Effect of Transverse Beam Size on the Wakefields and Driver Beam Dynamics in Electron Beam Driven Plasma Wakefield Acceleration

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