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物理学中，汤姆孙散射是指电磁辐射和一个自由带电粒子产生的弹性散射。入射电磁波的电场使粒子加速，从而激发粒子产生和入射波频率相同的辐射，而入射波则被散射。汤姆孙散射是等离子物理学中的一个重要现象，它首先由英国物理学家J. J. 汤姆孙解释。

只要粒子的运动是非相对论性的（即速度远小于光速），粒子加速的主要原因都来自入射波的电场分量，而磁场的作用可被忽略。粒子将会在电场振动的方向上开始运动，从而产生电磁偶极辐射。运动粒子在垂直於运动方向上的辐射最强，而辐射沿着粒子的运动方向产生偏振。从而，取决于观察者的位置，从一个小体元散射的电磁波存在程度不同的偏振。

入射波和观察到的散射波的电场都可以分解为位於观察平面（由入射波和散射波构成的平面）内和垂直於观察平面的分量。习惯上，那些位於平面内的分量被称作“径向”，而垂直於平面的分量被称作“切向”，这是对於观察者而言的。

右图所示的是散射在观察平面内的情形，图中显示了入射电场的径向分量是造成位於散射点的带电粒子在该方向上发生运动的原因，并且这一运动也位於观察平面内。此外还可以看出散射波的振幅正比于入射波与散射波夹角χ的余弦，而散射波的光强正比於振幅的平方，从而含有cos²(χ)这一因子。而垂直於观察平面的切向分量则不会产生类似的影响。

描述散射的最佳方法是引入一个发射系数ε，而ε dt dV dΩ dλ是在时间间隔dt内被体元$dV$散射至固体角dΩ这一方向内，且波长介于λ和λ+dλ之间的入射波能量。从观察者的角度而言，汤姆孙散射存在有两个发射系数，一个是对应着径向偏振波的发射系数ε_r，另一个是对应着切向偏振波的发射系数ε。它们分别由下面关系给出：

$\epsilon _{t}={\frac {\pi \sigma }{2}}~I\,n$

$\epsilon _{r}={\frac {\pi \sigma }{2}}~I\,n\,\cos ^{2}(\chi )$

where n is the density of charged particles

at the scattering point, I is incident flux (i.e. energy/time/area/wavelength) and

σ is the Thomson differential cross section for the charged particles (area/solid angle), which is

$\sigma \equiv \left({\frac {q^{2}}{mc^{2}}}\right)^{2}=\left({\frac {q^{2}}{4\pi \epsilon _{0}mc^{2}}}\right)^{2}$

where the first expression is in cgs units, the second in SI units; q is the charge per particle, m the mass per particle, and $\epsilon _{0}$ a constant, the permittivity of free space.

Note that this is the square of the classical radius

of a point particle of mass m and charge q.

For example, for an electron, the differential cross section is:

$\sigma =\left({\frac {\alpha \lambda _{e}}{2\pi }}\right)^{2}=\left({\frac {\alpha \hbar }{m_{e}c}}\right)^{2}$

$\sigma =\left({\frac {\alpha \hbar }{m_{e}c}}\right)^{2}$

$\sigma =7.9407875\ldots \times 10^{-26}~{\textrm {cm}}^{2}$

Where $\lambda _{e}$ is the Compton wavelength of an electron.

The total energy radiated is found by integrating the sum of the emission coefficients over

all directions:

$\int _{0}^{2\pi }d\phi \int _{0}^{\pi }d\chi \left(\epsilon _{t}+\epsilon _{r}\right)\sin \chi =I\,\sigma _{T}\,n$

where σ_T is the total cross section:

$\lambda _{e}={\frac {h}{m_{e}c}}$

$\sigma _{T}={\frac {8\pi }{3}}\sigma ={\frac {8\pi }{3}}\left({\frac {\alpha \lambda _{e}}{2\pi }}\right)^{2}={\frac {8\pi }{3}}\left({\frac {\alpha \hbar }{m_{e}c}}\right)^{2}$

$\sigma _{T}={\frac {8\pi }{3}}\left({\frac {\alpha \hbar }{m_{e}c}}\right)^{2}$

For an electron, this cross-section is:

$\sigma _{T}=6.6524586\ldots \times 10^{-25}~{\textrm {cm}}^{2}$

Examples of Thomson scattering

The cosmic microwave background is thought to be linearly polarized as a result of Thomson scattering. Probes such as WMAP and the current Planck mission attempt to measure this polarization.

The solar K-corona is the result of the Thomson scattering of solar radiation from solar coronal electrons. NASA's STEREO mission will generate three-dimensional images of the electron density around the sun by measuring this K-corona from two separate satellites.

In tokamaks and other experimental fusion devices, the electron temperatures and densities in the plasma can be measured with high accuracy by detecting the effect of Thomson scattering of a high-intensity laser beam.

Inverse-Compton scattering can be viewed as Thomson scattering in the rest frame of the relativistic particle.

See also

• Compton scattering

• Klein-Nishina formula

External links

• Lecture notes on Thomson scattering

• Thomson scattering notes

References

• Billings, Donald E., ``A Guide to the Solar Corona, Academic Press, New York 1966.