Collisional Damping of Wakes in Doped Semiconductors

We examine the role of collisional damping in plasmonic wakefield accelerators. Three regimes are identified for wakefields driven in a doped semi-conductor by a charged particle beam: At low intensities of the driver pulse, the mobility of the free carrier electrons is limited by collisions. The mean free path of an electron is short compared to the quiver amplitude of a free electron, and the resulting wake is very small. A threshold intensity is found above which the conduction electrons in the semiconductor are driven to such high speeds that their Coulomb collision cross-section drops sharply, and the resulting wake can resemble that in a hollow collisionless plasma of density equal to that of the conduction electrons in the semi-conductor tube. At yet higher intensities, the entire tube can be ionized during the pulse rise, and electrons in the latter portion of the wake fill in the hollow region of the tube. This is the "crunch-in" or non-linear hollow plasma wakefield regime that can potentially produce TeV/m peak acceleration gradients. Lattice effects and laser drivers are briefly discussed.