  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.
