Threshold for Trapping Positrons in the Wake Driven by a Ultra-relativistic Electron Bunch

We have recently proposed a new concept for generating, injecting and accelerating positrons in a plasma using a double-pulse electron bunch. Monte Carlo simulations show that the number of the positrons produced in a foil target has an exponentially decay energy spectrum. The energy threshold for the trapping of these positrons in a ultra-relativistic electron wake is investigated numerically. For a typical 28.5 GeV electron drive bunch, the trapping threshold for the positrons is a few MeV, and therefore a majority of positrons generated in the foil target are focused and accelerated by the plasma wake.