Froissart–Stora equation

The Froissart–Stora equation describes the change in polarization which a high energy charged particle beam in a storage ring will undergo as it passes through a resonance in the spin tune.[1] [2] It is named after the French physicists Marcel Froissart and Raymond Stora. The polarization following passage through the resonance is given by

${\displaystyle P_{y}=P_{y0}\left[2\exp \left({-{\frac {\pi |\epsilon |^{2}}{2\alpha _{0}}}}\right)-1\right]}$

where ${\displaystyle \epsilon }$ is the resonance strength and ${\displaystyle \alpha _{0}}$ is the speed at which the resonance is crossed. ${\displaystyle P_{y0}}$ 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 effect. [3]