Schematic of the basic principle of increasing the plasma density (tapering) to compensate for slippage between the plasma wave and a relativistic particle such that the particle (represented by a circle) remains in a constant phase of the plasma wave. (a) Longitudinal electric field at the initial density . (b) Longitudinal electric field at the twice the initial density . Laser centroid is located at .
The normalized plasma frequency vs for phase locking the accelerating force (constant phase ) for and . The dashed curves are the approximate solution, Eq. (34).
Normalized laser spot size and channel radius and plasma frequency vs propagation distance (normalized to the Rayleigh range) to maintain a constant phase in the accelerating and focusing phases for and .
Normalized plasma wave accelerating field at with and vs propagation distance for the cases: without taper (dotted curve), taper given by Eq. (34) (solid curve), and taper given by Eq. (37) (dashed curve). The initial phase of the particle is .
Normalized energy gain with , , and vs propagation distance for the cases: without taper (dotted curve), taper given by Eq. (34) (solid curve), and taper given by Eq. (37) (dashed curve).
Normalized energy gain vs normalized initial laser pulse duration for (dashed curve), (solid curve), and (dotted curve). corresponds to an initially linearly resonant laser pulse.
The normalized plasma frequency vs with initial phase and , for , , and the optimal taper (dashed curve) given by Eq. (34).
Normalized energy gain for linear tapers with and for and vs propagation distance . Dashed curve is energy gain with optimal taper.
Normalized plasma frequency vs distance with . Solid curve is the density taper for a beam that is in the initial phase and moves to the phase after the density discontinuity at . Dashed curve is the continuous density taper for a beam at the phase .
Normalized energy gain with for the taper cases shown in Fig. 9: Solid curve is the discontinuous taper case and dashed curve is the continuous taper case.
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