Space-time development of the selffocusing instability in a plasma layer

Self-focusing instability in laser plasma resulting in laser beam decomposition into thin filaments is considered. Consideration is conducted with regard to occuring electromagnetic field perturbation and plasma density dependence on time. It is shown that diffraction and thermal pressure accounting in the course of considering filamentation in laser plasma leads to the occurrance of plasma density and HF pressure perurbations non-monotonously changing in time and space. Depending on the pumping wave amplitude value these perturbations are either close to a standing wave (weak pumping) or appear to be a travelling wave propagating deep into the plasma (strong pumping). These waves' amplitude grow with time and with the increase of the distance from the boundary