On Energy Transfer in the Plasma Wake Field

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 4 1 + k2Z2Aymc2 P , where 2 is the bunch length, and A,ymc2 the average energy loss of driving electrons. Due to 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 7i = 150, A7/7i 2 7O%, with an energy gain 1 GeV. Transverse effects are briefly discussed. The idea of using one bunch of relativistic electrons to accelerate another to higher energy through the wake plasma wave set up by the leading bunch, was first suggested by Chen et.al. ’ in a paper employing the electrostatic approximation; later2 the treatment was generalized to a fully electromagnetic one. Although the exact values depend on many parameters, accelerating fields of 1 GeV/m seemed reasonable. On the other hand, Ruth et a1.3 recognized the analogy between this scheme and collinear wake field acceleration in conventional metallic accelerating structures (MWFA), and called the former the plasma wake field accelerator (PWFA). 0 nce this is seen, existing studies of MWFA can be directly connected to the PWFA. One of the outstanding questions concerning wake field acceleration has been the limitation on the energy that can be transferred from the driving beam to the trailing beam. A useful parameter which describes this energy transfer is the transformer ratio R, defined as the ratio of the maximum accelerating electric + field behind the driving bunch E,, to the maximum retarding electric field within the bunch E;. If a mono-energetic driving bunch excites a wake field, and if within distance L the particle in the bunch that experiences the maximum retarding field E;, which would stop the earliest, loses energy Aymc2 = eLLE;, then the maximum possible energy gain for a test charge behind the bunch will be RAymc2 in the same distance. It can be proven that,4 for any finite length bunch with a symmetric longitudinal charge distribution traversing an EM cavity supporting only a single mode, the transformer ratio cannot be larger than two; this is a generalized version of the fundamental theorem of beam loading. 5 Since the plasma in the PWFA is assumed to be cold, one expects that only a single mode, i.e. the oscillation at