Strength of Higher-Order Spin-Orbit Resonances

When polarized particles are accelerated in a synchrotron, the spin precession can be periodically driven by Fourier components of the electromagnetic fields through which the particles travel. This leads to resonant perturbations when the spin-precession frequency is close to a linear combination of the orbital frequencies. When such resonance conditions are crossed, partial depolarization or spin flip can occur. The amount of polarization that survives after resonance crossing is a function of the resonance strength and the crossing speed. This function is commonly called the Froissart-Stora formula. It is very useful for predicting the amount of polarization after an acceleration cycle of a synchrotron or for computing the required speed of the acceleration cycle to maintain a required amount of polarization. However, the resonance strength could in general only be computed for first-order resonances and for synchrotron sidebands. When Siberian Snakes adjust the spin tune to be 1/2, as is required for high energy accelerators, first-order resonances do not appear and higher-order resonances become dominant. Here we will introduce the strength of a higher-order spin-orbit resonance, and also present an efficient method of computing it. Several tracking examples will show that the so computed resonance strength can indeed be used in the Froissart-Stora formula. HERA-p is used for these examples which demonstrate that our results are very relevant for existing accelerators.Comment: 10 pages, 6 figure

Parametrically forced sine-Gordon equation and domain walls dynamics in ferromagnets

A parametrically forced sine-Gordon equation with a fast periodic {\em mean-zero} forcing is considered. It is shown that $\pi$-kinks represent a class of solitary-wave solutions of the equation. This result is applied to quasi-one-dimensional ferromagnets with an easy plane anisotropy, in a rapidly oscillating magnetic field. In this case the $\pi$-kink solution we have introduced corresponds to the uniform ``true'' domain wall motion, since the magnetization directions on opposite sides of the wall are anti-parallel. In contrast to previous work, no additional anisotropy is required to obtain a true domain wall. Numerical simulations showed good qualitative agreement with the theory.Comment: 3 pages, 1 figure, revte