  The nonlinearity of the plasma medium provides for an interesting prospect
for High Harmonic Generation (HHG) of electromagnetic (EM) wave. One can tune
the characteristic features of harmonics by varying the plasma as well as the
EM wave properties. It is shown here that an application of an external
magnetic field adds to the richness of the HHG generation mechanisms in the
plasma medium. The plasma dispersion properties get modified in the presence of
a magnetic field and it opens various possibilities for HHG both in O-mode and
X-mode configurations. This has been shown here with the help of
Particle-In-Cell (PIC) simulations of a moderately intense laser (to avoid
complications arising from relativistic nonlinearities) of sub-picoseconds
duration falling on a plasma with an applied external magnetic field. The
observations have been analyzed and an understanding of the mechanism has been
provided. A discussion of the appropriate parameter regime and pertinent
conditions has also been provided.
