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.

By sophisticated application of particle-in-cell simulations, we demonstrate the ultimate role of non-linear pulse evolutions in accelerating electrons during the entrance of an intense laser pulse into a preformed density profile. As a key point in our discussions, the non-linear pulse evolutions are found to be very fast even at very low plasma densities, provided that the pulse length exceeds the local plasma wavelength. Therefore, these evolutions are sufficiently developed during the propagation of typical short density scale lengths occurred at high contrast ratios of the pulse, and lead to plasma heating via stochastic acceleration in multi-waves. Further analysis of simulation data at different physical parameters indicates that the rate of evolutions increases with the plasma density leading to higher plasma heating and overgrown energetic electrons. In the same way, shortening the density scale length results into increase in the evolution rate and, simultaneously, decrease in the interaction time. This behavior can describe the observed optimum value of pre-plasma scale length for the maximum electron heating.

Characterization of self-consistent laser-plasma evolutions serves as a fundamental issue in the field of relativistic laser-plasma interactions. In this paper, we present an analysis framework for description of these evolutions during propagation of a short intense laser pulse in a sub-critical high-density plasma (the pulse length exceeds the plasma wavelength). In this context, the pulse evolutions are attributed to the wakefield induced self-modulation and destabilization via parametric exponentiation of the initial noise content. The self-consistent plasma evolutions are formulated in terms of quantities which used to be motion constants in the absence of pulse evolutions. This proves very useful both in understanding plasma evolutions during self-modulation and also in facilitating the instability studies in the strongly nonlinear regime, via refinement of unstable plasma perturbations.General analytical solutions, at arbitrary pulse conditions, are derived for selfmodulation, indicating that the envelop evolutions are driven by the induced spatial frequency-chirp. Also, these results state that the envelope attains fine modulations

In this paper, plasma heating is numerically investigated using a 1D-3V particle-in-cell simulation code through the interaction between an intense short laser pulse with temporal duration, τ L = 60 fs, and a plasma having a slightly overcritical bulk density and an exponential pre-plasma density profile. The aim is to identify, via suitable parametric analysis, the most relevant nonlinear mechanisms as a function of the system parameters. As key points of our research, simulation results revealed that, for pulse-lengths less than the local nonlinear plasma wavelength, L p λ nl p , mechanisms such as vacuum-plasma interface wave-break and longitudinal plasma oscillations are the dominant mechanisms for the initiation of electron acceleration and plasma heating at earlier times. Further, for variable density scale lengths our results have proven that the heating mechanisms mentioned above can be ignored for the laser intensities less than a specific threshold value, a 0 < 3, even for short density scale length, L p = 3 µm. Meanwhile, by increasing the laser intensity to higher values, it is observed that the trend of the time history curve for the mean temperature changed in a way that the total level of temperature increased. Also, by lengthening the scale length, at first the amounts of the mean temperature curve increased, and then smoothly decreased.

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