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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 Ponderomotive force ： ウィキペディア英語版 Ponderomotive force In physics, a ponderomotive force is a nonlinear force that a charged particle experiences in an inhomogeneous oscillating electromagnetic field. The ponderomotive force Fp is expressed by :$\backslash mathbf\_$$\backslash nabla$$(E^2)$ which has units of newtons/ampere (in SI units) and where ''e'' is the electrical charge of the particle, ''m'' is its mass, ''ω'' is the angular frequency of oscillation of the field, and ''E'' is the amplitude of the electric field. At low enough amplitudes the magnetic field exerts very little force. This equation means that a charged particle in an inhomogeneous oscillating field not only oscillates at the frequency of ''ω'' of the field, but is also accelerated by Fp toward the weak field direction. It is noteworthy that this is a rare case where the sign of the charge on the particle does not change the direction of the force, unlike the Lorentz force. The mechanism of the ponderomotive force can be easily understood by considering the motion of a charge in an oscillating electric field. In the case of a homogeneous field, the charge returns to its initial position after one cycle of oscillation. In the case of an inhomogeneous field, the force exerted on the charge during the half-cycle it spends in the area with higher field amplitude points in the direction where the field is weaker. It is larger than the force exerted during the half-cycle spent in the area with a lower field amplitude, which points towards the strong field area. Thus, averaged over a full cycle there is a net force that drives the charge toward the weak field area. ==Derivation== The derivation of the ponderomotive force expression proceeds as follows. Consider a particle under the action of a non-uniform electric field oscillating at frequency $\backslash omega$ in the x-direction. The equation of motion is given by: :$\backslash ddot=g(x)\backslash cos(\backslash omega\; t),$ neglecting the effect of the associated oscillating magnetic field. If the length scale of variation of $g(x)$ is large enough, then the particle trajectory can be divided into a slow time motion and a fast time motion:〔''Introduction to Plasma Theory'', second edition, by Nicholson, Dwight R., Wiley Publications (1983), ISBN 0-471-09045-X〕 :$x=x\_0+x\_1$ where $x\_0$ is the slow drift motion and $x\_1$ represents fast oscillations. Now, let us also assume that $x\_1\; \backslash ll\; x\_0$. Under this assumption, we can use Taylor expansion on the force equation about $x\_0$ to get, :$\backslash ddot+\backslash ddot=\backslash left(g\text{'}(x\_0)\backslash right)\backslash cos(\backslash omega\; t)$ :$\backslash ddot\; \backslash ll\; \backslash ddot$, and because $x\_1$ is small, $g(x\_0)\; \backslash gg\; x\_1\; g\text{'}(x\_0)$, so :$\backslash ddot=g(x\_0)\backslash cos(\backslash omega\; t)$ On the time scale on which $x\_1$ oscillates, $x\_0$ is essentially a constant. Thus, the above can be integrated to get, :$x\_1=-\backslash frac\; \backslash cos(\backslash omega\; t)$ Substituting this in the force equation and averaging over the $2\backslash pi\; /\; \backslash omega$ timescale, we get, :$\backslash ddot=-\backslash frac$ :$\backslash Rightarrow\; \backslash ddot=-\backslash frac\backslash left.\backslash frac\backslash left()\backslash right|\_$ Thus, we have obtained an expression for the drift motion of a charged particle under the effect of a non-uniform oscillating field. 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「Ponderomotive 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.