Numerical modeling of laser wakefield electron acceleration inside a gas filled dielectric capillary tube is presented. Guiding of a short pulse laser inside a dielectric capillary tube over a long distance (∼1 m) and acceleration of an externally injected electron bunch to ultra-relativistic energies (∼5-10 GeV) are demonstrated in the quasi-linear regime of laser wakefield acceleration. Two dimensional axisymmetric simulations were performed with the code WAKE-EP (Extended Performances), which allows computationally efficient simulations of such long scale plasma. The code is an upgrade of the quasi-static particle code, WAKE [P. Mora and T. M. Antonsen, Jr., Phys. Plasmas 4, 217 (1997)], to simulate the acceleration of an externally injected electron bunch (including beam loading effect) and propagation of the laser beam inside a dielectric capillary. The influence of the transverse electric field of the plasma wake on the radial loss of the accelerated electrons to the dielectric wall is investigated. The stable acceleration of electrons to multi-GeV energy with a non-resonant laser pulse with a large spot-size is demonstrated.

By seeding an optical-field-ionized population-inverted plasma amplifier with the 25th harmonic of an IR laser, we have achieved what we believe to be the first aberration-free laser beam in the soft x-ray spectral range. This laser emits within a cone of 1.34 mrad(1/e(2)) at a repetition rate of 10 Hz at a central wavelength of 32.8 nm. The beam exhibits a circular profile and wavefront distortions as low as lambda/17. A theoretical analysis of these results shows that this high beam quality is due to spatial filtering of the seed beam by the plasma amplifier aperture.

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