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For the considered scheme of the external electron bunch injection in front of a laser pulse, the influence of the nonlinear driving laser pulse dynamics and electron bunch self-action to the processes of electron bunch compression and acceleration in the laser wakefield is analyzed. Self-consistent modelling results confirm that the nonlinear laser pulse dynamics limits the bunch compression due to variations of the phase velocity of the wake. A growth of the injected bunch charge leads to some extent to an increase of the trapped and accelerated bunch charge and to decrease of the trapped bunch radius and emittance due to increased self-focusing bunch. The three-dimensional theoretical model is elaborated and used to describe the propagation of laser pulses in dielectric capillary waveguides under imperfect coupling and focusing conditions with broken cylindrical symmetry. The role of cone entrances to the cylindrical part of a capillary is analyzed, and it is demonstrated that matching cones can considerably increase the transmission of laser pulses through the capillary, but cannot mitigate the requirements on the precision of the laser pulse focusing into a capillary. In order to avoid a speckle structure and strong transverse gradients of the fields, which can prevent the process of regular electron bunch acceleration, one has to ensure a small laser angle of incidence into the capillary not exceeding 1 mrad.

Acceleration of electrons to the 100 GeV range in laser wakefield accelerators using multi-petawatt lasers is numerically modelled. It is demonstrated that an externally injected electron bunch with an initial energy of 50 MeV can achieve an energy gain of 100 GeV in the weakly non-linear regime of laser wakefield acceleration. The guiding of the laser is achieved by a plasma channel having a parabolic radial density profile. A comparative study of plasma channels (matched and unmatched) is performed to investigate the sensitivity of electron acceleration to the matching condition in this regime. It is found that unmatched channels restrict energy gain to ∼60 GeV and lead to radial loss of injected charge due to the oscillation of the spot size of the laser inside the channels.