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 B_y > 0, and this is where 1ω and 2ω add constructively (blue contours). The opposite spin-flip dominantly happens when B_y < 0, where the 1ω and 2ω components of the laser are out of phase (orange contours)^[40].

Fig. 4. Scheme for laser-based polarized positron beam production^[42].

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 S_y as a function of the deflection angles θ_x,y; (b) corresponding logarithmic electron-density distribution. The assumed laser peak intensity is I ≈ 1.38 × 10²² W/cm² (a₀ = 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 χ₀ and the bichromaticity parameter c₂ (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., a₀(χ₀ = 1) = 16.5^[40].

Fig. 11. Average polarization S_y as a function of the relative phase ϕ of the two-color laser pulse for different laser waist radii σ₀. The assumed laser intensities are a_0,1 = 2a_0,2 = 100, I₁ = 4I₂ = 1.37 × 10²² W/cm^2[41].

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 a₀ = 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].

Fig. 21. Schematic view of the setup for proton polarization measurements by Raab et al.^[72] Protons are accelerated from an unpolarized gold foil to energies of about 3 MeV, scattered in a silicon foil (scattering target) and finally detected with CR-39 detectors.