By Gwenael J Fubiani; Lawrence Berkeley National Laboratory.; United States. Dept. of Energy. Office of Scientific and Technical Information.; USDOE Director. Office of Science. Office of High EnergyPhysics
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However a general overview of the physical effect may be given; a sufficiently long interaction in time (t ωp−1 ) between the laser pulse and the plasma density modulation of the wake is necessary for the instability to build up from noise. The laser fields experience a local change of index of refraction, both radially and axially, due to the plasma density modulations. Regions where ∇δn > 0 induce an increase of local laser energy whereas ∇δn < 0 on the contrary enhance diffraction. This cause both the longitudinal and transverse laser envelope to become modulated at λp , which subsequently enhances the growth of the plasma wave, and the process proceeds in a highly nonlinear manner.
02 kp2 L2 inside the drive pulse and ψo = −π/2−kp L/2 modulo 2π outside. Unstable fixed points (“X” points) lie at uz = γφ βφ and ψx = −3π/2 − kp L/2 modulo 2π. The boundary between trapped and untrapped orbits defines the separatrix orbit, which is specified by Hc = H(γφ βφ , ψx ) and crosses the X-point. 5 as obtained from Eqs. 18). The corresponding phase space orbits are plotted in Fig. 3(b) as obtained from Eq. 44). Shown are the cold fluid orbit, separatrix between trapped and untrapped orbits, and the trapped and focused (2D) separatrix.
Furthermore, the CPI concept offers detailed control of the injection process: the injection phase can be controlled via the position of the forward injection pulse, the beat phase velocity via ∆ω, the injection energy via 28 Chapter 3. Electron injection into plasma waves using two laser pulses the pulse amplitudes, and the injection time (number of trapped electrons) via the backward pulse duration. In this Chapter, a simplified configuration of the CPI concept is proposed and analyzed that uses only two laser pulses with parallel polarizations: an intense pump pulse for wakefield generation and a single counterpropagating (or propagating at a finite angle) injection pulse.