A note on thermal effects in non-linear models for plasma-based acceleration

We investigate the impact of a non-negligible background temperature on relativistic plasma wake-fields generated when a beam of charged particles passes through a neutral plasma at rest. We focus on the blowout regime, wherein the plasma response is highly non-linear: plasma electrons are radially blown out and expelled away from the propagation axis of the beam particles, creating a region (bubble) of ions without electrons. Our study builds upon earlier investigations for non-linear models of plasma wakefields developed in the limit of zero background temperature (Lu et al., Phys. Rev. Lett. 96, 165002 (2006)). In the presence of a non-zero background temperature, we characterize the model and focus on its predictions for the bubble size and the electromagnetic fields inside the bubble. Model predictions are studied in combination with PIC simulations.