Energy Transfer in the Plasma Wake-Field Accelerator

The transfer of energy from the driving beam to the trailing beam in the plasma wake-field accelerator is studied in computer simulations. We show that with an asymmetric current distribution in the driving bunch, trailing particles can gain energies up to ${(1+k_{p}^{}{}_{}{}^{2}{Z}^{2})}^{\frac{1}{2}}\ensuremath{\Delta}\ensuremath{\gamma}m{c}^{2}$, where $Z$ is the bunch length and $\ensuremath{\Delta}\ensuremath{\gamma}m{c}^{2}$ the average energy loss of driving electrons. Because of the relative phase slippage and the two-stream instability, the process of energy gain degrades before the driving beam loses all of its energy; however, even for ${\ensuremath{\gamma}}_{i}=150$, $\frac{\ensuremath{\Delta}\ensuremath{\gamma}}{{\ensuremath{\gamma}}_{i}}\ensuremath{\gtrsim}70%$, with an energy gain \ensuremath{\sim} 1 GeV. Transverse effects are briefly discussed.