High Power Laser Science and Engineering, 2020, 8 (4): 04000e36, Published Online: Nov. 23, 2020
Generation of polarized particle beams at relativistic laser intensities 
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Fig. 1. Scenario of the generation of spin-polarized electron beams via nonlinear Compton scattering: a relativistic electron bunch generated by laser-wakefield acceleration collides head-on with an elliptically polarized laser pulse and splits along the propagation direction into two parts with opposite transverse polarization[34]. OAP, optical parametric amplification.
Fig. 2. Schematic representation of electron spin polarization employing the standing wave of two colliding, circularly polarized laser pulses[39].
Fig. 3. Electrons propagating through a bichromatic laser pulse perform spin-flips dominantly in certain phases of the field: electrons initially polarized along the +y direction (yellow trajectories) flip their spin to down (trajectory colored purple) dominantly when By > 0, and this is where 1ω and 2ω add constructively (blue contours). The opposite spin-flip dominantly happens when By < 0, where the 1ω and 2ω components of the laser are out of phase (orange contours)[40].
Fig. 5. Sketch of the all-optical laser-driven polarized electron acceleration scheme using a pre-polarized target[46]. LG, Laguerre–Gaussian; OAP, optical parametric amplification.
Fig. 6. Schematic diagram showing laser acceleration of polarized protons from a dense hydrogen chloride gas target (brown). HCl molecules are initially aligned along the accelerating laser (indicated by the green area) propagation direction via a weak infrared (IR) laser. Blue and white balls represent the nuclei of hydrogen and chlorine atoms, respectively. Before the acceleration, a weak circularly polarized UV laser (purple area) is used to generate the polarized atoms along the longitudinal direction via molecular photo-dissociation. The brown curve indicates the initial density distribution of the gas-jet target. The polarized proton beam is shown on the right (blue) with arrows (red) presenting the polarization direction[54].
Fig. 7. Measured 3,4He2+ energy spectra accelerated from unpolarized helium gas jets[56]. IP, image plate.
Fig. 8. Sketch of the interplay between single particle trajectories (blue), spin (red) and radiation (yellow)[48].
Fig. 9. (a) Transverse distribution of the electron spin component Sy as a function of the deflection angles θx,y ; (b) corresponding logarithmic electron-density distribution. The assumed laser peak intensity is I ≈ 1.38 × 1022 W/cm2 (a 0 = 100), wavelength λ = 1 μm, the pulse duration amounts to five laser periods, focal radius 5 μm and ellipticity 0.05. The electron bunch with kinetic energy of 4 GeV and energy spread 6% has an initial angular divergence of 0.3 mrad[34].
Fig. 10. Achievable degree of electron polarization as a function of a quantum nonlinearity parameter χ 0 and the bichromaticity parameter c 2 (defining the fraction of the total pulse energy in the second harmonic, 
). The calculations have been performed for 5 GeV electrons colliding with a 161 fs laser pulse, i.e., a 0(χ0 = 1) = 16.5[40].
Fig. 11. Average polarization Sy as a function of the relative phase ϕ of the two-color laser pulse for different laser waist radii σ 0. The assumed laser intensities are a 0,1 = 2a 0,2 = 100, I 1 = 4I 2 = 1.37 × 1022 W/cm2[41].
41]." class="imgSplash img-thumbnail" style="cursor:pointer;">Fig. 12. Prediction from Wu et al. [46] for the achievable electron polarization dependent upon the electron current. More than 80% polarization can be achieved when a vortex LG laser pulse is used for the acceleration.
Fig. 13. Electron polarization distributions in the transverse phase space during laser-wakefield acceleration[49].
Fig. 14. Three-dimensional PIC simulation of proton acceleration assuming a gaseous HCl target with a hydrogen density of 8.5 × 1019 cm−3 and a circularly polarized laser pulse with 800 nm wavelength and a normalized amplitude of a 0 = 200. (a) Simulated proton density; (b) polarization as a function of the proton energy[53].
Fig. 15. (a) Three-dimensional PIC simulation for a gaseous HCl target with molecular density of 1019 cm−3 and 1.3 PW laser with phase-space distribution; (b) spin spread of protons with energy E > 20 MeV on the Bloch sphere[54].
Fig. 16. Simulated normalized He2+ ion-number density during the passage of a peta-watt laser pulse (6.5 ps after it entered the simulation box at the left boundary) through an unpolarized helium gas jet target. (a) 2%; (b) 3%; (c) 4%; (d) 12% critical density[56].
Fig. 17. Perspective view of the 3D model of the fully mounted magnetic system inside the PHELIX chamber[57,67].
Fig. 18. The 1064 nm IR laser propagates along the x -axis to align the bonds of the HCl molecules, and then UV light with a wavelength of 213 nm, propagating along the z -axis, is used to photo-dissociate the HCl molecules. A 234.62 nm UV light is used to ionize the Cl atoms. Thermal expansion of the electrons creates a large Coulomb field that expels the Cl ions. A fully polarized electron target is therefore produced for sequential acceleration[46].
Fig. 19. Technical drawing of the optical setup including the JuSPARC_MIRA laser system and the target chamber for the polarized proton target[64].
Fig. 20. Schematic view of the interaction chamber for production and storage of polarized H2, D2, HD and 
foils[71].
Markus Büscher, Anna Hützen, Liangliang Ji, Andreas Lehrach. Generation of polarized particle beams at relativistic laser intensities[J]. High Power Laser Science and Engineering, 2020, 8(4): 04000e36.
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