Sokolov-Ternov effect

The Sokolov–Ternov effect is the effect of self-polarization of relativistic electrons or positrons moving at high energy in a magnetic field. The self-polarization occurs through the emission of spin-flip synchrotron radiation. The effect was predicted by Igor Ternov and the prediction rigorously justified by Arseny Sokolov using exact solutions to the Dirac equation.

An electron in a magnetic field can have its spin oriented in the same ("spin up") or in the opposite ("spin down") direction with respect to the direction of the magnetic field (which is assumed to be oriented "up"). The "spin down" state has a higher energy than "spin up" state. The polarization arises due to the fact that the rate of transition through emission of synchrotron radiation to the "spin down" state is slightly greater than the probability of transition to the "spin up" state. As a result, an initially unpolarized beam of high-energy electrons circulating in a storage ring after sufficiently long time will have spins oriented in the direction opposite to the magnetic field. Saturation is not complete and is explicitly described by the formula

where ${\displaystyle \scriptstyle A\;=\;8{\sqrt {3}}/15\;\approx \;0.924}$ is the limiting degree of polarization (92.4%) and ${\displaystyle \scriptstyle \tau }$ is the relaxation time,

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