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 ${(1+k_p^{}{}_{}{}^2{Z}^2)}^{\frac{1}{2}}\Delta \gamma m{c}^2$, where $Z$ is the bunch length and $\Delta \gamma m{c}^2$ 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 ${\gamma }_i=150\mathrm{}$, $\frac{\Delta \gamma }{{\gamma }_i}\gtrsim 70\%$, with an energy gain ∼ 1 GeV. Transverse effects are briefly discussed.