Abstract
In Frenkel model of charged particle possessing magnetic moment the magnetic dipole interaction with external field manifests itself not only in Stern–Gerlach (SG) force but in particle’s inertia as well. Within this model there exists general procedure to obtain spin corrections to the system of Lorentz and BMT equations which here is applied to the event of the constant field and \(G={\mathcal{O}}(1)\) ( \(G=1.8\) for protons). We obtain the reduced system of Frenkel equations for the trajectory and spin which guarantees the constraint \(S\cdot\dot{x}=0\) and differs from Lorentz–BMT system by the non-linear spin corrections. The relative magnitude of these corrections is about \(\chi\simeq\mu F/mc^{2}\) ( \(\mu F\) being the magnetic moment energy in the rest frame (RF) of the particle) and is, generally, comparable in magnitude with the effects of non-homogeneity. The influence of non-linear spin corrections on the trajectory and spin evolution is examplified through the consideration of the proton moving in homogeneous magnetic field.
