Measuring the Electron Beam Energy in a Magnetic Bunch ... - DESY

at the exit of the chicane earlier than the low-energy electrons. If the electron bunch is
given a longitudinal energy dependence (chirp) by accelerating it off of the crest of the
RF wave in the cavity, the electrons in the head of the bunch gain less energy than the
electrons in the tail of the bunch (Fig. 2.3.1). The energy dependent path through the
bunch compressor will make the head arrive later and the tail arrive earlier, thereby
shortening the bunch.
E
Figure 2.3.1 The phase of the accelerating RF relative to the beam determines the
energy chirp of the beam. Here, the head gains less energy than the tail of
the bunch.
Due to the curvature of the RF wave, the bunch acquires a non-linear energy
chirp. When a bunch with a non-linear energy chirp travels through the chicane, it is
compressed inhomogeneously, resulting in a sharp, leading spike with a high charge
density followed by a long trailing tail. An RF module operating at the third-harmonic of
the 1.3 GHz accelerator frequency will remove the non-linearity of the energy chirp and
enable homogeneous compression of the bunch.
In Fig. 2.3.2, plots of the beam distribution for non-linear compression in the first
chicane of FLASH were generated by a particle tracking simulation which used a particle
distribution from the gun which was generated with ASTRA together with transport
matrices for the first accelerator section and for the bunch compressor. The evolution of
the transverse distribution is poorly described by this simulation because the lattice is
designed for a space-charge-limited beam and space charge effects were not taken into
account after the gun. This results in a simulated transverse beam size which is much
larger than it would be in reality. The plots, however, serve to demonstrate the
gymnastics of longitudinal bunch compression.
In the first pair of plots in Fig. 2.3.2, the energy chirp is shown on the right and
the particle distribution in the horizontal and longitudinal planes is shown on the left. The
beam is spread out over ~7 mm of longitudinal space and it has a longitudinal energy
chirp which is curved due to the curvature of the accelerating RF. In the second pair of
plots, the higher energy particles have begun to overtake the lower energy particles and
the bunch has become shorter longitudinally and wider in the horizontal plane of the
bunch compressor. The slice emittance increase in the tail of the bunch is due to a
mismatched lattice; if a quadrupole strength is changed slightly, the emittance increase
appears in the head of the bunch and not the tail. This is partially an artifact of the
particular simulation used. Space-charge forces were only used up to the exit of the RF
gun, but they too significant to ignore in the first four modules of the accelerator section,
and this creates a mismatched result in the simulation. With proper matching, the slice
emittance of the beam will be smaller and the beam will look like a curved strip in the
second pair of plots. In the last pair of plots, the horizontal position spread has returned to
the value it had before entering the compressor and the bunch has been compressed into a
10