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The quasi-static code WAKE [P. Mora and T. Antonsen, Phys. Plasmas {\bf 4},217(1997)] is upgraded to model the propagation of an ultra-relativisticcharged particle beam through a warm background plasma in plasma wakefieldacceleration. The upgraded code is benchmarked against the fullparticle-in-cell code OSIRIS [Hemker et al., Phys. Rev. ST Accel. Beams {\bf3}, 061301(2000)] and the quasi-static code QuickPIC [Huang et al., J. Comp.Phys. {\bf 217}, 658 (2006)]. The effect of non-zero plasma temperature on thepeak accelerating electric field is studied for a two bunch electron beamdriver with parameters corresponding to the plasma wakefield accelerationexperiments at FACET. It is shown that plasma temperature does not affect theenergy gain and spread of the accelerated particles despite suppressing thepeak accelerating electric field. The role of plasma temperature in improvingthe numerical convergence of the electric field with the grid resolution isdiscussed.

Plasma wakefield acceleration studies using the quasi-static code WAKE