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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> | |||
==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 23:15, 13 October 2013
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.[1][2]
Theory
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[3]
where is the limiting degree of polarization (92.4%) and is the relaxation time,
Here is as before, and are the mass and charge of the electron, is the speed of light, G is the Schwinger field, is the magnetic field, and is the electron energy.
The limiting degree of polarization 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.[4]
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.[3][5]
- 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.[6]
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
Notes
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The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - ↑ 3.0 3.1 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 Section 21.3 for the theory and section 27.2 for experimental verifications of the Sokolov–Ternov effect. - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 Section 6.2. - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ http://pra.aps.org/abstract/PRA/v37/i2/p456_1 "Calculations of Bell and Leinaas and Derbenev and Kondratenko for radiative electron polarization"