論される。

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Magnetohydrodynamics
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