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 rigorously justified by him and Arsenij Sokolov using exact solutions to the Dirac equation [cite journal|author=A. A. Sokolov and I. M. Ternov|title=Polarization and Spin Effects in the Theory of Synchrotron Radiation|journal=Dokl. Akad. Nauk SSSR|volume=153|pages=1053|year=1963|url= [in Russian] .] [cite journal|author=A. A. Sokolov and I. M. Ternov|title=On Polarization and Spin Effects in Synchrotron Radiation Theory|journal=Sov. Phys. Dokl.|volume=8|pages=1203|year=1964|url= ] .

Theory

Electron in a magnetic field can have 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 lower 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 formulacite book|last=A. A. Sokolov and I. M. Ternov|publisher=American Institute of Physics Translation Series. Edited by C. W. Kilmister|location=New York|title=Radiation from Relativistic Electrons|year=1986|isbn=0883185075 Section 21.3 for the theory and section 27.2 for experimental verifications of the Sokolov-Ternov effect.]
$xi(t)=ABigl(1-e^\{-t/\; au\}Bigr)$
where $A=8sqrt\{3\}/15approx\; 0.924$ is the limiting degree of polarization (92,4%) and $au$ is the relaxation time,
$au=$8{hbar}^2}over {5sqrt{3}mc{e}^2Bigl(mc^2}over {EBigr)^2Bigl({H_0over H}Bigr)^3
Here $m$ and $e$ are the mass and charge of the electron, $c$ is the speed of light, $H\_0approx\; 4.41\; imes\; 10^\{13\}$ G is the Schwinger field, $H$ is the magnetic field, and $E$ is the electron energy.

The limiting degree of polarization $A$ is less than one due to the existence of spin-orbital energy exchange which allows for transitions to the "spin up" state (with probability 25.25 times less than to the "spin down" state).

Typical relaxation time is on the order of minutes and hours. Thus producing a highly polarized beam requires a long enough time and the use of storage rings.

The self-polarization effect for positrons is similar, with the only difference that positrons will tend to have spins oriented in the direction parallel to the direction of the magnetic field [cite book|last=J. Kessler|publisher=Springer|location=Berlin|title=Polarized Electrons. 2nd edition|year=1985 Section 6.2.] .

Experimental observation

Sokolov-Ternov effect was experimentally observed in the USSR, France, Germany, USA, Japan, and Switzerland in storage rings with electrons of energy 1-50 GeV. [cite book|last=V. A. Bordovitsyn (editor)|publisher=World Scientific|location=Singapore|title=Synchrotron Radiation Theory and Its Development: in Memory of I. M. Ternov|year=1999|isbn=9810231563|url=http://www.worldscibooks.com/physics/3492.html]

*1971 — Budker Institute of Nuclear Physics (first observation), with the use of 625 MeV storage ring VEPP-2.
*1971 — Orsay (France), with the use of 536 MeV АСО storage ring.
*1975 — Stanford (USA), with the use of 2.4 GeV SPEAR storage ring.
*1980 — DESY, Hamburg (Germany), with the use of 15.2 GeV PETRA.

Applications

The effect of radiative polarization provides a unique capability for creating polarized beams of high-energy electrons and positrons that can be used for various experiments.

The effect also gives strong evidence for experimental observation of the Unruh and Hawking radiations. Under experimentally achievable conditions for gravitational systems these radiations are too small to be observed. Recent work [Emil T. Akhmedov and Douglas Singleton. [http://arxiv.org/abs/0705.2525v3 On the physical meaning of the Unruh effect] .] shows that if one takes an accelerated observer to be an electron circularly orbiting in a constant external magnetic field, then the Sokolov-Ternov effect coincides with the Unruh effect, which is closely connected to the Hawking radiation.

Patent

* Sokolov A. A. and Ternov I. M. (1973): Award N 131 of 7 August 1973 with priority of 26 June 1963, Byull. Otkr. i Izobr., vol. 47.

References

ee also

*Unruh effect
*Hawking radiation