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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク toroidal and poloidal ： ウィキペディア英語版 toroidal and poloidal The earliest use of these terms cited by the Oxford English Dictionary (OED) is by Walter M. Elsasser (1946) in the context of the generation of the Earth's magnetic field by currents in the core, with "toroidal" being parallel to lines of latitude and "poloidal" being in the direction of the magnetic field (i.e. towards the poles). The OED also records the later usage of these terms in the context of toroidally confined plasmas, as encountered in magnetic confinement fusion. In the plasma context, the toroidal direction is the long way around the torus, the corresponding coordinate being denoted by ''z'' in the slab approximation or $\backslash zeta$ or $\backslash phi$ in magnetic coordinates; the poloidal direction is the short way around the torus, the corresponding coordinate being denoted by ''y'' in the slab approximation or $\backslash theta$ in magnetic coordinates. (The third direction, normal to the magnetic surfaces, is often called the "radial direction", denoted by ''x'' in the slab approximation and variously $\backslash psi$, $\backslash chi$, ''r'', $\backslash rho$, or ''s'' in magnetic coordinates.) ==Toroidal and poloidal coordinates== As a simple example from the physics of magnetically confined plasmas, consider an axisymmetric system with circular, concentric magnetic flux surfaces of radius $r$ (a crude approximation to the magnetic field geometry in an early Tokamak but topologically equivalent to any toroidal magnetic confinement system with nested flux surfaces) and denote the toroidal angle by $\backslash zeta$ and the poloidal angle by $\backslash theta$. Then the Toroidal/Poloidal coordinate system relates to standard Cartesian Coordinates by these transformation rules: :$x\; =\; (R\_0\; +r\; \backslash cos\; \backslash theta)\; \backslash cos\backslash zeta\; \backslash ,$ :$y\; =\; s\_\backslash zeta\; (R\_0\; +\; r\; \backslash cos\; \backslash theta)\; \backslash sin\backslash zeta\; \backslash ,$ :$z\; =\; s\_\backslash theta\; r\; \backslash sin\; \backslash theta.\; \backslash ,$ where $s\_\backslash theta\; =\; \backslash pm\; 1,\; s\_\backslash zeta\; =\; \backslash pm\; 1$. The natural choice geometrically is to take $s\_\backslash theta\; =\; s\_\backslash zeta\; =\; +1$, giving the toroidal and poloidal directions shown by the arrows in the figure above, but this makes $r,\backslash theta,\backslash zeta$ a left-handed curvilinear coordinate system. As it is usually assumed in setting up (coordinates'' ) for describing magnetically confined plasmas that the set $r,\backslash theta,\backslash zeta$ forms a ''right''-handed coordinate system, $\backslash nabla\; r\backslash cdot\backslash nabla\backslash theta\backslash times\backslash nabla\backslash zeta\; >\; 0$, we must either reverse the poloidal direction by taking $s\_\backslash theta\; =\; -1,\; s\_\backslash zeta\; =\; +1$, or reverse the toroidal direction by taking $s\_\backslash theta\; =\; +1,\; s\_\backslash zeta\; =\; -1$. Both choices are used in the literature. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「toroidal and poloidal」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.