强激光束在等离子体通道中传输的变分法研究

关键词：     

Allowable propagation of short pulse laser beam in a plasma channel and electromagnetic solitary waves

Nonparaxial and nonlinear propagation of a short intense laser beam in a parabolic plasma channel is analyzed by means of the variational method and nonlinear dynamics. The beam propagation properties are classified by five kinds of behaviors. In particularly, the electromagnetic solitary wave for finite pulse laser is found beside the other four propagation cases including beam periodically oscillating with defocussing and focusing amplitude, constant spot size, beam catastrophic focusing. It is also found that the laser pulse can be allowed to propagate in the plasma channel only when a certain relation for laser parameters and plasma channel parameters is satisfied. For the solitary wave, it may provide an effective way to obtain ultra-short laser pulse.     

超短强激光脉冲在等离子体隧道中传输的理论与数值模拟研究

研究了超短强激光脉冲在非扰动抛物型部分电离的预等离子体隧道中的传输特性.从Maxwell方程出发得到了两个包含衍射、三阶强度非线性、等离子体散焦、等离子体隧道聚焦以及相对论自聚焦等效应在内的激光场演化方程，即折射率方程和哈密顿-雅可比方程.在此基础 上得到了激光在等离子体隧道中传输的包络方程以及光斑半径与传输距离、隧道宽度等初始 参量的关系. 关键词： 等离子体隧道聚焦 相对论自聚焦 势阱     

Nonlinear propagation of an intense Laguerre–Gaussian laser pulse in a plasma channel

The nonlinear propagation of an intense Laguerre–Gaussian(LG) laser pulse in a parabolic preformed plasma channel is analyzed by means of the variational method. The evolution equation of the spot size is derived including the effects of relativistic self-focusing, preformed channel focusing, and ponderomotive self-channeling. The parametric conditions of the LG laser pulse and plasma channel for propagating with constant spot size, periodically focusing and defocusing oscillation,catastrophic focusing, and solitary waves are obtained. Compared with the laser pulse with fundamental Gaussian(FG)mode, it is found that the effect of vacuum diffraction is reduced by half and the effects of relativistic and wakefield focusing are decreased by a quarter due to the hollow transverse intensity profile of the LG laser pulse, while the effect of channel focusing is the same order of magnitude with that of the FG laser pulse. Thus, the matched condition for the intense LG laser pulse with constant spot size is released obviously, while the parameters of the laser and plasma for the existence of solitary waves nearly coincide with those of the FG laser pulse.     

强激光在等离子体中的传播特性

分别讨论了非相对论条件下短脉冲和长脉冲激光在完全电离的等离子体中的传播特性。短脉冲情况下，激光的有效瑞利长度会增加，但不会出现自导引；长脉冲激光的传播取决于激光功率和等离子体温度之比，当该比值超过一定阈值时会出现自导引现象，激光束被限制在一个相对稳定的通道内，其半径对光束的初始半径有很强的依赖性。     

Effects of channel alternating corrugation on a laser beam propagation in plasmas

The propagation of an intense laser beam in an alternating corrugated plasma channel, which has a wide region and a narrow region in one corrugated space period, is investigated. Compared with the usual corrugated plasma channel, it is found that there are many more resonance peaks and many more abundant beat-like wave phenomena for the laser beam in this extended channel. Moreover, the much narrower region in some special alternating corrugated channels can play the role like a plasma lens for some laser beams, i.e., it can obviously change the laser spot size from small (large) to large (small) amplitude when the laser passes through the narrow region. These results are well confirmed by the final numerical simulations of wave equation and particle-in-cell approach.     

Compton散射强光子流在等离子体通道中的传输特性

给出了冷等离子体中高阶相对论下多光下非线性Compton散射的光子流在等离子体通道中的传输方程,研究了高阶相对论效应对散射光子流传输的影响。在近轴近似下,散射强光子流依然有较浅的“势阱”方程。当散射强光子流强度较大时,高阶相对论效应变得更加重要：它减小了散射光束宽的振荡幅度,同时加快了散射光束宽的振荡速度。当散射强光子流功率大于或等于相对论临界功率时,高阶相对论效应避免了散射强光子流强度随传输距离出现无限大的奇异性。给出了散射强光子流的平衡解存在的条件。     

Non‐linear interaction of a q‐Gaussian laser beam in a plasma channel created by the ignitor‐heater technique

This paper presents a theoretical investigation of the propagation characteristics of a q‐Gaussian laser beam propagating through a plasma channel created by the ignitor‐heater technique. The ignitor beam creates the plasma by tunnel‐ionization of air. The heater beam heats the plasma electrons and establishes a parabolic channel. The third beam (q‐Gaussian beam) is guided in the plasma channel under the combined effects of density non‐uniformity and non‐uniform ohmic heating of the plasma channel. Numerical solutions of the non‐linear Schrodinger wave equation (NSWE) for the fields of laser beams are obtained with the help of the moment theory approach. Particular emphasis is placed on the dynamical variations of the spot size of the laser beams and the longitudinal phase shift of the guided beam with the distance of propagation.     

Effects of Higher-Order Relativistic Nonlinearity and Wakefield During a Moderately Intense Laser Pulse Propagation in a Plasma Channel

Using a variational approach, the propagation of a moderately intense laser pulse in a parabolic preformed plasma channel is investigated. The effects of higher-order relativistic nonlinearity (HRN) and wakefield are included. The effect of HRN serves as an additional defocusing mechanism and has the same order of magnitude in the spot size as that of the transverse wakefield (TWF). The effect of longitudinal wakefield is much larger than those of HRN and TWF for an intense laser pulse with the pulse length equaling the plasma wavelength. The catastrophic focusing of the laser spot size would be prevented in the present of HRN and then it varies with periodic focusing oscillations.     

强激光脉冲在部分离化等离子体中的传播特性

采用变分法给出了强激光脉冲在部分离化等离子体中传播的参数演化方程,其中考虑了相对论自聚焦、有质动力激发尾波场以及部分离化非线性极化强度的影响。通过非线性动力学分析的方法,得到了强激光脉冲以恒定焦斑半径传播时的激光、等离子体参数匹配条件。研究表明:在部分离化等离子体中,激光自聚焦随着电离程度的增大而增强;有质动力激发的尾波场进一步增强激光脉冲的自聚焦;相对于等离子体密度而言,激光强度对激光脉冲的自聚焦更有影响。     

Effects of Higher-Order Relativistic Nonlinearity and Wakefield During a Moderately Intense Laser Pulse Propagation in a Plasma Channel

Using a variational approach,the propagation of a moderately intense laser pulse in a parabolic preformed plasma channel is investigated.The effects of higher-order relativistic nonlinearity (HRN) and wakefield are included.The effect of HRN serves as an additional defocusing mechanism and has the same order of magnitude in the spot size as that of the transverse wakefield (TWF).The effect of longitudinal wakefield is much larger than those of HRN and TWF for an intense laser pulse with the pulse length equaling the plasma wavelength.The catastrophic focusing of the laser spot size would be prevented in the present of HRN and then it varies with periodic focusing oscillations.     

Effects of Relativistic and Ponderomotive Nonlinearities on an Intense Laser Pulse Propagation in a Plasma Channel

The optical guiding of a moderately intense laser pulse in a parabolic preformed plasma channel is analyzed by means of the variational method.Relativistic,ponderomotive and their coupling nonlinearities are included.The conditions for periodic defocusing and focusing,as well as constant spot size propagation are given.It is found that the laser focusing is released by the coupling of relativistic and ponderomotive nonlinearities.     

超短超强激光导引及对电子加速的影响

使用粒子模拟程序对30 fs超短超强激光在均匀与抛物型两种密度分布等离子体中的传输, 以及在稳定传输状态下尾场的电子注入与加速形成的电子能谱进行了模拟与分析. 固定入射激光束斑尺寸, 在(0.4-2)×10¹⁹/cm³等离子体密度范围, 对比分析了归一化峰值强度从1-6范围的激光脉冲在上述两种密度分布等离子 体中传输时激光束斑尺寸的演化, 结果表明抛物型分布的等离子体密度通道能够对超短超强脉冲实现良好的导引, 有利于高能电子加速. 对于较高密度情况,即使在均匀等离子体中依靠相对论自聚 焦等机制也可以实现良好的自导引传输,有利于实验简化以及产生更大电量的加速电子.     

Formation of plasma channels in the interaction of a nanosecond laser pulse at moderate intensities with helium gas jets

We report on a detailed study of channel formation in the interaction of a nanosecond laser pulse with a He gas jet. A complete set of diagnostics is used in order to characterize the plasma precisely. The evolution of the plasma radius and of the electron density and temperature are measured by Thomson scattering, Schlieren imaging, and Mach-Zehnder interferometry. In gas jets, one observes the formation of a channel with a deep density depletion on axis. Because of ionization-induced defocusing which increases the size of the focal spot and decreases the maximum laser intensity, no channel is observed in the case of a gas-filled chamber. The results obtained in various gas-jet and laser conditions show that the channel radius, as well as the density along the propagation axis, can be adjusted by changing the laser energy and gas-jet pressure. This is a crucial issue when one wants to adapt the channel parameters in order to guide a subsequent high-intensity laser pulse. The experimental results and their comparison with one-dimensional (1D) and two-dimensional hydrodynamic simulations show that the main mechanism for channel formation is the hydrodynamic evolution behind a supersonic electron heat wave propagating radially in the plasma. It is also shown from 2D simulations that a fraction of the long pulse can be self-guided in the channel it creates. The preliminary results and analyses on this subject have been published before [V. Malka et al., Phys. Rev. Lett. 79, 2979 (1997)].     

Distribution regimes of intense laser beam in a self-consistent plasma channel

In the present work, we investigate the distributed regimes of an intense laser beam in a self-consistent plasma channel. As the intensity of the laser beam increases, the relativistic mass effect as well as the ponderomotive expulsion of electrons modifies the dielectric function of the medium due to which the medium exhibits nonlinearity. Based on Wentzel–Kramers–Brillouin and paraxial ray theory, the steady-state solution of an intense, Gaussian electromagnetic beam is studied. A differential equation of the beamwidth parameter with the distance of propagation is derived, including the effects of relativistic self-focusing (SF) and ponderomotive self-channeling. The nature of propagation and radial dynamics of the beam in plasma depend on the power, width of the beam, and Ω _p, the ratio of plasma to wave frequency. For a given value of Ω _p (<1), the distribution regimes have been obtained in beampower–beamwidth plane, characterizing the regimes of propagation as steady divergence, oscillatory divergence, and SF. The related focusing parameters are optimized introducing plasma density ramp function, and spot size of the laser beam is analyzed for inhomogeneous plasma. This results in overcoming the diffraction and guiding the laser beam over long distance. Numerical computations are performed for typical parameters of relativistic laser–plasma interaction studies.     

Self-focusing of Hermite–Gaussian laser beams in plasma under plasma density ramp

Self-focusing of Hermite–Gaussian laser beams in plasma under plasma density ramp has been investigated. It is known that a laser beam shows an oscillatory self-focusing and defocusing behavior with the propagation distance. To overcome the defocusing, localized upward plasma density ramp is introduced, so that the laser beam attains a minimum spot size and maintains it with only a mild ripple. The density ramp could be important for the self-focusing of a Hermite–Gaussian laser by choosing the laser and plasma parameters appropriately. Self-focusing becomes stronger as the propagation distance increases. The behavior of beam-width parameters with the distance of propagation is presented graphically.     

Formation and evolution of intense, post-filamentation, ionization-free low divergence beams

The mechanisms related to the formation and propagation of post-filamentation intense light channels were rigorously investigated experimentally and numerically. It was found that they originate from a hot spot formed by diffraction of the pulse energy reservoir onto the plasma. Once the hot spot was formed, a channel with intensity estimated at 0.5 TW/cm² could maintain its diameter over several tens of meters such that air was not ionized, but the self-focusing produced was sufficiently high to balance linear diffraction. This propagation regime is of high interest to propagate high intensity laser pulses with limited losses.     

Enhanced acceleration of injected electrons in a laser-beat-wave-induced plasma channel

Enhanced energy gain of externally injected electrons by a approximately 3 cm long, high-gradient relativistic plasma wave (RPW) is demonstrated. Using a CO2 laser beat wave of duration longer than the ion motion time across the laser spot size, a laser self-guiding process is initiated in a plasma channel. Guiding compensates for ionization-induced defocusing (IID) creating a longer plasma, which extends the interaction length between electrons and the RPW. In contrast to a maximum energy gain of 10 MeV when IID is dominant, the electrons gain up to 38 MeV energy in a laser-beat-wave-induced plasma channel.     

Dynamics of quadruple laser pulses in under‐dense plasmas

An analysis of dynamics of a quadruple laser pulse propagating through an under‐dense plasma is presented. The Drude model is used to derive the dielectric function of the plasma for relativistic non‐linearity in the electron mass. An approximate numerical solution of the nonlinear Schrödinger wave equation for the field of the laser beam is obtained with the help of the moment theory approach in the Wentzel–Kramers–Brillouin (WKB) approximation. Particular emphases are placed on the variations of spot size, pulse width, and longitudinal phase delay with the distance of propagation through the plasma. Self‐trapping of the laser pulse is also investigated.