Figure 4

Simulated betatron source dynamics (also see movie in SM). The evolution of the laser, bubble and the injected electron beam is shown for different positions along the jet indicated in (j) as “1” (a)–(c), “2” (d)–(f) and “3” (g)–(i). The laser is moving to the right (i.e. in positive z-direction). The asymmetric longitudinal laser pulse profile leads to a transverse asymmetry in the bubble shape and off-axis electron injection during the density downramp (a)–(c). The field of the laser front is depleted by a half cycle, leading to a field spike with opposite sign and an asymmetry into the opposite direction (d)–(f). The controlled off-axis injection leads to a correlated transverse momentum distribution (c), (f), and (i) and coherent electron oscillations in the laser polarization (x, z) plane. Near the plasma density minimum, the bubble evolves into a super-structure, highly suppressing longitudinal accelerating fields (g)–(i). This leads to electron propagation with nearly constant energy as can be seen from the trajectories of 1429 macro particles from near the head of the electron bunch (k). The laser electric field \(E_x\) is normalized to \(E_0=mc^2 k_p/e\), the longitudinal and transverse electron momenta (color coded) are normalized to mc and the plasma density to the peak density \(n_0 = 1 \times 10^{19} \, \mathrm {cm}^{-3}\).