“…This is valuable for both fundamental research on physics of matter in extreme conditions and various applications. The notable directions are: laser-driven electron acceleration to the ultrarelativistic energies [3], acceleration of ion beams to tens and hundreds MeV / nucleon [4,5], generation of X-ray and gamma ray radiation including pulses of atto-and zeptosecond duration [6], and QED effects in ultrahigh intensity field, namely electron-positron pair production and nonlinear optics of vacuum [7,8]. The applications are fast ignition of inertial confinement fusion targets [9], hadron therapy for cancer treatment [10], protonography, xray imaging [11], etc.…”