Radiation of a charged particle with a quadratic Hamiltonian

This paper considers the motion and radiation of a charged particle in a homogeneous magnetic field and the field of a quadrupole condenser using the method of integrals of motion and the method of coherent states in the case of electric and magnetic fields arbitrarily depending on time and periodic-in-time fields. The radiation due to the charge transfer between coherent states is reviewed. The radiation due to the transitions between quasienergy states is computed for periodic-in-time fields. It was noted that the effect of amplification of the incident radiation with the satellite’s frequencies can be observed.