Relativistic self-focusing of laser beams in time-harmonic plane waves: arbitrary intensity

This paper presents a paraxial theory of relativistic self-focusing of a Gaussian laser beam in plasma for a time-harmonic plane wave at arbitrary beam intensity. Since the relativistic mechanism is instantaneous, the theory is also applicable to self-focusing of laser pulses. The analysis leads to two values for the critical beam power for self-focusing, P_cr1 and P_cr2. When P < P_cr1 < P_cr2, the beam diverges. When P_cr1 <P <p_cr2, it first converges, then diverges, and so on. When P > P_cr2 it first diverges, then converges, and so on.