A charged particle in a time-varying magnetic field

Abstract

Electron interaction with a uniform magnetic field, suddenly (by leaps) changing in time, is considered theoretically. Characteristic features of the switching-on process are derived; in particular, it is shown that at low values E/B (E is the energy of the electron before switching, B is the intensity of the magnetic field) transitions are possible only to even Landau states, and at large E/B there is an interaction only with high-lying levels. Generalizations to more than one switching are presented. If the magnetic field is switched off and switched on again after time T, then electrons from an even (odd) Landau state can make transitions only to an even (odd) level. Varying the ratio omega B/ omega ( omega B is the cyclotron frequency, omega = pi /T), one can efficiently control the probabilities of electromagnetic emission or absorption. Various results of calculations of the switching process from B1 not=0 to B2 not=0 are also presented. In the appendix some properties of the functions Hn*(x)=(-i)nHn(ix) are given.