Beam loading compensation for acceleration of multi-bunch electron beam train

The laser undulator compact X-ray source (LUCX) is a test bench used with the compact, high-brightness X-ray generator at KEK (High Energy Accelerator Research Organization). Our group is conducting experiments with LUCX to demonstrate the possibility of K-edge digital subtraction angiography, based on Compton scattering. One of the challenging problems is to generate high-brightness multi-bunch electron beams to compensate for the energy difference arising from the beam loading effect. In this paper we calculate the transient beam loading voltage and energy gain from the RF field in the gun and accelerating tube for a multi-bunch train. To do so we consider the process by which the RF field builds up in the gun and accelerating tube, and the special shape of the RF pulse. We generate and accelerate 100 bunches with a 50 nC electron bunch train, effectively compensating for the beam loading effect by adjusting the injection timing. Using a beam position monitor (BPM) and optical transition radiation (OTR) system, we measure the electron beam energy bunch by bunch. The average energy of a 100-bunch train is 40.5 MeV and the maximum energy difference from bunch to bunch is 0.26 MeV.