In a recent series of publications, a new theory of electromagnetic ra
diation with emission frequency close to the plasma frequency and/or i
ts harmonic (i.e., the plasma emission) was presented; In this theory,
the emission of radiation takes place as a result of excitation of lo
ng wavelength modes by a nonlinear beam-plasma instability, which are
converted to radiative electromagnetic waves by a nonlinear mode conve
rsion process. Unlike standard theories, the new theory;predicts high
radiation growth rate. In all the previous efforts on this theory, how
ever, effects due to the presence of constant background magnetic fiel
d were ignored. The purpose of this article is to generalize the new t
heory to the case of weakly magnetized plasmas. (C) 1997 American Inst
itute of Physics.