(Color online) (a) Peak laser intensity (black) and length of the accelerating phase [red (gray)] vs propagation distance. Data from positions (1) to (3) are used to describe the process of monoenergetic electron bunch formation in Fig. 3. (b) Energy of test electrons vs their initial positions after one period of bubble size oscillation [position (3)]. All electrons accelerated beyond 100 MeV were collected during the interval of bubble expansion.
(Color online) Fully expanded electron bubble from the wake simulation. Dashed red (dark gray) contour in panels (a) and (d) is the isocontour of laser intensity at of the peak. (a) Trajectories of the quasistatic macroparticles. Green (light gray) and black trajectories correspond to passing electrons. The red (dark gray) ones correspond to sheath electrons—injection candidates. (b) Normalized slippage time as a function of the impact parameter, . (c) Longitudinal (, solid line) and transverse (, dashed line) momenta of macroparticles at the rear of the bubble (point of trajectory crossing). Sheath electrons have the largest slippage time and become relativistic before crossing the axis. (d) Top: the quasistatic electron density; grayscale is linear with a cutoff at . Solid red (dark gray) line is the trajectory of the macroparticle with the greatest slippage time. Bottom: radial positions of nonquasistatic test electrons. Red (dark gray) dots are the electrons with . (e) Impact parameters of test electrons from panel (d) vs energy.
(Color online) Phase space rotation and formation of a monoenergetic bunch. (a) Fully expanded bubble [cf. position (2) of Fig. 1(a)]. (c) Contracted bubble [cf. position (3) of Fig. 1(a)]. Top half: quasistatic electron density (in ); bottom: number density of nonquasistatic test electrons. The dashed curve is a laser intensity isocontour at of the peak. Panels (b) and (d): blowup of the bubble rear from panels (a) and (c); test electrons are color coded according to [red (dark gray)], [green (light gray)], (black). (e) Phase space rotation of injected test electrons. Longitudinal phase space is shown at the positions (1)–(3) of Fig. 1(a). (1) Injection begins. (2) The bubble is fully expanded, injection stops, and phase space rotation begins. The bucket slightly contracts between positions (2) and (3). (3) Electrons injected lately equalize in energy with those injected earlier. Quasi-monoenergetic bunch forms. Inset shows vs energy gain for the fully expanded (2) and contracted (3) bubble. (f) Axial line-outs of the accelerating gradient (normalized to GV/cm).
(Color online) Pulse self-compression and continuous injection. (a) Peak laser intensity (black) and the length of the accelerating phase vs propagation length [red (gray)]. (b) Energy of test electrons versus their initial positions at . The leading quasi-monoenergetic electron beam forms during stage I (one period of bubble size oscillation). Continuous bubble expansion during stage II causes continuous injection with broad energy spectrum. Panels (c), (e), and (g) show electron density (in ) and test electrons with [red (gray) dots]. Panels (d), (f), and (h): normalized laser intensity ; red (gray) line: isocontour of an incident pulse intensity at of the peak. Panels (c) and (d); (e) and (f); and (g) and (h) correspond to the positions (1), (2), and (3) of panel (a), respectively. Contraction of the driver pulse (formation of a relativistic piston) causes elongation of the bubble and continuous injection.
(Color online) Pulse redshifting and formation of the relativistic piston. (a) Axial lineouts of normalized intensity [red (gray)] and nonlinear refractive index (black) at the position (1) of Fig. 4(a). (b) Same for the position (3) of Fig. 4(a). (c) Laser frequency spectra. Solid black corresponds to panel (a), red (gray) – to panel (b), dashed black – to the incident pulse. Strong redshifting and spectral broadening are partly caused by the comoving nonlinear index gradient. Panel (b) shows that the spectrally broadened pulse is compressed to approximately two cycles.
(Color) Continuous injection in quasistatic (wake with test particles) and full 3D PIC (calder-circ) simulations. (a)–(c) Electron density from calder-circ (top half) and wake (bottom) runs. Yellow dots are the test electrons with . (d)–(f) Electron energy spectrum (calder-circ). (g)–(i) Longitudinal phase space (colormap— calder-circ; wake test electrons—yellow dots). Panels (a), (b), and (c) are counterparts of Figs. 4(c), 4(e), and 4(g).
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