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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 Magnetic tension force ： ウィキペディア英語版 Magnetic tension force The magnetic tension force is a restoring force (SI unit: Pa·m−1) that acts to straighten bent magnetic field lines. It equals: :$\backslash frac\}\; \backslash ,\; (\backslash text)\; \backslash qquad$ \frac \,(\text) It is analogous to rubber bands and their restoring force. The force is directed antiradially. Although magnetic tension is referred to as a force, it is actually a pressure gradient (Pa m−1) which is also a force density (N m−3). The magnetic pressure is the energy density of the magnetic field and it increases as magnetic field lines convene with each other. In contrast, magnetic tension force is determined by how much the magnetic pressure changes with distance. Magnetic tension forces also rely on vector current densities $\backslash mathbf$ and their interaction with the magnetic field $\backslash mathbf$. Plotting magnetic tension along adjacent field lines can give a picture as to their divergence and convergence with respect to each other as well as current densities $\backslash mathbf$. ==Use in Plasma Physics== Magnetic tension is particularly important in plasma physics and magnetohydrodynamics, where it controls dynamics of some systems and the shape of magnetized structures. In magnetohydrodynamics, the magnetic tension force can be derived from the momentum equation of plasma physics: $$ \rho\left(\frac+ \mathbf\cdot\nabla \right)\mathbf = \mathbf\times\mathbf - \nabla p . The first term on the right hand side of the above equation represents electromagnetic forces and the second term represents pressure gradient forces. Using the relation $\backslash mu\_0\backslash mathbf=\backslash nabla\backslash times\backslash mathbf$ and the vector identity $$ \boldsymbol(\textbf\textbf)=(\textbf\boldsymbol)\textbf+(\textbf\boldsymbol)\textbf+\textbf\times(\boldsymbol\times\textbf)+\textbf\times(\boldsymbol\times\textbf), we obtain the following equation: $$ \rho\left(\frac+ \mathbf\cdot\nabla \right)\mathbf =-\boldsymbol(B^2/2\mu_0) + \textbf \over \mu_0} - \nabla p. The first and last gradient terms are associated with the total pressure which is the sum of the magnetic and thermal pressures; $p+B^2/2\backslash mu\_0$. The second term represents the magnetic tension. A more rigorous way to look at this is through Maxwell stress tensor. The Lorentz force law :$\backslash mathbf\; =\; q(\backslash mathbf\; +\; \backslash mathbf\backslash times\backslash mathbf)$ gives the force per unit volume: :$$ \mathbf = \rho\mathbf + \mathbf\times\mathbf This, after some algebra and using Maxwell's equations to replace the current, leads to :$\backslash mathbf\; =\; \backslash epsilon\_0\backslash left((\backslash boldsymbol\backslash cdot\; \backslash mathbf\; )\backslash mathbf\; +\; (\backslash mathbf\backslash cdot\backslash boldsymbol)\; \backslash mathbf\; \backslash right)\; +\; \backslash frac\; \backslash left(\backslash mathbf\; )\backslash mathbf\; +\; (\backslash mathbf\backslash cdot\backslash boldsymbol)\; \backslash mathbf\; \backslash right)\; -\; \backslash frac\; \backslash boldsymbol\backslash left(\backslash epsilon\_0\; E^2\; +\; \backslash frac\; B^2\; \backslash right)$ - \epsilon_0\frac\left( \mathbf\times \mathbf\right). This result can be re-written more compactly by introducing the Maxwell stress tensor, :$\backslash sigma\_\; \backslash equiv\; \backslash epsilon\_0\; \backslash left(E\_i\; E\_j\; -\; \backslash frac\; \backslash delta\_\; E^2\backslash right)\; +\; \backslash frac\; \backslash left(B\_i\; B\_j\; -\; \backslash frac\; \backslash delta\_\; B^2\backslash right).$ All but the last term of the above expression for the force density, $\backslash mathbf$, can be written as the divergence of the Maxwell tensor: :$\backslash mathbf\; +\; \backslash epsilon\_0\; \backslash mu\_0\; \backslash frac\backslash ,\; =\; \backslash nabla\; \backslash cdot\; \backslash mathbf$, which gives the electromagnetic force density in terms of Maxwell stress tensor, $\backslash sigma\_$, and the Poynting vector, $\backslash mathbf\; =\; \backslash mathbf\backslash times\backslash mathbf/\backslash mu\_0$. Now, the magnetic tension is implicitly included inside $\backslash sigma\_$. The implication of the above relation is the conservation of momentum. Here, $\backslash nabla\; \backslash cdot\; \backslash mathbf$ is the momentum flux density and plays a role similar to $\backslash mathbf$ in Poynting's theorem. 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「Magnetic tension force」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.