Influence of the wake wave on the driver´s electrons

Summary form only given. In plasma wakefield accelerators the field in the plasma is driven by an electron beam (driver) Wake wave may reach very high values, up to several tens of GV/m. For practical application of PWFA the high amplitude of electric field is not sufficient. The field should retain its regular structure over long distance with no degradation. But the driver itself experiences both longitudinal and transverse (focusing or defocusing) forces. Due to-high relativistic factor /spl gamma//sub b/ of the driver, the influence of longitudinal and transverse force can be of significantly various kinds. The influence of the wake wave on the behaviour of driver electrons and on the driver as whole is an important aspect of the theory of plasma-based accelerators. Usually, the influence of the excited plasma wake on bunch is considered using various complicated codes. Present investigation considers influence of wake field on bunch electrons. It is assumed that bunch-plasma interaction takes place in two stages. The first one is formation of wake field in plasma by rigid bunch. Second stage is the influence of the induced fields on the bunch. This assumption is valid, due to presence of two different time scales: time /spl tau//sub s/ needed for formation of stationary wake in plasma, and time /spl tau//sub p/ required for change of the bunch electron momentum. The conditions satisfies, when /spl gamma/ /sub b//spl Gt/1. The generation of wake field by given bunch is considered by many authors. In present investigation we proceed from expressions in, and consider motion of the bunch´s electrons in the field. After some simplifications equation of longitudinal motion become identical to the well known equation of mathematical pendulum. Energy of nonlinear oscillations of bunch electrons depends on distance from bunch edges. The bunch electron first decelerated and is left behind the unperturbed trajectory, then come up.