(Color online). Schematic representation of hyperbolas which are solutions of equations and , where the vector corresponds to the flow defined by Eq. (26). The intersections of these hyperbolas (marked by circles) correspond to the two critical points and .
A schematic illustration of the ladder similarity (see text).
Electron density taken from the 3D PIC simulation (iv) with parameters , after the laser has propagated the distance in plasma. The wake field takes the form of a single cavity (the bubble) (Ref. 11), free from cold background electrons. The dense bunch of trapped and accelerated electrons is structured and has a sharp leading edge.
(Color online). Electron energy spectra obtained in the simulations (i)–(iv) (see text). The control points 1–5 were taken after the propagation distances , , , , . The spectra evolve similarly. The quasimonoenergetic peak positions scale and the number of electrons in a 1% energy range also scales in agreement with the analytic scalings (15) and (16).
(Color online). Electron energy spectra obtained in the simulations (v) (see text). The control points 1–9 were taken after the propagation distances , , , , , , , , . The spectral evolution for the control points 1–5 is similar to that of the simulation cases (i)–(iv). The spectra 6–9 correspond to a new evolution that cannot be directly scaled from the previous simulations.
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