Effect of transverse beam size on the wakefields and driver beam dynamics in plasma wakefield acceleration schemes

In this paper, wakefields driven by a relativistic electron beam in a cold homogeneous plasma are studied using 2D fluid simulation techniques. It has been shown that in the limit when the transverse size of a rigid beam is greater than the longitudinal extension, the wake wave acquires a purely electrostatic form, and the simulation results show a good agreement with the 1D results given by Bera et al. [Phys. Plasmas 22, 073109 (2015)]. In the other limit when the transverse dimensions are equal to or smaller than the longitudinal extension, the wake waves are electromagnetic in nature, and 2D effects play a crucial role. Furthermore, a linear theoretical analysis of 2D wakefields for a rigid bi-parabolic beam has also been carried out and compared with the simulations. It has also been shown that the transformer ratio, which is a key parameter that measures the efficiency in the process of acceleration, becomes higher for a 2D system (i.e., for a beam having a smaller transverse extension compared to the longitudinal length) than the 1D system (i.e., for a beam having a larger transverse extension compared to the longitudinal length). Furthermore, including the self-consistent evolution of the driver beam in the simulation, we have seen that the beam propagating inside the plasma undergoes transverse pinching, which occurs much earlier than the longitudinal modification. Due to the presence of transverse dimensions in the system, the 1D rigidity limit given by Tsiklauri [Phys. Plasmas 25, 032114 (2018)] gets modified. We have also demonstrated the modified rigidity limit for the driver beam in a 2D beam–plasma system.