A narrow electromagnetic beam propagating parallel to an external magn
etic field in a plasma is considered theoretically. The theory assumes
that the plasma pressure is larger than the electromagnetic one. It i
s found that under the paraxial approximation the beam having a Gaussi
an cross section can propagate. The Rayleigh range is enlarged or shor
tened depending on the dielectric coefficients of the plasma. The beam
is either right- or left-hand polarized and both modes have the longi
tudinal component of the electric held as the Gaussian beam does in va
cuum. The phase velocities can become less than the light velocity c f
or some plasma parameters for which those velocities of the plane R- a
nd the L-waves are always greater than c.