In this article, the effect of ionization on the energy spectrum of electrons within the interaction of a laser pulse with hydrogen atoms is investigated using particle-in-cell simulation codes. The results show that the behaviour of electrons' energy distribution function in the field-ionized plasma, which occurred due to the field ionization, compared with that in the pre-plasma strongly depends on the pulse shape. For short rise-time pulses (here 30 fs), due to the rapid enhancement of laser electric field, ionization occurs quickly, and as a result, there is not much difference in the electron energy in both the media. However, for pulses with rise time of 40 fs, in the pre-plasma state, the electron population reaches higher energies compared with the field-ionized plasma state. The main reason for this difference is the nonlinear wave breaking that happens earlier due to density inhomogeneity in the field-ionized plasma. On the other hand, at longer rise-time pulses (here 60 and 70 fs), electrons achieve higher energies in the field-ionized plasma than those in the case of pre-plasma. In this case, because of density fluctuations in the field-ionized plasma, the Raman backscattered radiations are seeded by a strong initial noise at the earlier times and the Mendonca condition for chaos threshold is met sooner. Therefore, the electrons gain more energy through the stochastic mechanism that is in agreement with chaotic nature of the motion.

中文翻译：

---

场电离等离子体中的电子能谱

在本文中，使用粒子内细胞模拟代码研究了激光脉冲与氢原子相互作用时电离对电子能谱的影响。结果表明，与前等离子体相比，场电离等离子体中电子能量分布函数的行为很大程度上取决于脉冲形状。对于短上升时间脉冲（此处为 30 fs），由于激光电场的快速增强，电离发生很快，因此两种介质中的电子能量差异不大。然而，对于上升时间为 40 fs 的脉冲，在前等离子体状态下，与场电离等离子体状态相比，电子群达到更高的能量。这种差异的主要原因是由于场电离等离子体中的密度不均匀而较早发生的非线性波中断。另一方面，在较长的上升时间脉冲（此处为 60 和 70 fs）下，电子在场电离等离子体中获得的能量比在预等离子体的情况下更高。在这种情况下，由于场电离等离子体中的密度波动，拉曼背散射辐射在较早时间被强初始噪声播种，并且较早满足混沌阈值的 Mendonca 条件。因此，电子通过与运动的混沌性质一致的随机机制获得更多能量。电子在场电离等离子体中比在前等离子体中获得更高的能量。在这种情况下，由于场电离等离子体中的密度波动，拉曼背散射辐射在较早时间被强初始噪声播种，并且较早满足混沌阈值的 Mendonca 条件。因此，电子通过与运动的混沌性质一致的随机机制获得更多能量。电子在场电离等离子体中比在前等离子体中获得更高的能量。在这种情况下，由于场电离等离子体中的密度波动，拉曼背散射辐射在较早时间被强初始噪声播种，并且较早满足混沌阈值的 Mendonca 条件。因此，电子通过与运动的混沌性质一致的随机机制获得更多能量。