Fig. 1: Electron acceleration by a helical beam transmitted through a relativistically transparent target and the vacuum field structure of the beam.

a Longitudinal electric field E_x (red/blue) and electron density n_e (green) shortly after a circularly-polarized helical beam (l = −1, σ = 1, and p = 0) passes through a near-critical target with \(\max ({n}_{{{{{{{{\rm{e}}}}}}}}})=0.5{n}_{{{{{{{{\rm{c}}}}}}}}}\) (prior to the arrival of the laser). The red/blue colors correspond to E_x ≷ 0 and the contours show ∣e∣E_x/m_ecω = ±1, 2, 4, 6, 8 in decreasing opacity. The green color shows n_e between 0.025n_c (transparent green) and 0.05n_c (fully opaque green). b Trajectories of four energetic electrons that are located within the central-most bunch at t = 398.3 fs. The dashed vertical lines mark the initial target boundary. Color-coded is the kinetic energy ε_k = (γ − 1)m_ec². c Time evolution of the energy distribution for forward-moving electrons (p_x > 10m_ec) that are close to the central axis of the laser beam. The specific selection criterion is ∣y∣ < 1 μm, ∣z∣ < 1 μm, and x > 0 within the moving window used in the simulation. The time t = 0 is the time when the peak of the laser envelope passes through x = 0 in the absence of the target. d–h Vacuum (in the absence of the target) field structure of the circularly-polarized laser beam at t = −1.7 fs. The vertical dashed line in (d) and (e) indicates where the planes shown in these panels intersect. The same dashed line is shown in (g) and (h). d, g Transverse, E_z, and longitudinal, E_x, an electric field in the (x, y)-plane at z = 0. e, h Transverse, E_z, and longitudinal, E_x, electric field in the (z, y)-plane at x marked by the dashed line in (d) and (g). f Line-outs of the transverse and longitudinally electric fields along the dashed line are shown in (d) and (e) for the transverse field and in (g) and (h) for the longitudinal field. The subscript s denotes z for the solid blue curve and x for the dot-dashed orange curve. The thin vertical dashed lines mark the boundaries of the region where the longitudinal field dominates.