  The Thomson scattering spectra by an electron moving in the laser-magnetic
resonance acceleration regime are computed numerically and analytically. The
dependence of fundamental frequency on the laser intensity and magnetic
resonance parameter is examined carefully. By calculating the emission of a
single electron in a circularly polarized plane-wave laser field and constant
external magnetic field, the scale invariance of the radiation spectra is
evident in terms of harmonic orders. The scaling law of backscattered spectra
are exhibited remarkably for the laser intensity as well for the initial axial
momentum of the electron when the cyclotron frequency of the electron
approaches the laser frequency. The results indicate that the magnetic
resonance parameter plays an important role on the strength of emission. And
the rich features of scattering spectra found may be applicable to the
radiation source tunability.
