Projected and Slice Emittance Growth in a Plasma-Based Accelerator

Plasma based accelerators are a promising, compact alternative to conventional electron accelerators. These accelerators must preserve the transverse emittance of the beam in order to satisfy the requirements for collider and light source applications. If not carefully designed, a plasma-based accelerator will increase the beam’s emittance through the process of chromatic phase spreading. We present a general approach to analytically describing the transverse evolution of the witness beam within a nonlinear plasma-based accelerator. Our approach includes the effects of density ramps on the plasma source, energy gain, and wake loading. In addition, our method can handle emittance growth from both beam-plasma mismatch and a transverse offset between the witness beam and the wake. Using this approach, we derive a set of saturation lengths for the projected emittance, longitudinal slice emittance, and energy slice emittance. These analytic expressions can help narrow down the design parameters of a plasma-based accelerator before resorting to expensive simulations.