Enhanced betatron radiation by a modulating laser pulse in laser wakefield acceleration

We propose a new idea to enhance and control the betatron radiation by using a modulating laser pulse in laser wakefield acceleration. In this scheme, a high-power laser pulse is used for self-trapping and acceleration of the plasma electrons and the accelerated electron beam is modulated by a separately-propagating laser pulse for large amplitude betatron oscillations and microbunching. In this way, the relatively low power modulating laser pulse can enhance the X-ray photon flux and energy significantly. We performed two-dimensional particle-in-cell simulations to demonstrate the idea and the results show that a sub-TW laser pulse is enough for electron beam modulation and it can generate easily-controllable fs X-ray pulses with a wide range of photon energies from soft X-rays to hard X-rays.     

锐真空-等离子体边界倾角对激光尾波场加速中电子注入的影响

超短超强激光脉冲在气体等离子体中激发的尾波场加速在过去40年里有了长足的发展,人们已经在厘米加速距离内获得了数GeV的准单能电子加速,激光尾波加速的最高电子能量已经达到8 GeV.为了进一步提升加速电子束的稳定性和品质,多种电子注入方式先后被提出.本文研究了基于锐真空-等离子体边界面的密度跃变注入,着重讨论了不同角度的倾斜边界面对注入电子品质的影响.二维粒子模拟研究表明,与倾角为0°的垂直边界面相比,在合适的倾斜边界角下,第二个尾波空泡内产生的注入电量可以有近三倍的提升,同时偏振方向与入射面平行的驱动激光可以增加第一个空泡内注入电子的电量.根据不同激光入射角度时尾波场中电子自注入的起始位置差异,分析了电子电量与横向振荡增强的原因.这些研究有利于提升基于Betatron运动的尾波场辐射及其应用.     

Parameters of the electron beam in a betatron with radial comb-type poles

Expressions for the vector potential and components of the magnetic field induction vector of a betatron with radial comb-type poles are derived. The dynamics of the electron beam in the electromagnetic betatron field is investigated in the process of electron injection and acceleration. It is demonstrated that the azimuthally varying field engender beam beats. However, the amplitudes of beam particle oscillations during acceleration do not exceed their values estimated from the symmetric azimuthal component of the betatron magnetic field induction. The energy spectrum of accelerated electrons is not described by a normal law. In the electron energy spectrum, the relative number of electrons whose energy exceeds the average value is large. Application of poles with radial combs improves the efficiency of electron capture in acceleration. Results of investigations can find application in the development and adjustment of electron beam accelerating systems. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 27–34, October, 2005.     

The Dynamics of Electron Orbits during the Acceleration of Electrons in a Betatron

This paper presents a system of equations that describe the motion of charged particles in the electromagnetic field of a betatron. This system of equation was successfully used to study the behavior of the electron orbits and to determine the principal parameters of the electron beam in the electromagnetic field of a betatron during the electron acceleration and deceleration. The results of this study may find application in developing systems designed to accelerate electron beams. It has been shown that in the course of acceleration there is no damping of the betatron oscillations by the law B _z ^–1/2 and, correspondingly, no decrease in beam cross section. In contrast to the existing belief, the initial departure of the kinetic energy (momentum) of the injected electrons from the energy (momentum) of the electrons following the equilibrium orbit is not preserved in the course of acceleration. In the betatron chamber, the electron beam, when accelerated, does not constrict to form a ring but occupies a broad zone, whose dimensions are determined by the initial double amplitudes of the vertical and horizontal oscillations. Despite the large double amplitude of the oscillations of the beam particles, the average energy of the electrons differs from the energy of the electrons following the equilibrium orbit only slightly, and the departure of the average energy from the energy of the equilibrium electrons varies proportionally to the (varying) field of the betatron.     

On the production of flat electron bunches for laser wakefield acceleration

We suggest a novel method for the injection of electrons into the acceleration phase of particle accelerators, producing low-emittance beams appropriate even for the demanding high-energy linear collider specifications. We discuss the injection mechanism into the acceleration phase of the wakefield in a plasma behind a high-intensity laser pulse, which takes advantage of the laser polarization and focusing. The scheme uses the structurally stable regime of transverse wakewave breaking, when the electron trajectory self-intersection leads to the formation of a flat electron bunch. As shown in three-dimensional particle-in-cell simulations of the interaction of a laser pulse elongated in the transverse direction with an underdense plasma, the electrons injected via the transverse wakewave breaking and accelerated by the wakewave perform betatron oscillations with different amplitudes and frequencies along the two transverse coordinates. The polarization and focusing geometry lead to a way to produce relativistic electron bunches with an asymmetric emittance (flat beam). An approach for generating flat laser-accelerated ion beams is briefly discussed. The text was submitted by the authors in English.     

空泡机制产生betatron X射线辐射的数值模拟

针对SILEX钛宝石激光器参数,采用PIC数值模拟程序VORPAL对激光尾波场加速进行了模拟,得到了电子轨迹及能量数据,进而通过理论计算得到了空泡机制下X射线辐射特性。结果表明,空泡机制下高能电子在空泡中做betatron振荡且多数电子被加速到170 MeV左右;加速能量较低的电子（约100 MeV）, 其辐射谱为临界能量约3 keV的类同步辐射谱,发散角约为8 mrad,而能量较高的电子（约170 MeV）对应的光子临界能量约为10 keV。     

空泡机制产生betatron X射线辐射的数值模拟

针对SILEX钛宝石激光器参数,采用PIC数值模拟程序VORPAL对激光尾波场加速进行了模拟,得到了电子轨迹及能量数据,进而通过理论计算得到了空泡机制下X射线辐射特性。结果表明,空泡机制下高能电子在空泡中做betatron振荡且多数电子被加速到170 MeV左右;加速能量较低的电子（约100 MeV）, 其辐射谱为临界能量约3 keV的类同步辐射谱,发散角约为8 mrad,而能量较高的电子（约170 MeV）对应的光子临界能量约为10 keV。     

Formation and dynamics of a plasma in superstrong laser fields including radiative and quantum electrodynamics effects

Studies of phenomena accompanying the interaction of superstrong electromagnetic fields with matter, in particular, the generation of an electron–positron plasma, acceleration of electrons and ions, and the generation of hard electromagnetic radiation are briefly reviewed. The possibility of using thin films to initiate quantum electrodynamics cascades in the field of converging laser pulses is analyzed. A model is developed to describe the formation of a plasma cavity behind a laser pulse in the transversely inhomogeneous plasma and the generation of betatron radiation by electrons accelerated in this cavity. Features of the generation of gamma radiation, as well as the effect of quantum electrodynamics effects on the acceleration of ions, at the interaction of intense laser pulses with solid targets are studied.     

Multiple acceleration of ionospheric electrons in the approximation of continuous energy losses due to collisions

The multiple acceleration of electrons during active experiments in the ionosphere is related to their returning to a thin layer of the turbulent plasma, created by the powerful radio wave, due to elastic collisions with neutral particles. This effect depends on the magnitude and type of collisional energy losses by the electrons. In this paper, we formulate a system of equations that allows one to describe the process of multiple electron acceleration taking into account collisions of the accelerated particles with thermal electrons and assuming that collisional energy losses are continuous. The above-mentioned collisions become important at small energies where the primary electron acceleration takes place. We obtain asymptotic solutions of the formulated equations using the model power-law dependence of the collision frequency on electron energy. These solutions show that the effect of multiple acceleration of electrons in the ionospheric F-layer can lead to the formation of a slowly-varying high-energy “tail” in the distribution of the accelerated particles at energies of about tens of electron-volts. Institute for Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation of the Russian Academy of Sciences, Troitsk, Moscow Region, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 1, pp. 3–16, January 2000.     

Acceleration and radiation of externally injected electrons in laser plasma wakefield driven by a Laguerre-Gaussian pulse

By using three-dimensional particle-in-cell simulations, externally injected electron beam acceleration and radiation in donut-like wake fields driven by a Laguerre-Gaussian pulse are investigated. Studies show that in the acceleration process the total charge and azimuthal momenta of electrons can be stably maintained at a distance of a few hundreds of micrometers. Electrons experience low-frequency spiral rotation and high-frequency betatron oscillation, which leads to a synchrotron-like radiation. The radiation spectrum is mainly determined by the betatron motion of electrons. The far field distribution of radiation intensity shows axial symmetry due to the uniform transverse injection and spiral rotation of electrons. Our studies suggest a new way to simultaneously generate hollow electron beam and radiation source from a compact laser plasma accelerator.     

低密等离子体通道中的非共振激光直接加速

在低密等离子体通道中, 横向有质动力可以有效调制电子的横向振荡过程. 一方面, 横向有质动力可以向外推动电子, 增大电子横向振荡振幅, 减小失相率, 使电子获得能量增益; 另一方面, 横向有质动力也可以通过对失相率的非线性调制来降低失相率, 在电子横向振荡振幅很小的情况下导致激光直接加速. 横向有质动力调制的大小由等离子体密度、激光强度和束宽共同决定. 三维模型结果也证实可以通过参数放大实现激光直接加速, 弥补了准二维模型的局限性.     

Production of a keV x-ray beam from synchrotron radiation in relativistic laser-plasma interaction

We demonstrate that a beam of x-ray radiation can be generated by simply focusing a single high-intensity laser pulse into a gas jet. A millimeter-scale laser-produced plasma creates, accelerates, and wiggles an ultrashort and relativistic electron bunch. As they propagate in the ion channel produced in the wake of the laser pulse, the accelerated electrons undergo betatron oscillations, generating a femtosecond pulse of synchrotron radiation, which has keV energy and lies within a narrow (50 mrad) cone angle.     

双束平行入射电子束引导的自注入电子加速效果的研究

在粒子束引导的等离子尾波场加速机制中,为了加速电子获得最大能量,大量研究集中于改变单束牵引粒子束的线度、形状、电荷性质等参数. 综合考虑已有的实验结果,本文提出了一种相比于单束电子牵引更为有效的加速方式,利用双束平行电子束来加速自注入的电子. 通过2.5维粒子程序模拟,发现在牵引电子束具有相同能量、电量、尺寸的条件下,通过双束平行电子束加速得到的电子具有长程加速、高能和准单能性的特性. 同时在空泡内形成了一束独特的回流电子,进一步使得自注入电子具有更好的准直性. 关键词： 电子束尾波场加速 双束平行电子束 粒子模拟     

Synchrotron maser emission in the saturated regime

Using the method of Einstein coefficients, we derive a quasi-linear kinetic equation for relativistic electrons, in which synchrotron emission of the particles is taken into account. We discuss the evolution of the electron distribution taking into account the effect of weak radiative diffusion of the particles over pitch angles. We analyze a solution of the quasi-linear kinetic equation for electrons and the radiation transfer equation in a stationary thick plasma layer in which maser amplification of the synchrotron radiation takes place. In this case, we assume that population inversion in the electron distribution and, thus, stationary synchrotron emission occur due to an external (nonsynchrotron) acceleration mechanism. The efficiency of this acceleration mechanism is assumed to have a power-law dependence of the electron energy. Under these conditions, we find the spectra of synchrotron maser emission, which are entirely determined by the external acceleration. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 7, pp. 575–594, July, 2000.     

Beschleunigung von Elektronen in einem Plasmabetatron

A plasma was produced by a high frequency electric quadrupole field (v=200 Megacycles) at gas pressures of 10^?4 to 5·10^?3 mm Hg in a quarz glass torus. The torus was placed between the poles of an air-core betatron with the following properties: radius of equilibrium orbit 20 cm, maximum accelerating field strength 80 V/cm, end energy 1.5 MeV. Associated with conduction currents of some 100 A, energetic Bremsstrahlung was observed and attributed to 1,2 MeV electrons. The number of accelerated electrons was of the order of 10¹¹ per pulse. The intensity and energy of the radiation, together with the time dependence of the plasma current, were observed as function of different parameters, such as the gas pressure, high frequency amplitude, induced acceleration field strength, for different gases. The energetic radiation disappears when, because of the self-induced magnetic field, the stability condition for the betatron equilibrium is no longer fulfilled.     

Channeling of relativistic laser pulses, surface waves, and electron acceleration

The interaction of a high-energy relativistic laser pulse with an underdense plasma is studied by means of 3-dimensional particle in cell simulations and theoretical analysis. For powers above the threshold for channeling, the laser pulse propagates as a single mode in an electron-free channel during a time of the order of 1?picosecond. The steep laser front gives rise to the excitation of a surface wave along the sharp boundaries of the ion channel. The surface wave first traps electrons at the channel wall and preaccelerates them to relativistic energies. These particles then have enough energy to be further accelerated in a second stage through an interplay between the acceleration due to the betatron resonance and the acceleration caused by the longitudinal part of the surface wave electric field. It is necessary to introduce this two-stage process to explain the large number of high-energy electrons observed in the simulations.     

激光尾场加速电子的密度梯度注入的解析处理

在激光尾场加速电子的机理中, 引入适当的密度梯度容易实现并控制电子注入到等离子体波中实现加速. 迄今对密度梯度注入的理论研究主要采用粒子模拟. 本文发展了一种解析处理密度梯度注入的方法, 分析了密度下降区域中电子的注入和加速. 给出了一维密度梯度中电子注入发生的条件, 采用哈密顿力学得到了线性条件下密度梯度区的电子相空间分界线(separatrix); 讨论了密度梯度区电子注入的时间对电子进入密度均匀区持续加速的影响. 用粒子模拟验证了分析结果.     

Electron acceleration during the breaking of an intense plasma wave in an inhomogeneous plasma

We investigate the dynamics of the electron acceleration when an intense plasma wave breaks near resonance at the plasma frequency (focus) in an inhomogeneous magnetized plasma. The breaking threshold has been determined. We compare our experimental dependences of the current and energy of fast electrons on the intensity of the incident wave at various times with theoretical estimates. We show that when the breaking threshold is significantly exceeded, up to 50% of the electrons at plasma resonance are captured and accelerated by the wave.     

Particle simulation on electron acceleration process by the laser ponderomotive force in inhomogeneous underdense plasma layers

The mechanism of electron ponderomotive acceleration due to increasing group velocity of laser pulse in inhomogeneous underdense plasma layers is studied by two-dimensional relativistic parallel particle-in-cell code. The electrons within the laser pulse move with it and can be strongly accelerated ponderomotively when the duration of laser pulse is much shorter than the duration of optimum condition for acceleration in the wake. The extra energy gain can be attributed to the change of laser group velocity. More high energy electrons are generated in the plasma layer with descending density profile than that with ascending density profile. The process and character of electron acceleration in three kinds of underdense plasma layers are presented and compared.     

激光与固体靶相互作用中低密度预等离子体对高能电子产生的影响

对线极化、圆极化的超短超强激光脉冲与靶前有一段低密度预等离子体的固体靶的相互作用进行了理论和粒子模拟研究。激光通过有质动力加速机制加速预等离子体中的电子,研究了电子获得的最大能量随激光强度和预等离子体密度的变化。当激光脉冲与靶直接作用时,靶中的电子由于JB机制而得到加速,所获得的能量比预等离子体中电子低。研究表明,在超短超强激光脉冲与固体靶相互作用中,预等离子体的存在有利于高能电子的产生。