Laser guiding in a nonuniform plasma channel

Summary form only given. Laser guiding is a key issue in laser wakefield accelerators. For such investigation, a laser pulse produces a plasma channel of axially nonuniform density. Through such performed plasma channels, when a delayed second pulse propagates, the modulation phenomena come into play. We have solved the nonlinear parabolic partial differential equation governing the propagation characteristics for an approximate analytical solution by using variational approach. Particular emphasis is put on the variation of both beam radius and longitudinal phase delay, which are crucial to plasma based accelerators.