  A phenomenological pion-nucleon interaction is used to obtain pionic mass
modification in presence of constant homogeneous magnetic field background at
finite temperature and chemical potential in the real time formalism of thermal
field theory. The magnetically modified propagator in its complete form is used
to obtain the one loop self-energy for pions. For charged pions we find that
the effective mass increases with the magnetic field at given temperature and
chemical potential. Since the transverse momentum of charged pion is quantized
and its contribution to Dyson-Schwinger Equation is large compared to the loop
correction, the charged pion mass remains constant with both temperature and
chemical potential for a given landau level. In order to unveil the role of the
real part of the self-energy, we also calculate the effective mass neglecting
the trivial shift. The effective mass for charged pions shows an oscillatory
behavior which is attributed to the thermal contribution of the self-energy. It
is argued that the magnetic field dependent vacuum contribution to the
self-energy influences the behavior of the effective mass both qualitatively
and quantitatively. We also find that very large field is necessary for neutral
pions to condense.
