Transformer ratio studies for single bunch plasma wakefield acceleration

In Plasma Wakefield Acceleration (PWFA) plasma oscillations are driven by ultra relativistic electron beams. The ratio of the maximum accelerating field behind the driving beam (bunch) and the maximum decelerating field inside the driving beam (bunch) is defined as Transformer Ratio, a key parameter that determines the energy gain in particle acceleration. We investigate the transformer ratio for different shapes of a single driving bunch. One dimensional, fluid, relativistic, cold plasma equations have been numerically solved. A complete map of the transformer ratio is obtained by varying: bunch shape, bunch length and density ratio. It is found that the transformer ratio critically depends on the bunch shape and on the density ratio. Moreover both in the linear as well as in the non-linear regime the theoretical limit of 2 for the transformer ratio of a single symmetric bunch can be exceeded using asymmetric bunches in the linear regime as well as symmetric bunches in nonlinear regime.