Relativistic Extension of the Accelerating-Focusing Phase in 3D Nonlinear Laser Wake

It is demonstrated that the accelerating and focusing phases of the nonlinear three-dimensional axi-symmetric laser wake can almost entirely overlap starting from a certain distance behind the laser pulse in homogeneous plasma. Such field structure results from the curvature of phase fronts due to the radially inhomogeneous relativistic plasma frequency shift. Consequently, the number of trapped low-energy electrons can be much greater than that predicted by the linear wake theory. This effect is favorable for quasi-monoenergetic acceleration of a considerable charge (several hundreds of pC) to about 1 GeV per electron in the plasma wakefield driven by an ultrashort (∼ 30 fs) weakly focused (r0 ∼ 100 μm) petawatt laser pulse