Diffusion of an annular plasma in positron acceleration

Electron acceleration to multi-GeV energies has been demonstrated using plasma wakefields in a tunnel-ionized plasma. However, coherent wakefields for positron acceleration may require hollow plasmas pre-ionized by a laser beam. The lifetime of such a plasma is determined by an unusual diffusion problem in which the diffusion rate varies by an order of magnitude inside the hole. The problem is solved by numerical differentiation without using a particle-in-cell code. The densities assumed in this work match those in existing positron experiments and are low compared with those in electron experiments. Future positron experiments at higher densities will not exhibit the nonlinear diffusion treated here because they will be dominated by recombination and tunneling ionization by the beam