The filamentation instability is one of the basic beam‐plasma instabilities that play a significant role in the energy deposition mechanism of the relativistic electrons generated by the laser‐plasma interaction in the fast ignition scenario. In this paper, the effect of the density gradient into plasma on the filamentation instability was investigated in the Weibel unstable plasma, where the plasma temperature anisotropy can play an important role. Results indicated that the density gradient enhances the instability growth rate so that decreasing the density gradient from the critical surface to the core of fuel leads to instability for longer regions in k space. Also, investigations in the region close to the critical surface showed that for decreasing the beam number density nb ≤ 0.01n0, the instability occurs for urn:x-wiley:08631042:media:ctpp202100027:ctpp202100027-math-0001 while this can be different for higher values. Increasing the beam relativistic factor causes a decreasing peak of instability growth rate because of a reduction in beam current, whereas the initial thermal spread of plasma amplifies the filamentation instability.
