View source for Froissart–Stora equation

The '''Froissart–Stora equation''' describes the change in [[spin polarization|polarization]] which a high energy charged particle beam in a [[storage ring]] will undergo
as it passes through a [[resonance]] in the [[Spin (physics)|spin]] tune.<ref>{{cite journal | doi=10.1016/0029-554X(60)90033-1 | volume=7 | issue=3 | title=Depolarisation d'un faisceau de protons polarises dans un synchrotron | journal=Nuclear Instruments and Methods | pages=297–305|bibcode = 1960NucIM...7..297F | date=June 1960 | last1=Froissart | first1=Marcel | last2=Stora | first2=Raymond }}</ref>
<ref>http://iopscience.iop.org/0034-4885/68/9/R01/ "Spin-polarized charged particle beams in high-energy accelerators" by S. Mane et al. (2005)</ref> It is named after the French physicists [[:fr:Marcel Froissart|Marcel Froissart]] and [[Raymond Stora]].
The polarization following passage through the resonance is given by
:<math> P_y = P_{y0}\left[2\exp\left({-\frac{\pi|\epsilon|^2}{2\alpha_0}}\right)-1\right]</math>
where <math>\epsilon</math> is the resonance strength and <math>\alpha_0</math> is the speed at which the resonance is crossed.  <math>P_{y0}</math> is the initial polarization before resonance crossing.

The resonance may be crossed by raising the energy so that the spin tune passes through a resonance, or driven with a transverse magnetic field at a frequency that is in resonance with the spin oscillations.

The Froissart–Stora equation has a direct analogy in condensed matter physics in the [[Landau–Zener formula|Landau–Zener]] effect.
<ref>{{cite journal | doi=10.1016/0375-9601(82)90757-5 | volume=87 | issue=9 | title=Dynamics of traversing an avoided level crossing | journal=Physics Letters A | pages=455–456|bibcode = 1982PhLA...87..455T | date=1982-02-08 | last1=Turrin | first1=A. }}</ref>

==Other spin-dynamics effects==
The original Froissart–Stora equation was derived for polarized protons.  It may also be applied to polarized electrons in storage rings.  In this case, there are additional polarization effects resulting from the synchrotron radiation.  In particular, the [[Sokolov–Ternov effect]] describes the polarization due to spin flip radiation.  In the case of a non-planar ring, this must be generalized as was done by Derbenev and Kondratenko.<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>

==Notes==
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[[Category:Accelerator physics]]
[[Category:Eponymous equations of physics]]
[[Category:Quantum mechanics]]