  Nonlinear Thomson scattering of an electron motion in a combining field
constituted by an elliptically polarized laser and a background magnetic field
is investigated. The dependence of the electron trajectories, the fundamental
frequency, the maximum radiation power in spatial distribution and
corresponding spatial angle on ellipticity are obtained. In addition, we find
that the angular distributions of scattering spectra with respect to the
azimuthal angle exhibits the symmetry no matter what the order of harmonics,
the laser intensity, the magnetic resonance parameter and the initial axial
momentum are. Meanwhile, the polar angle distribution of the spectra approaches
more and more the laser propagation direction with the laser intensity, the
magnetic resonance parameter and the initial axial momentum. The maximum
radiated power increases and the corresponding polar angle decreases. The
optimal angle for the maximum radiated power per unit of solid, the
corresponding photon number and the photons brightness can be obtained, which
implies that the high quality XUV or/and x-ray can be generated by the studied
scheme when the suitable parameters are chosen.
