Noncollapsing vectorial twisted laser beam in plasma under the paraxial approximation

Using the source-dependent expansion method and the paraxial approximation, the evolution of the vectorial beam width in laser-plasma interaction is investigated. By considering parabolic nonlinearity, the self-focusing of the Laguerre-Gaussian beam in a plasma medium is studied. It is shown that, at self-focusing of the beam in a plasma with Kerr-type nonlinearity, the effect coming out from the divergence term dominates over modifications related to other vectorial effects. This term is interpreted as nonlinear diffraction which plays the role of an effective saturation. The effect of the vortex charge number l, initial (input) beam intensity and plasma temperature on self-focusing of the vectorial Laguerre-Gaussian beam is explored. Since the Laguerre-Gaussian modes can be used to control focusing forces and improve the electron bunch quality in laser-plasma accelerators, the condition for self-focusing of a doughnut vectorial beam in a Kerr-like plasma medium is established and the expression for critical power is obtained. Also, it is shown that vectorial effects lead to the arrest of catastrophic collapse, and a beam width focusing-defocusing oscillation can occur.