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

摘要

We analyze the general radiation emission mechanism from a charged particlemoving in a curved inhomogeneous magnetic field. The consideration of thegradient makes the curved vacuum magnetic field compatible with the Maxwellequations and adds a non-trivial term to the transverse drift velocity and,consequently, to the general radiation spectrum. To obtain the radiationspectrum in the classical domain a general expression for the spectraldistribution and characteristic frequency of an electron in arbitrary motion isderived by using Schwinger's method. The radiation patterns of theultrarelativistic electron are represented in terms of the acceleration of theparticle. The same results can be obtained by considering that the motion ofthe electron can be formally described as an evolution due to magnetic andelectric forces. By defining an effective electromagnetic field, which combinesthe magnetic field with the fictitious electric field associated to thecurvature and drift motion, one can obtain all the physical characteristics ofthe radiation by replacing the constant magnetic field with the effectivefield. The power, angular distribution and spectral distribution of all threecomponents (synchrotron, curvature and gradient) of the radiation areconsidered in both classical and quantum domain in the framework of thisunified formalism. In the quantum domain the proposed approach allows the studyof the effects of the inhomogeneities and curvature of the magnetic field onthe radiative transitions rates of electrons between low-lying Landau levelsand the ground state.