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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 Thomson cross section ： ウィキペディア英語版 Thomson scattering Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism. It is just the low-energy limit of Compton scattering: the particle kinetic energy and photon frequency are the same before and after the scattering. This limit is valid as long as the photon energy is much less than the mass energy of the particle: $\backslash nu\backslash ll\; mc^2/h$, or equivalently, if the wavelength of the light is much greater than the Compton wavelength of the particle. The classical description is also the low-intensity limit.〔http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1076&context=physicsumstadter - Experimental observation of relativistic nonlinear Thomson scattering〕 == Description of the phenomenon == In the low-energy limit, the electric field of the incident wave (photon) accelerates the charged particle, causing it, in turn, to emit radiation at the same frequency as the incident wave, and thus the wave is scattered. Thomson scattering is an important phenomenon in plasma physics and was first explained by the physicist J. J. Thomson. As long as the motion of the particle is non-relativistic (i.e. its speed is much less than the speed of light), the main cause of the acceleration of the particle will be due to the electric field component of the incident wave. In a first approximation, the influence of the magnetic field can be neglected.〔http://vixra.org/abs/1310.0260 The Influence of the Magnetic Field in the Thomson Scattering〕 The particle will move in the direction of the oscillating electric field, resulting in electromagnetic dipole radiation. The moving particle radiates most strongly in a direction perpendicular to its acceleration and that radiation will be polarized along the direction of its motion. Therefore, depending on where an observer is located, the light scattered from a small volume element may appear to be more or less polarized. The electric fields of the incoming and observed wave (i.e. the outgoing wave) can be divided up into those components lying in the plane of observation (formed by the incoming and observed waves) and those components perpendicular to that plane. Those components lying in the plane are referred to as "radial" and those perpendicular to the plane are "tangential". (It is difficult to make these terms seem natural, but it is standard terminology.) The diagram on the right depicts the plane of observation. It shows the radial component of the incident electric field, which causes the charged particles at the scattering point to exhibit a radial component of acceleration (i.e, a component tangent to the plane of observation). It can be shown that the amplitude of the observed wave will be proportional to the cosine of χ, the angle between the incident and observed waves. The intensity, which is the square of the amplitude, will then be diminished by a factor of cos2(χ). It can be seen that the tangential components (perpendicular to the plane of the diagram) will not be affected in this way. The scattering is best described by an emission coefficient which is defined as ε where ε dt dV dΩ dλ is the energy scattered by a volume element $dV$ in time dt into solid angle dΩ between wavelengths λ and λ+dλ. From the point of view of an observer, there are two emission coefficients, εr corresponding to radially polarized light and εt corresponding to tangentially polarized light. For unpolarized incident light, these are given by: :$$ \epsilon_t = \frac~I\,n :$$ \epsilon_r = \frac~I\,n\,\cos^2\chi where n is the density of charged particles at the scattering point, I is incident flux (i.e. energy/time/area/wavelength) and $\backslash sigma\_t$ is the Thomson cross section for the charged particle, defined below. The total energy radiated by a volume element $dV$ in time dt between wavelengths λ and λ+dλ is found by integrating the sum of the emission coefficients over all directions (solid angle): :$$ \int\epsilon d\Omega = \int_0^d\phi \int_0^\pi d\chi \left(\epsilon_t+\epsilon_r\right) \sin \chi = I\,\sigma_t\,n\,(2 + 2/3)\pi^2 = I\,\sigma_t\,n\,(8/3)\pi^2. The Thomson differential cross section, related to the sum of the emissivity coefficients, is given by : $$ \frac = \left(\frac\right)^2\frac expressed in SI units; q is the charge per particle, m the mass of particle, and $\backslash epsilon\_0$ a constant, the permittivity of free space. (To obtain an expression in cgs units, drop the factor of 4πε0.) Integrating over the solid angle, we obtain the Thomson cross section :$$ \sigma_t =\frac\left(\frac\right)^2 in SI units. The important feature is that the cross section is independent of photon frequency. The cross section is proportional by a simple numerical factor to the square of the classical radius of a point particle of mass m and charge q, namely :$$ \sigma_t = \fracr_e^2 Alternatively, this can be expressed in terms of $\backslash lambda\_c$, the Compton wavelength, and the fine structure constant: :$$ \sigma_t = \frac \left(\frac\right)^2 For an electron, the Thomson cross-section is numerically given by: :$$ \sigma_t =\frac \left(\frac\right)^2 = 6.652458734 \ldots\times 10^~\textrm^2=66.52458734 \ldots~\textrm^2 〔(【引用サイトリンク】 title=National Institute of Standards and Technology )〕 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「Thomson scattering」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.