标题： PLASMON-X 中超强飞秒激光脉冲的传播 显示英文标题

标题： Propagation of ultrastrong femtosecond laser pulses in PLASMON-X

摘要： 推导了描述等离子体中超短激光脉冲传播的非线性方程，在Plasmon-X装置中。 显示用于电子加速的Plasmon-X方案使用了一个足够宽的光束（$L_\bot\sim 130\,\,\mu{\rm m}$），这使得在电子流体动力学方程中使用标准的一维定态近似是合理的，因为脉冲宽度远大于脉冲长度（$\sim 7.5\,\,\mu{\rm m}$）。 此外，当激光功率为$W\leq 250$TW且光斑尺寸为$130\,\,\mu{\rm m}$时，无量纲激光矢势足够小$|A_{\bot_0}|^2/{2} = ({W}/{c^2\epsilon_0})({\lambda^2}/{8 \pi^2 c})({4}/{\pi L_\bot^2})({e}/{m_0 c})^2 \sim 0.26$，非线性足够弱，允许在非线性泊松方程中进行功率展开。 这种近似产生了一个带有反应性非局部非线性项的非线性薛定谔方程。 非局部性包含积分下的余弦函数，表明振荡的尾波。 对于用于汤姆逊散射的较小光斑尺寸，$L_\bot = 10\,\, \mu$m，脉冲的长度和宽度是可比较的，因此无法在流体动力学方程中使用一维近似。 在如此小的光斑尺寸下，激光强度非常大，很可能在等离子体中会发生某种引导（等离子体局部耗尽得如此严重，以至于电磁波几乎在真空中传播）。 显示英文摘要

摘要： The derivation is presented of the nonlinear equations that describe the propagation of ultrashort laser pulses in a plasma, in the Plasmon-X device. It is shown that the Plasmon-X scheme used for the electron acceleration uses a sufficiently broad beam ($L_\bot\sim 130\,\,\mu{\rm m}$) that justifies the use of the standard stationary 1-D approximation in the electron hydrodynamic equations, since the pulse width is sufficiently bigger than the pulse length ($\sim 7.5\,\,\mu{\rm m}$). Furthermore, with the laser power of $W\leq 250$ TW and the $130\,\,\mu{\rm m}$ spot size, the dimensionless laser vector potential is sufficiently small $|A_{\bot_0}|^2/{2} = ({W}/{c^2\epsilon_0})({\lambda^2}/{8 \pi^2 c})({4}/{\pi L_\bot^2})({e}/{m_0 c})^2 \sim 0.26$, the nonlinearity is sufficiently weak to allow the power expansion in the nonlinear Poissons's equation. Such approximation yields a nonlinear Schr\" odinger equation with a reactive nonlocal nonlinear term. The nonlocality contains a cosine function under the integral, indicating the oscillating wake. For a smaller spot size that is used for the Thomson scattering, $L_\bot = 10\,\, \mu$m, the length and the width of the pulse are comparable, and it is not possible to use the 1-D approximation in the hydrodynamic equations. With such small spot size, the laser intensity is very large, and most likely some sort of chanelling in the plasma would take place (the plasma gets locally depleted so much that the electromagnetic wave practically propagates in vacuum).