图 1  在激光、电子对撞情况下, 激光强度(波长为800 nm)和电子能量对应的非线性量子参数$ {\chi }_{\mathrm{e}} $和辐射反作用效应参数$ R $

Fig. 1.  The nonlinear quantum parameter $ {\chi }_{\mathrm{e}} $ and radiation-reaction effect parameter $ R $ as a function of the laser intensity (at wavelength of 800 nm) and electron energy in the case of laser and electron collision.

图 2  电子与激光对撞在方位角$ \phi ={180}^{\circ } $处的角度能谱　(a) 无辐射反作用; (b) 有辐射反作用. 激光强度为$ 5\times {10}^{22}\;\mathrm{W}\cdot \mathrm{c}{\mathrm{m}}^{-2} $, 电子能量为40 MeV

Fig. 2.  Angle energy spectrum for electron and laser colliding at azimuth angle $ \phi ={180}^{\circ } $: (a) Without radiation reaction; (b) with radiation reaction. The laser intensity is $ 5\times {10}^{22}\;\mathrm{W}\cdot \mathrm{c}{\mathrm{m}}^{-2} $ and the electron energy is 40 MeV.

图 3  不同电子能量$ {\gamma }_{0} $与不同场强$ {a}_{0} $的激光对撞后电子被反射的比例　(a)基于LL方程的试探粒子模拟结果, 白线为(5)式给出的边界; (b)考虑量子修正因子(6)式的结果

Fig. 3.  The ratio of electrons reflected after colliding with laser pulse at different electron energy $ {\gamma }_{0} $ and laser field amplitude $ {a}_{0} $: (a) From test particle simulations using the LL equation, the white line corresponds to the threshold defined in Eq. (5); (b) after considering the quantum correction factor according to Eq. (6).

图 4  (a) $ {\gamma }_{0}=1000 $的电子和不同脉宽激光对撞后辐射的光子数量, $ \tau $为激光周期数, 直线为Monte-Carlo模拟的结果, 点为解析结果^[45]; (b)两种途径的光子数量相对误差^[45]; (c) 不同激光参数下能谱的对比, 其中$ f=\delta $, 灰色实线为QED结果, 虚线为Monte-Carlo结果. 垂直的虚线为第一阶非线性Compton的边界${f}_{\mathrm{C}}\approx 2\dfrac{{\chi }_{\mathrm{e}}}{{a}_{0}^{3}}$^[45]

Fig. 4.  (a) The number of photons emitted by electrons of $ {\gamma }_{0} $=1000 head-on colliding with a laser pulse with different pulse width (τ is the pulse duration in laser period). Lines are the result from Monte-Carlo simulations while points are from analytical result^[45]; (b) relative error of the photon number between the two approaches^[45]; (c) comparison of energy spectra under different laser parameters where $ f=\delta $. The solid gray line gives the QED result, and the dashed line is the Monte-Carlo result, respectively. The perpendicular dotted line is the boundary of the first order nonlinear Compton${f}_{\mathrm{C}}\approx 2\dfrac{{\chi }_{\mathrm{e}}}{{a}_{0}^{3}}$^[45].

图 5  500 MeV电子与a₀ = 100激光场对撞的电子轨迹, 黑线为QED-MC方法计算20次给出的轨迹, 红线、蓝线分别为Lorentz方程、LL方程的轨迹

Fig. 5.  Trajectories of electrons with 500 MeV colliding with a₀ = 100 laser field. Black solid lines are the ones given by the QED-MC method (repeated 20 times at exactly the same condition). The red and blue solid lines are the trajectory from Lorentz equation and LL equation, respectively.

图 6  电子束与(a)中的激光对撞后的能谱变化, 其中激光强度约为$ {a}_{0}=68 $, 电子中心能量约为1 GeV^[46]; (b) 量子随机辐射模型^[46]; (c) LL方程^[46]; (d) 量子修正的LL方程^[46]

Fig. 6.  The energy spectra after the electron beam collides with the laser in (a), where the laser intensity is about $ {a}_{0}=68 $ and the electron center energy is about 1 GeV; (b) quantum stochastic radiation model; (c) LL equation; (d) the quantum-modified LL equation^[46].

图 7  半周期(左)、单周期(右)激光和电子对撞的空间轨迹(上)和能量变化趋势(下)^[28]

Fig. 7.  Trajectories (top) and energy evolution (bottom) of electrons in collision with half-cycle (left) and one-cycle (right) laser pulse^[28].

图 8  (a)—(f) Lorentz方程、LL方程和QED光子辐射给出的两种电子能量下的运动轨迹, 其中红色箭头表示反常透射与反射的电子^[21]; (g)—(i) 不同激光强度和电子能量下电子被激光反射的比例, 红色和蓝色方块而分别为第二列和第一列所对应的参数^[21]

Fig. 8.  (a)–(f) Electron trajectories at two given values of kinetic energy, modelled by the Lorentz equation, the LL equation and the QED photon radiation. The red arrows represent anomalously transmitted and reflected electrons^[21]. (g)–(i) Proportion of electrons reflected by the laser pulse at different laser intensities and electron energies. The red and blue squares correspond to the parameters in the second and first columns, respectively^[21].

图 9  电子束在存储环中极化率随时间的变化^[51]

Fig. 9.  Polarization evolution of an electron beam in a storage ring^[51].

图 10  圆偏振驻波场中不同场强对应的电子极化率随时间的演化^[52]

Fig. 10.  Electron polarization evolution as a function of the laser amplitude in circularly polarized standing wave field^[52].

图 11  极化电子在激光场中的振荡${\Delta }{p}_{x}$表示无自旋电子在半周期内由于辐射反作用产生的动量变化, $ \pm $表示相反的自旋极化方向^[31]

Fig. 11.  The oscillation of polarized electrons in laser field. ${\Delta }{p}_{x}$ represents the momentum shift of unpolarized electrons in a half cycle, plus or minus sign denote electron initially polarized parallel or anti-parallel to the laser magnetic field^[31].

图 12  考虑与不考虑辐射反作用力的结果对比^[68]　(a)电子x-p_x分布; (b)质子x-p_x分布; (c)电子能谱; (d)质子能谱

Fig. 12.  Simulation results with and without radiation reaction^[68]: (a) x-p_x distribution of electrons; (b) x-p_x distribution of protons; (c) energy spectrum of electrons; (d) energy spectrum of protons^[68].

图 13  $ {a}_{0}=500 $的激光和$ {n}_{\mathrm{e}}=20{n}_{\mathrm{c}} $的等离子相互作用, 在$ t=80{T}_{0} $时刻电子、质子、电磁场和$ \gamma $光子的分布^[71]　(a)—(c) 无辐射反作用; (d)—(g) 存在辐射反作用

Fig. 13.  The distribution of electrons, protons, electromagnetic fields, and gamma photons at t = 80T₀ when a laser of $ {a}_{0}=500 $ interacts with a plasma of $ {n}_{\mathrm{e}}=20{n}_{\mathrm{c}} $^[71]: (a)–(c) with radiation reaction; (d)–(g) without of radiation reaction.

图 14  (a) 不同场强下电子在驻波场中的密度分布, 电子的辐射过程采用QED-MC模型^[72]; (b) 辐射模型为经典辐射^[72]; (c) 不同场强下典型的电子轨迹^[72]

Fig. 14.  (a) Density distribution of electrons in the standing wave field at different field intensities. Photon emission is modelled via QED-MC method^[72]; (b) the result from classical radiation-reaction model^[72]; (c) typical electron trajectories at different field intensities^[72].

图 15  (a)有辐射反作用力情况下, 不同等离子体密度下电子的轨迹^[77]; (b)辐射反作用力所做的功^[77]; (c) 等离子体场的空间尺度、场强^[77]. 图例中Eq.(4)是等离子体场电势$ \phi ={E}_{x0}d/{\gamma }_{x} $

Fig. 15.  (a) Electron trajectories at different plasma densities^[77]; (b) work done by the radiation reaction force; (c) length scale and field strength of plasma field at different plasma densities^[77]. Eq. (4) is the electric potential of the plasma field $ \phi ={E}_{x0}d/{\gamma }_{x} $.

图 16  能量为1 GeV的电子和$ 5\times {10}^{22}\;\mathrm{W}\cdot \mathrm{c}{\mathrm{m}}^{-2} $(${a}_{0}= $$ 154$)激光对撞产生的辐射谱^[78]. 黑线和红色虚线为量子辐射情况下有、无辐射反作用的辐射谱线; 蓝色虚线和红色点线是经典理论给出的有、无辐射反作用的辐射谱线

Fig. 16.  The radiation spectrum from the collision between 1 GeV electrons and $ 5\times {10}^{22}\;\mathrm{W}\cdot \mathrm{c}{\mathrm{m}}^{-2} $($ {a}_{0}=154 $) laser pulse^[78]. The black and red dotted lines are the spectra with and without radiation reaction in quantum radiation. The blue dotted and red dotted lines are the ones given by classical theory, with and without radiation reaction.

图 17  不同激光光强下,　(a) 激光到等离子体的总能量转换效率和 (b) 激光到伽马光子的能量转换效率^[82]

Fig. 17.  The total energy conversion efficiency of laser to plasma (a) and the energy conversion efficiency of laser to gamma photon (b) as a function of laser intensity^[82].

图 18  全光探测辐射反作用效应示意图. 电子束经过尾场加速后, 与散射激光对撞产生高能光子^[87]

Fig. 18.  A sketch of all-light detection of radiation reaction. After the electron beam accelerates through the tail field, it collides with the scattering laser to produce high-energy photons^[87].

图 19  (a)激光加速电子进入微通道靶后经过薄膜的反射与电子对撞^[89]; (b)电子能量的角分布^[89]

Fig. 19.  (a) The laser accelerates the electron into the microchannel target and then collides with the electron through the reflection of the film^[89]; (b) angular distribution of electron energy^[89].

图 20  高能正电子束穿过晶体后测量光子能谱及其与不同模型计算结果对比^[88]　(a)靶厚为3.8 mm; (b)靶厚为10.0 mm, 其中QRRM为量子辐射模型, QnoRRM为量子无辐射模型, SCRRM为半经典辐射模型, CRRM为经典辐射模型

Fig. 20.  Measured photon energy spectra generated by high-energy positron beam penetrating crystal and its comparison with theoretical results from different models^[88]: (a) Target thickness of 3.8 mm; (b) target thickness of 10.0 mm. QRRM is the quantum RR model, QNorRM is the quantum model without RR, ScrRM is the semi-classical RR model, and CrRM is the classical RR model.

图 21  电子以及卤化物极化率和激光波长的关系, 质子极化与电子一致^[113]

Fig. 21.  Polarization of electrons and the halide as a function of the ionization laser wavelength^[113].

图 22  基于激光尾场的预极化电子加速的(a)实验设计和(b)相互作用流程^[22]

Fig. 22.  (a) Experimental design and (b) interaction processes for polarized electron acceleration based on laser-driven wakefield^[22].

图 23  添加自旋模块后的PIC流程

Fig. 23.  PIC flow after adding spin module.

图 24  激光尾场加速过程中电子束极化率随时间演化(a)及与激光强度的关系(b)^[23]

Fig. 24.  The electron beam polarization versus time (a) and laser amplitude (b) in laser wakefield acceleration^[23].

图 25  LG涡旋光和高斯光作为驱动源时　(a)横向预极化和(b)纵向预极化尾场极化电子束峰值电流与极化率的关系^[22]

Fig. 25.  The electron beam polarization as a function of the peak current for wakefield acceleration driven by LG vortex and Gaussian laser for (a) transverse pre-polarized case and (b) longitudinal pre-polarized case^[22].

图 26  激光尾场加速横向预极化电子时电子束极化率的横向相空间分布, 分别对应纵向s_x, 横向s_y与s_z, 初始自旋为s_z方向^[107]

Fig. 26.  The transverse phase space distribution of electron beam polarization in laser wakefield acceleration for transversely pre-polarized electrons(s_z direction). Left to right: longitudinal polarization s_x, transverse polarization s_y and s_z^[107].

图 27  尾场加速横向预极化电子的(a)自旋过滤器示意图, (b)激光驱动和电子束驱动对比及(c)不同筛选角下极化率与归一化参数ψ的关系^[107]

Fig. 27.  (a) Sketch of the spin filter, (b) beam polarization in laser driven and electron beam driven scenarios, and (c) the relationship between the polarization and the normalized parameter ψ at different screening angles^[107].