Unified Classical and Quantum Radiation Mechanism for Ultra-Relativistic Electrons in Curved and Inhomogeneous Magnetic Fields

Abstract

We analyze the general radiation emission mechanism from a charged particle moving in a curved inhomogeneous magnetic field. The consideration of the gradient makes the curved vacuum magnetic field compatible with the Maxwell equations and adds a non-trivial term to the transverse drift velocity and, consequently, to the general radiation spectrum. To obtain the radiation spectrum in the classical domain a general expression for the spectral distribution and characteristic frequency of an electron in arbitrary motion is derived by using Schwinger's method. The radiation patterns of the ultrarelativistic electron are represented in terms of the acceleration of the particle. The same results can be obtained by considering that the motion of the electron can be formally described as an evolution due to magnetic and electric forces. By defining an effective electromagnetic field, which combines the magnetic field with the fictitious electric field associated to the curvature and drift motion, one can obtain all the physical characteristics of the radiation by replacing the constant magnetic field with the effective field. The power, angular distribution and spectral distribution of all three components (synchrotron, curvature and gradient) of the radiation are considered in both classical and quantum domain in the framework of this unified formalism. In the quantum domain the proposed approach allows the study of the effects of the inhomogeneities and curvature of the magnetic field on the radiative transitions rates of electrons between low-lying Landau levels and the ground state.