Extended Data Fig. 4: Simulation results for high energy gain when using a longer plasma and a more powerful laser.
The plasma has a 2.4 mm-long up-ramp identical to the experimental condition as the matching section, and a 20 cm-long plateau as the acceleration section (see panel a). A 200 TW laser is focused to a spot size w0 = 35 μm with a0 = 2.2 at the beginning of the plateau (z = 2.4 mm). The plasma transverse profile is set to a parabolic channel \(n_{p,0} \times \left( {1 + 0.4 \times \frac{{x^2 + y^2}}{{w_0^2}}} \right)\) for laser guiding, where np,0 is the on-axis density with the plateau value of 2 × 1017 cm−3. A 50 pC, 25 MeV, 10 fs full duration (flat-top current profile) electron beam with 0.6% FWHM (no chirp) energy spread and 1 mm mrad normalized emittance is focused to z = 0 with a transverse waist size of 4 μm r.m.s. (left inset in panel a). The matching section can transport the beam from this waist to another waist with spot size of ~1.5 μm r.m.s. and energy of ~50 MeV at z = 2.4 mm (right inset in panel a), which is nearly matched to the plasma focusing fields in the acceleration section. b, The simulated Ez at z = 2.4 mm (upper half) and z = 93.6 mm (lower half). The blue and red lines show the lineouts of on-axis Ez values for z = 2.4 mm and z = 93.6 mm, respectively. The electron beam is first over-loaded (blue line), and then as the beam phase slips forward the wake, the longitudinal field within the beam is gradually flattened (red line). After that, the beam is under-loaded. The green and yellow lines show the contours of the laser (e−2 of its peak intensity) and the electron beam (full bunch length in ξ and r.m.s. spot size in x), respectively. c, Evolutions of the beam r.m.s. spot size (green line), normalized emittance (blue line) and central energy (red line). The shaded regions correspond to the beam r.m.s. energy spread (times 5 for visual clarity). d, The final beam longitudinal phase space.
