Relativistic effects on intense laser beam propagation in plasma channels

Propagation characteristics of a radiation beam in a preformed, tapered plasma channel are analyzed by means of an envelope equation for the beam spot size. The model allows for relativistic focusing and ponderomotive channeling, radial and axial density gradients, and is valid for arbitrary intensity. The characteristics of laser beam propagation are shown to be governed by two parameters, the ratio of laser power to the critical power for relativistic focusing, and a dimensionless focusing strength parameter that includes contributions from both relativistic and channel focusing. The envelope equation provides a unified approach for exploring diverse applications such as designing a tapered laser wakefield accelerator or a plasma lens. The model is employed in interpretation of pump–probe laser propagation experiments and an x-ray source experiment. Full-scale simulations of a plasma channel lens are presented and shown to be in excellent agreement with the analytical results.