A multi-sheath model for highly nonlinear plasma wakefields

High gradient, high efficiency acceleration and high quality beam generation are important goals of plasma-based acceleration (PBA). To understand these processes, an accurate description of nonlinear wakefields is required. These wakefields can be excited by intense particle beams or lasers pushing plasma electrons radially outward and forward, creating an ion bubble surrounded by a sheath of electrons characterized by the source term S=−(ρ−J_z/c)/en_p. Previously, the sheath source term was described as positive-definite, resulting in a positive-definite wake potential. In reality, the wake potential is negative at the rear of the bubble, which is important for accurate self-injection and beam loading models. To account for this, we present an improved multi-sheath model in which the plasma source term, S, can be negative in regions outside the ion bubble [1]. Using this model, a new expression for the wake potential and a modified differential equation for the bubble radius are obtained. Numerical results obtained from these equations are compared to PIC simulations for unloaded and loaded wakes. The new model is shown to provide accurate predictions of trailing bunch current profiles that flatten plasma wakefields. It is also used to design a trailing bunch for a desired longitudinally varying wakefield. Beam loading results for laser wakefields are also presented.

[1] T. N. Dalichaouch et al., Phys. Plasmas 28, 063103 (2021).