Beam head erosion in self-ionized plasma wakefield accelerators

In the recent plasma wakefield accelerator experiments at SLAC, the energy of the particles in the tail of the 42 GeV electron beam were doubled in less than one meter. Simulations suggest that the acceleration length was limited by a new phenomenon - beam head erosion in self-ionized plasmas. In vacuum, a particle beam expands transversely in a distance given by beta. In the blowout regime of a plasma wakefield, the majority of the beam is focused by the ion channel, while the beam head slowly spreads since it takes a finite time for the ion channel to form. It is observed that in self-ionized plasmas, the head spreading is exacerbated compared to that in pre-ionized plasmas, causing the ionization front to move backward (erode). A simple theoretical model is used to estimate the upper limit of the erosion rate for a bi-gaussian beam by assuming free expansion of the beam head before the ionization front. Comparison with simulations suggests that half this maximum value can serve as an estimate for the erosion rate. Critical parameters to the erosion rate are discussed.