Self-trapping of a laser beam of ultrarelativistic intensities

Since a theory that can justify the condition of matching of the laser and plasma parameters to implement the relativistic self-trapping regime for laser light in a plasma, which is the most efficient for the acceleration of electrons, is still absent, doubts remain in the necessity of the corresponding extensive experimental studies, particularly in view of the lack of justification or completion of previous theories. The presented theoretical analytical approach, which includes the relativistic nonlinearity of the electron mass and electron cavitation in the plasma, allows one to overcome this problem and provides an analytical justification of the conditions of such matching for ultrarelativistic laser beams at the quantitative level, which is in agreement with the multidimensional numerical simulation.