  Plasmas may be used as gain media for amplifying intense lasers, and external
magnetic fields may be applied to improve the performance. For mid-infrared
lasers, the requisite magnetic field is on megagauss scale, which can already
be provided by current technologies. Designing the laser amplifier requires
knowing the magnetized three-wave coupling coefficient, which is mapped out
systematically in this paper. By numerically evaluating its formula, we
demonstrate how the coupling depends on angle of wave propagation, laser
polarization, magnetic field strength, plasma temperature, and plasma density
in the backscattering geometry. Since the mediation is now provided by
magnetized plasma waves, the coupling can differ significantly from
unmagnetized Raman and Brillouin scatterings.
