Self generated axial magnetic field due to ponderomotive force in a laser produced plasmas is discussed. When an intense laser beam propagates in an expanding plasma, spatial inhomogeneities present in the intensity profile of the incident laser beam can grow rapidly due to self-focusing effect, which result in localized filamentation of higher intensity. This filamentation can directly cause localized heating of the target, thus destroying the uniformity in the ablative acceleration necessary for high compression implosions. In view of experimental observations a small fluctuation in the intensity profile of a plane electromagnetic beam grows as it propagates in the plasma where the self-generated axial magnetic field cannot be neglected. Based on these observations we discuss a mechanism of filamentation instability due to ponderomotive forces in laser produced plasmas.