# X-ray Free Electron Laser Accelerator Lattice Design Using Laser-Assisted Bunch Compression
## 2 Accelerator Lattice Overview  
The accelerator lattice discussed was located between the exit of the photoinjector and the entrance of the X-ray undulator. The schematic of the accelerator lattice is shown in Figure 1. In this paper, we discuss two sets of accelerator lattice footprint designs, each with a distinct configuration of the first bunch compressor (BC1). The first set of accelerator lattice (referred to as \"lattice 1\", hereafter) used a conventional C-chicane of four bending magnets as its BC1, and the second set (referred to as \"lattice 2\", hereafter) used a double C-chicane as its BC1. The evolution of the Twiss parameters along the beamlines of both lattice 1 and 2 are shown in Figure 2 a and b, respectively. The total length of lattice 1 was 192 m and for lattice 2, 219 m. The greater length of lattice 2 was primarily contributed by the longer double C-chicane in its BC1. In the \(\beta\)-function plots in Figure 2, the \(\beta\)-function values of several intermediate sections reach around 1000 m, and these seemingly enormous values were due to the increase in the transverse beam size with the ultra-low emittance preserved. In all the Elegant simulations, we used a beam file of 29.9 million macroparticles, with a total electron beam charge of 100 pC. Figure 1: Schematic of the proposed MaRIE XFEL accelerator lattice using an LABC scheme for the second stage of the bunch compression. The two different configurations of the first bunch compressor (BC1) are shown. The evolution of the beam properties in lattice 1 using a conventional C-chicane as BC1 is shown at the top, and for lattice 2, which uses a double C-chicane as its BC1, is shown at the bottom. The evolution of the energy modulation, given in the variation of the Lorentz factor, is shown at the exits of BC1, the laser modulator (LM), and the second bunch compressor (BC2), explaining the development of the sequence of the high current spikes to be used for lasing in the X-ray undulator at the end of the lattice. In the figure, the instances of the matching optics (MO) are also shown. The electron beam entered the first section of the linac (L1) at an energy of 153 MeV, with a beam current of 20 A. The L1 comprised two sections: the 5.699 GHz (C-band) accelerator and the 17.098 GHz (Ku-band) linearizer. The combination of the accelerator and the linearizer created an energy chirp in the beam in the longitudinal direction for the bunch compression in the BC1 downstream. The L1 accelerator section performed the off-crest acceleration of the beam to create a longitudinal variation of the beam energy, and the higher harmonic L1 linearizer section finalized the shaping of the chirp. At the exit of the L1, the mean energy of the beam reached 750 MeV. The first bunch compressor compressed the electron bunch with a compression ratio of 25, enhancing the beam current from 20 A to 500 A. As shown in Figure 1, two different configurations of BC1 were investigated. The BC1 design using a conventional C-chicane as in lattice 1 had advantages, such as its intrinsic simplicity and a comparatively short length, but the beam at the bunch compressor exit had a non-trivial and non-uniform horizontal momentum shift along the beam due to the CSR effects. In comparison, the BC1 configuration using a double C-chicane, as in lattice 2, showed merits in outputting a beam with little horizontal momentum shift and a smaller horizontal emittance [37; 38; 39], though the total length of the bunch compressor was greater. After the first stage of the bunch compression, the electron beam was modulated by a laser beam in a laser modulator. The laser modulator applied energy modulation within the beam by coupling to the horizontal motion of the electrons inside the undulator.