Self-focusing is one of the key issues in laser plasma physics applications.
Problems involving a multidimensional beam within an inhomogeneous plasma are
diffficult to handle. This paper presents the investigation of two-dimensional self-focusing
of a laser beam in a plasma whose density n(r, z) is a function of radial as
well as z coordinates. The nonlinear mechanism responsible for modification of the
background density and the dielectric function is of ponderomotive type. A variational
technique is used here for deriving the equations for the beam width and the
longitudinal phase. It is observed numerically that an initially diffracting beam
is accompanied by oscillatory self-focusing of the beam with distance of propagation.
The effect of inhomogeneity scale lengths is also observed. The increase in
Lr (= L∥/L⊥) results in oscillatory self-focusing and defocusing with distance of
propagation. Furthermore, critical fields for self-trapping of a laser beam as a function
of refraction, diffraction lengths and scale lengths of inhomogeneities are also
evaluated. Lastly, whatever parameters are chosen, the phase is always negative.