In this paper, we present a new description of self-consistent wake excitation by an intense short laser pulse, based on applying the quasi-static approximation (slow variations of the pulse-envelope) in the instantaneous Lorentz-boosted pulse co-moving frame (PCMF), and best verify our results through comparison with particle-in-cell simulations. According to this theory, the plasma motion can be treated perturbatively in the PCMF due to its high initial-velocity and produces a quasi-static wakefield in this frame. The pulse envelope, on the other hand, is governed by a form of the Schrödinger equation in the PCMF, in which the wakefield acts as an effective potential. In this context, pulse evolutions are characterized by local conservation laws resulted from this equation and subjected to Lorentz transformation into the laboratory frame. Using these conservation laws, precise formulas are obtained for spatiotemporal pulse evolutions and related wakefield variations at initial stages, and new equations are derived for instantaneous group velocity and carrier frequency. In addition, based on properties of the Schrödinger equation, spectral-evolutions of the pulse are described and the emergence of an anomalous dispersion branch with linear relation ( is the light speed) is predicted. Our results are carefully discussed versus previous publications and the significance of our approach is described by showing almost all suggestive definitions of group-velocity based on energy arguments fail to reproduce our formula and correctly describe the instantaneous pulse-velocity.
在本文中，我们提出了一种对强短激光脉冲自洽尾场激发的新描述，其基础是在瞬时洛伦兹加速脉冲共动系（PCMF）中应用准静态近似（脉冲包络的缓变），并通过与粒子网格模拟的比较验证了我们的结果。根据这一理论，由于PCMF中初始速度很高，等离子体运动可被微扰处理，并在该参考系中产生准静态尾场。另一方面，脉冲包络由PCMF中的一种薛定谔方程形式所支配，其中尾场充当有效势。在此背景下，脉冲演化由该方程导出的局部守恒律所表征，并需经洛伦兹变换转换到实验室系。利用这些守恒律，我们获得了脉冲时空演化及尾场在初始阶段的精确公式，并推导出瞬时群速度和载波频率的新方程。此外，基于薛定谔方程的性质，我们描述了脉冲的频谱演化，并预言了具有线性色散关系（其中光速为c）的反常色散支的出现。我们的结果与以往文献进行了详细比较，并展示了几乎所有基于能量定义的群速度建议均无法复现我们的公式，也无法正确描述脉冲的瞬时速度。