Fig. 1. Schematic of the experiment using two intense laser beams (denoted as α and β) irradiating a solid Au target (with a large-scale preplasma at the target front), with opposite incidence angles and a variable separation distance (δ_front) between the laser spots on the target front surface. In all cases, the focus of the laser beams coincides with the target surface. The outgoing hot electrons are diagnosed by image plate (IP) stacks, located along each laser beam axis, as well as in the target normal direction. The accelerated ions are characterized by a radiochromic film (RCF) stack located in the target normal direction.

Fig. 2. Electron signals as recorded by the IP stacks (a) along the laser direction for the single beam case (Case 0) and (b) and (c) along the target normal for the dual-beam cases, with either (b) δ_front = 120 μm (Case 1) or (c) δ_front = 0 (Case 2). Note that the stripped modulations observed for some shots are induced by a defective scanner readout, and hence are not physical. The associated laser and IP setup are sketched on the left. The IP were positioned with IP1 the closest to the target and IP5 the farthest from the target. Hence, the deepest IP5 can only be reached by the highest energy electrons. All IPs share the same colormap, as displayed on the right with normalized photo-stimulated luminescence (PSL) number. The angular scales (yellow bars) vary between the IP images because these are located at different distances from the target. Note also that the laser beam axes do not intersect the IPs positioned along the target normal in panels (b) and (c).

Fig. 3. Quantitative analysis of the electron signals as recorded by the IP stacks (a) along the laser axis and (b) along the target normal. Note that the normalized electron number in each IP is retrieved from the variation in the IP signal using Monte Carlo fluka simulations and the calibration conducted in Ref. 62. The data points represent the signal averaged over three shots performed under similar conditions, while the error bars correspond to the minimum and maximum values over those shots. The horizontal black dashed line represents the noise level at around 0.03. Simulation results are plotted as dotted lines and the associated numbers at the right end of the dotted lines indicate the injected electron temperatures (in MeV). Note that in (b), we use a two-temperature distribution, separated by the vertical black dashed line located at IP2.

Fig. 4. Enhancement of the proton cutoff energy and collimation brought about by coupling two intense laser beams. (a) Variation in the maximum proton energy (as inferred from the RCF data) when varying the spatial separation between the two beams at the front target surface, i.e., δ_front. The points represent the signal averaged over two to three shots performed in the same conditions, while the error bar represents the minimum and maximum values over those shots. The gray hashed area indicates the maximum proton energy obtained in the single-beam configuration (Case 0). The black data points correspond to two separated beams with varying interspacing (Case 1), the green data points represent the central small beam in the overlapped configuration, i.e., Case 2, marked by the green dashed contour in panel (d); while the red data point represents the wide beam (also in Case 2), having the standard divergence of TNSA proton beams, marked by the red dashed contour and blue arrows in panel (d). (b) Variation in the recorded half-angle subtended by the protons, as a function of their energy (normalized to the corresponding cutoff energy). The dashed line plots the energy-dependent angular distribution observed in many experiments to be characteristic of TNSA protons.⁴⁹ Note that the RCFs are positioned along the target normal, as shown in Fig. 1. (c) Raw RCF data, corresponding to protons of (c1) 7.3 and (c2) 8.6 MeV mean energy, in Case 1 with well separated lasers (δ_front = 120 μm). Two distinct standard TNSA beams (driven simultaneously but independently) can be identified, as marked by the black dashed contours and arrows. (d) Raw RCF data, corresponding to protons of (d1) 5.5 and (d2) 12.1 MeV mean energy, in Case 2 with overlapping laser beams. Two different beam signals can be identified. One is identified by the red dashed contour and arrow. The other is identified by the green dashed contour and arrow. Note that the hole in the RCF was managed for downstream spectrometry measurements (not shown).

Fig. 5. Electron acceleration, magnetic field generation and magnetic reconnection in the laser-driven preplasma corresponding to Case 2. (a) 3D rendering (yellow) of (|E_y|), depicting the two laser pulses coming from the left and focused onto the target surface (x = 12 μm). Overlaid is the 2D yz projection of the self-generated, laser-cycle-averaged ⟨B_z⟩ magnetic field (colormap on the right, in m_eω_pe/e units). The HEBs (gray volume rendering surrounded by blue dashed lines) generated (with energies above 5 MeV) by the α and β laser beams are indicated by blue arrows. The enhanced HEB (gray volume rendering surrounded by cyan dashed lines) around the MR region (between the laser beams) is marked by the cyan arrow (around x = 6.5 μm), while the MR-induced E_x field (red) is highlighted by the red arrow. (b) Sketch of MR in a yz plasma slice ahead of the target surface, as indicated by the dashed black box in (a). J_x represents the electron current density along the longitudinal x direction, B_y and B_z are the in-plane magnetic fields, and E_x is the MR-driven, out-of-plane electric field. The MR region is delineated by black dashed lines.

Fig. 6. Features of MR and resulting enhanced HEB generation (a1)–(c1) Out-of-plane electric field E_x (m_ecω_pe/e units). (a2)–(c2) Time-averaged power density due to out-of-plane electric field, ⟨J_xE_x⟩ (m_ec²ω_pen_c units). (a3)–(c3) Electron number density n_e (cm⁻³ units) in log₁₀ scale. (a4)–(c4) Kinetic energy density n_eE_kin (MeV cm⁻³ units) of electrons above 1 MeV in log₁₀ scale. Top row: one laser beam (Case 0). Middle row: two nonoverlapping laser beams (Case 1). Bottom row: two overlapping laser beams (Case 2). All panels show yz slices taken at t = 440 fs and averaged longitudinally over 6 < x < 10 μm, i.e., in front of the dense plasma region (12 < x < 15 μm).

Fig. 7. Time evolution of the spatially integrated electromagnetic field energies. (a) Energies associated with B_y and B_z in Cases 0 and 2. All curves are normalized to the maximum of the B_z energy in Case 2. (b) Energies associated with E_x in Cases 1–3. All curves are normalized to the maximum of the E_x energy in Case 2. In each panel, the dark vertical band indicates the period (330 ≲ t ≲ 500 fs) during which MR is effective in Case 2, i.e., when a portion of the B_z energy [red solid line in (a)] is transferred to both B_y [red dashed line in (a)] and E_x [red solid line in (b)]. The history of the E_x energy in Case 1 is plotted to quantify the contribution from the additional laser beam.

Fig. 8. Comparison of the outgoing hot-electron spectra in simulation Cases 1 and 2. The energy spectra are recorded behind the target, across the x = 18 μm plane. Each curve is normalized to its maximum value for better comparison, and fitted by two temperatures over energy ranges indicated by the thin dashed lines.

Fig. 9. Dynamics of a representative MR-accelerated electron. Electron trajectory as recorded in the (a) x-energy and (b) y-z spaces. In (b) the trajectory is superimposed on the ⟨J_xE_x⟩ map of Fig. 6(c2). In both panels, the red star marks the starting point of the trajectory indicates the approximate onset (respectively, end) of MR. A large energy gain is observed within the region and time period of MR activity.

Fig. 10. Four-beam case. (a) Out-of-plane electric field E_x (m_ecω_pe/e units). (b) Time-averaged power density ⟨J_xE_x⟩ (m_ec²ω_pen_c units). (c) Electron number density n_e (cm⁻³ units) in log₁₀ scale. (d) Kinetic energy density n_eE_kin (MeV cm⁻³ units) of electrons above 1 MeV in log₁₀ scale. All panels show yz slices recorded at t = 440 fs and averaged over 6 < x < 10 μm in front of the solid target. Panels (c) and (d) share the same colormap.

Fig. 11. Resistive magnetic field generation in the collisional dense target. (a) Case 2: two laser beams with δ_front = 0. (b) Case 0: single beam. Both snapshots are taken 1 ps after the start of the simulation. The magnetic field is averaged over the laser cycle.

Fig. 12. Angular distributions of the HEB within the dense target. The distributions of propagation angle are computed at times t = 240 fs (dashed curves) and t = 1 ps (solid curves) from the higher-energy (>1.5MeV) electrons contained in the area 5 < x < 9 μm and 15 < y < 25 μm (to suppress numerical boundary effects). Blue curves: single laser beam (Case 0). Red curves: two overlapping beams (Case 2). All curves are normalized to the maximum of the Case 2 curve at t = 1 ps. The gray dashed lines indicate the target normal (0°) and laser incidence (15°) directions.