Laser evolution and cold fluid plasma response ( and ) for , , and [(a)–(d)] (right) and [(e)–(h)] (left). Time increases from top to bottom. For : (a) ; (b) ; (c) ; and (d) . For : (e) ; (f) ; (g) ; and (h) . The evolution in the two cases follows the same general pattern: pulse steepening due to self-phase modulation leading to an increase in wakefield amplitude followed by a dramatic increase in the length of the laser pulse and a corresponding decrease in wake amplitude. The longitudinal electric field is shown as a multiple of while the plasma density is shown as a multiple of the initial density .
Details of the system evolution for , , and [(a)–(d)] (right) and [(e)–(h)] (left). Shown is the evolution of the laser pulse [(a) and (e)]; the wakefield [(b) and (f)]; the laser vector potential PSD in arbitrary units [(c) and (g)]; laser energy (red), the mean wavenumber computed from the first moment of the laser vector potential PSD (blue), each normalized to their respective initial values (left axis), and the relative change in the wave action (green; right axis) [(d) and (h)].
Laser pulse energy, normalized to the initial value, for various initial laser intensities and wavenumbers.
Evolution of the maximum wakefield amplitude, , for various initial laser intensities and wavenumbers.
Rate of change in laser energy, , (lines), compared to Eq. (7) (symbols: , crosses; , diamonds; and circles), for various initial laser intensities and wavenumbers.
Pump depletion lengths for selected fractional energy loss and various values of from direct solution of Eq. (1) (symbols) and with given by Eq. (10) for a resonant Gaussian laser pulse (gray line, no symbols).
Mean laser wavenumber, normalized to vs propagation distance , for various laser intensities.
Pulse length, , computed from the -variance of the energy density, vs propagation distance for various laser intensities.
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