Compression of femtosecond petawatt laser pulses in a plasma under the conditions of wake-wave excitation

We propose the concept of a plasma compressor capable of producing extremely short relativistic laser pulse, which is based on the studies of self-focusing of high-power laser pulses under the wake-wave excitation conditions. It is shown that, in the optimal regime, the compression of laser pulses up to a duration of one optical cycle is possible. We study the influence of hose instability on the process of pulse self-compression and have found that this instability is not important for a wide set of initial conditions. The matter is that the length of pulse distortion in both transverse and longitudinal directions is larger than the length of the pulse self-compression. Hose instability gives only negligible decrease of compression degree and weak deformation of pulse profile.