Transverse emittance and current of multi-GeV trapped electrons in a plasma wakefield accelerator

Multi-GeV trapped electron bunches in a plasma wakefield accelerator (PWFA) are observed with normalized transverse emittance divided by peak current, ϵN,x/Iₜ, below the level of 0.2 μm/kA. A theoretical model of the trapped electron emittance, developed here, indicates that emittance scales inversely with the square root of the plasma density in the nonlinear ``bubble'' regime of the PWFA. This model and simulations indicate that the observed values of ϵN,x/Iₜ result from multi-GeV trapped electron bunches with emittances of a few μm and multi-kA peak currents.