59:
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
360:
60:
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
217:
139:
528:
671:
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.
189:
597:
is less than one due to the existence of spin–orbital energy exchange, which allows transitions to the "spin up" state (with probability 25.25 times less than to the "spin down" state).
661:
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.
450:
64:
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
209:
595:
572:
552:
474:
423:
403:
383:
611:
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.
355:{\displaystyle \tau =A{\frac {4\pi \varepsilon _{0}\hbar ^{2}}{mce^{2}}}\left({\frac {mc^{2}}{E}}\right)^{2}\left({\frac {H_{0}}{H}}\right)^{3}.}
600:
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
70:
479:
632:
680:
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.
828:
628:
842:
794:
147:
623:, France, Germany, United States, Japan, and Switzerland in storage rings with electrons of energy 1–50 GeV.
938:
749:
948:
704:
933:
801:
Section 21.3 for the theory and section 27.2 for experimental verifications of the
Sokolov–Ternov effect.
729:
428:
943:
23:
is the effect of self-polarization of relativistic electrons or positrons moving at high energy in a
872:"Calculations of Bell and Leinaas and Derbenev and Kondratenko for radiative electron polarization"
871:
28:
886:
764:
194:
668:
which, up to now, under experimentally achievable conditions is too small to be observed.
8:
453:
890:
768:
910:
580:
557:
537:
459:
408:
388:
368:
902:
838:
790:
699:
914:
894:
834:
848:
531:
727:[Polarization and spin effects in the theory of synchrotron radiation].
56:
40:
36:
24:
927:
898:
830:
Synchrotron
Radiation Theory and Its Development: in Memory of I. M. Ternov
694:
665:
601:
61:
906:
32:
725:О поляризационных и спиновых эффектах в теории синхротронного излучения
641:
1975 – Stanford (USA), with the use of 2.4 GeV SPEAR storage ring.
638:
1971 – Orsay (France), with the use of 536 MeV АСО storage ring.
608:
52:
750:"On Polarization and Spin Effects in Synchrotron Radiation Theory"
27:. The self-polarization occurs through the emission of spin-flip
134:{\displaystyle \xi (t)=A\left(1-e^{-{\frac {t}{\tau }}}\right),}
631:(first observation), with the use of 625 MeV storage ring
523:{\displaystyle H_{0}\approx 4.414\times 10^{13}~{\text{gauss}}}
789:. New York: American Institute of Physics Translation Series.
649:
619:
The
Sokolov–Ternov effect was experimentally observed in the
785:
A. A. Sokolov; I. M. Ternov (1986). C. W. Kilmister (ed.).
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73:
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is the limiting degree of polarization (92.4%), and
722:
648:, Hamburg (Germany), with the use of 15.2 GeV
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522:
468:
444:
417:
397:
377:
354:
203:
183:
133:
826:
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184:{\displaystyle A=8{\sqrt {3}}/15\approx 0.924}
614:
35:and the prediction rigorously justified by
869:
810:
748:A. A. Sokolov & I. M. Ternov (1964).
425:are the mass and charge of the electron,
664:The effect also has been related to the
16:Physical phenomenon of spin-polarization
926:
780:
778:
723:Sokolov, A. A.; I. M. Ternov (1963).
787:Radiation from Relativistic Electrons
577:The limiting degree of polarization
870:Barber, D. P.; Mane, S. R. (1988).
775:
629:Budker Institute of Nuclear Physics
13:
14:
960:
815:(2nd ed.). Berlin: Springer.
607:The self-polarization effect for
55:in a magnetic field can have its
445:{\displaystyle \varepsilon _{0}}
827:V. A. Bordovitsyn, ed. (1999).
657:Applications and generalization
863:
820:
804:
741:
716:
83:
77:
31:. The effect was predicted by
1:
39:using exact solutions to the
7:
688:
554:is the magnetic field, and
10:
965:
730:Doklady Akademii Nauk SSSR
674:
46:
724:
710:
705:Froissart–Stora equation
615:Experimental observation
574:is the electron energy.
211:is the relaxation time:
899:10.1103/PhysRevA.37.456
476:is the speed of light,
591:
568:
548:
524:
470:
446:
419:
399:
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356:
205:
185:
135:
939:Synchrotron radiation
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471:
447:
420:
400:
380:
357:
206:
204:{\displaystyle \tau }
186:
136:
29:synchrotron radiation
21:Sokolov–Ternov effect
949:Polarization (waves)
581:
558:
538:
480:
460:
429:
409:
389:
369:
218:
195:
148:
71:
891:1988PhRvA..37..456B
813:Polarized Electrons
811:J. Kessler (1985).
769:1964SPhD....8.1203S
454:vacuum permittivity
934:Special relativity
587:
564:
544:
520:
466:
442:
415:
395:
375:
352:
201:
181:
131:
879:Physical Review A
851:on 3 January 2010
700:Hawking radiation
590:{\displaystyle A}
567:{\displaystyle E}
547:{\displaystyle H}
518:
514:
469:{\displaystyle c}
418:{\displaystyle e}
398:{\displaystyle m}
378:{\displaystyle A}
337:
305:
278:
165:
119:
956:
944:Particle physics
919:
918:
876:
867:
861:
860:
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847:. Archived from
835:World Scientific
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757:Sov. Phys. Dokl
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737:(5): 1052–1053.
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713:
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532:Schwinger field
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5:
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920:
885:(2): 456–463.
862:
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733:(in Russian).
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385:is as before,
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48:
45:
41:Dirac equation
37:Arseny Sokolov
25:magnetic field
15:
9:
6:
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3:
2:
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844:981-02-3156-3
840:
836:
833:. Singapore:
832:
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823:
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796:0-88318-507-5
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605:
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602:storage rings
598:
584:
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561:
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533:
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44:
42:
38:
34:
30:
26:
22:
882:
878:
865:
853:. Retrieved
849:the original
829:
822:
817:Section 6.2.
812:
806:
786:
760:
756:
743:
734:
728:
718:
695:Unruh effect
681:
670:
666:Unruh effect
663:
660:
618:
606:
599:
576:
364:
143:
62:storage ring
50:
20:
18:
33:Igor Ternov
928:Categories
855:17 August
609:positrons
500:×
494:≈
434:ε
251:ℏ
241:ε
237:π
222:τ
199:τ
176:≈
117:τ
109:−
101:−
75:ξ
915:29197700
763:: 1203.
689:See also
53:electron
907:9899676
887:Bibcode
765:Bibcode
644:1980 –
627:1971 –
530:is the
452:is the
913:
905:
841:
793:
675:Patent
633:VEPP-2
513:
144:where
47:Theory
911:S2CID
875:(PDF)
753:(PDF)
711:Notes
650:PETRA
517:gauss
497:4.414
365:Here
179:0.924
903:PMID
857:2008
839:ISBN
791:ISBN
646:DESY
621:USSR
405:and
57:spin
19:The
895:doi
735:153
51:An
930::
909:.
901:.
893:.
883:37
881:.
877:.
837:.
777:^
759:.
755:.
682:47
604:.
534:,
508:13
504:10
456:,
173:15
43:.
917:.
897::
889::
859:.
799:.
771:.
767::
761:8
684:.
652:.
635:.
585:A
562:E
542:H
489:0
485:H
464:c
438:0
413:e
393:m
373:A
350:.
345:3
340:)
335:H
330:0
326:H
320:(
313:2
308:)
303:E
297:2
293:c
289:m
283:(
273:2
269:e
265:c
262:m
255:2
245:0
234:4
228:A
225:=
169:/
163:3
158:8
155:=
152:A
129:,
125:)
114:t
105:e
98:1
94:(
90:A
87:=
84:)
81:t
78:(
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