Using a semi-classical quantum theory of the cyclotron radiation of a
nonrelativistic thermal electron in a very strong magnetic field, we p
resent the simplified formulae of the absorption coefficient of cyclot
ron resonance k(nu) and the absorption and/or scattering cross section
of cyclotron resonance sigma(nu) at base frequency omega(B) = eB/m(o)
c in the quadrupole approximation. The results can be conveniently use
d for studying the ''magnetic inverse-Compton scattering'', an importa
nt radiation mechanism in gamma-ray astronomy. (C) 1997 Elsevier Scien
ce B.V.