Nonlinear evolutions of an ultra-intense ultra-short laser pulse in a rarefied plasma through a new quasi-static theory

Abstract

Beginning from the set of cold-fluid plus Maxwell equations in the instantaneous, Lorentz-boosted Pulse Co-Moving Frame (PCMF), a new quasistatic theory is developed to describe the nonlinear pulse evolutions due to the wakefield excitation, and is verified through comparison with particle-in-cell (PIC) simulations. According to this theory, the plasma-motion can be treated perturbatively and produces quasi-static wakefield in the PCMF, and the pulse envelope is governed by a form of the Schrodinger equation. The pulse evolutions are characterized by local conservation laws resulted from this equation and subjected to Lorentz transformation into the laboratory frame. In this context, new formulas describing the time-behaviors of group velocity, wake amplitude and carrier frequency are derived and best confirmed by simulation data. The spectral evolutions of the radiation are described based on the properties of the Schrodinger equation, predicting the emergence of a new extra-ordinary dispersion branch with linear relation ck   ( c is the light speed) approved by simulations.

Self modulation and scattering instability of a relativistic short laser pulse in an underdense plasma

“…We consider the wakefiled induced pulse self-modulations within the slow envelope approximation (SEA) [2,21,22,43,44,46,47]. In this regard, it should be mentioned that SEA has been frequently applied to study ultra-short [21,43,44,46,47] and short (longer than plasma wavelength) [21,22] pulse interactions with plasma. Especially, we should mention the more recent work by Schroeder etal [44] on nonlinear evolutions of ultra-short laser pulses in plasma, which our treatment in this section is a generalization of this work to include general pulse lengths (short and ultra-short).…”

“…We consider the wakefiled induced pulse self-modulations within the slow envelope approximation (SEA) [2,21,22,43,44,46,47]. In this regard, it should be mentioned that SEA has been frequently applied to study ultra-short [21,43,44,46,47] and short (longer than plasma wavelength) [21,22] pulse interactions with plasma.…”

“…This allows for very longer pulse lengths in applying SEA, with respect to the condition / p p L c   (ultra-short pulse length) previously considered in this context [43,44,46,47].…”

“…A treatment of short laser pulses in the boosted frame is presented by Yazdanpanah [43] which reveals the importance of induced wakefied on pulse evolutions.…”

“…In the case of self-modulation, the approach under-consideration is an extension of works done by Schroeder etal [44] and Yazdanpanah [43] on ultra-short pulses (pulse lengths shorter than plasma wavelength), to include pulse lengths exceeding the plasma wavelength. Furthermore, by applying a technical mathematical treatment, the obtained self-modulation equations are solved and reduce to closed results which well agree with presented simulation results.…”