The plasma beat-wave accelerator (PBWA) in the Neptune Laboratory at UCLA utilizes a ～1 terawatt two-wavelength laser pulse to tunnel ionize hydrogen gas at conditions of resonance for driving relativistic plasma waves. This plasma wave is used as an accelerating structure for an externally injected ～11 MeV electron beam from the Neptune Photo-injector. Simulations in 2-D have been done to model this experiment for laser ionized plasmas with mobile ions for two focusing geometries, f/3 and f/18. Simulations have shown that ion motions in the transverse direction for small spot size cases (f/3 case) cannot be neglected, and that the acceleration of electrons is therefore limited by shortening of the effective interaction length due to deviations from the resonant density. In the f/18 case, while ion motions are not as severe as in the f/3 case, ionization induced refraction begins to limit the peak intensity of the laser. In addition, injection of the electron beam into the plasma wave is modeled to determine what acceleration is to be expected in experiments.
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