Evolution of self-focusing instability in a semiconfined plasma

A system of equations obtained in the linear approximation is used to describe the temporal and spatial dependences of the perturbations of the electron density and electromagnetic field pressure as a result of a self-focusing instability. An accurate solution of this system is obtained in a semiconfined plasma neglecting diffraction and the thermal pressure. From this it follows that filamentation occurs far from the plasma boundary, extending to regions increasingly close to the boundary as a function of time.