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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]] which then were rigorously justified by [[Arsenij Sokolov]] using exact solutions to the [[Dirac equation]].<ref>{{Cite journal|first=A. A.|last=Sokolov|coauthors=I. M. Ternov|title=О поляризационных и спиновых эффектах в теории синхротронного излучения|trans_title=Polarization and spin effects in the theory of synchrotron radiation|journal=[[Doklady Akademii Nauk SSSR]]|volume=153|issue=5|pages=1052–1053|year=1963|language=Russian}}</ref><ref>{{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=http://puhep1.princeton.edu/~mcdonald/examples/QED/sokolov_spd_8_1203_64.pdf|bibcode = 1964SPhD....8.1203S }}</ref>
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==Theory==
An [[electron]] in a magnetic field can have its [[spin (physics)|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<ref name="ref1">{{Cite 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=0-88318-507-5}} Section 21.3 for the theory and section 27.2 for experimental verifications of the Sokolov–Ternov effect.</ref>
:<math> \xi(t)=A\Bigl(1  -e^{-\frac{t}{\tau}}\Bigr)</math>
 
where <math>\scriptstyle A \;=\; 8\sqrt{3}/15 \;\approx\; 0.924</math> is the limiting degree of polarization (92.4%) and <math>\scriptstyle \tau</math> is the relaxation time,
:<math>\tau = A{{{\hbar}^2} \over {mc{e}^2}}\Bigl({{mc^2} \over {E}}\Bigr)^2\Bigl({H_0 \over H}\Bigr)^3</math>
 
Here <math>\scriptstyle A</math> is as before, <math>\scriptstyle m</math> and <math>\scriptstyle e</math> are the mass and charge of the electron, <math>\scriptstyle c</math> is the speed of light, <math>\scriptstyle H_0 \;\approx\; 4.41 \,\times\, 10^{13}</math> G is the [[Schwinger field]], <math>\scriptstyle H</math> is the magnetic field, and <math>\scriptstyle E</math> is the electron energy.
 
The limiting degree of polarization <math>A</math> 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 ring]]s.
 
The self-polarization effect for [[positron]]s 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.<ref>{{Cite book|last=J. Kessler|publisher=Springer|location=Berlin|title=Polarized Electrons. 2nd edition|year=1985}} Section 6.2.</ref>
 
==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.<ref name="ref1"/><ref>{{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=981-02-3156-3|url=http://www.worldscibooks.com/physics/3492.html}}</ref>
 
*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 and generalization==
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 has been related to the [[Unruh effect]] which, up to now, under experimentally achievable conditions is too small to be observed.
 
The equilibrium polarization given by the Sokolov and Ternov has corrections when the orbit is not perfectly planar. The formula has been generalized by Derbenev and Kondratenko and others.<ref>http://pra.aps.org/abstract/PRA/v37/i2/p456_1 "Calculations of Bell and Leinaas and Derbenev and Kondratenko for radiative electron polarization"</ref>
 
==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'''.
 
==See also==
*[[Unruh effect]]
*[[Hawking radiation]]
*[[Froissart Stora equation]]
 
==Notes==
{{Reflist|1}}
 
{{Use dmy dates|date=September 2010}}
 
{{DEFAULTSORT:Sokolov-Ternov Effect}}
[[Category:Special relativity]]
[[Category:Synchrotron radiation]]
[[Category:Particle physics]]
[[Category:Polarization (waves)]]

Revision as of 21:28, 26 February 2014

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