Laser‐Driven Coherent Betatron Oscillation in a Laser‐Wakefield Cavity: Formation of Sinusoid Beam Shapes and Coherent Trajectories

High amplitude coherent electron‐trajectories have been seen in 3D particle‐in‐cell simulations of the colliding pulse injection scheme of laser‐wakefield accelerators in the bubble regime, and explained as a consequence of laser‐driven coherent betatron oscillation in our recent paper [K. Nemeth et al., Phys. Rev. Lett. 100, 095002 (2008)]. In the present paper we provide more details on the shape of the trajectories, their relationship to the phase velocity of the laser and indicate the dependence of the phenomenon on the accuracy of the numerical representation and choice of laser/plasma parameters.