Numerical Simulation of an Electron Beam for Magnetic Bunch Compressor Commissioning at PITZ

A THz free electron laser (FEL) prototype has been developed at the Photo Injector Test Facility at DESY in Zeuthen (PITZ) for obtaining high intensity radiation for THz-pump and X-ray-probe experiments at the European XFEL. In this development, a magnetic chicane was recently installed to optimize the THz FEL performance. The aim of this study is to investigate the beam dynamics in the chicane for a trajectory commissioning by tracking the electron beam via ASTRA using a 3-dimensional (3-D) magnetic field of the chicane simulated with CST-EM Studio. The simulated results indicate the possibility to obtain a minimum-momentum dispersion of an electron beam after chicane with the high bunches charge of electron beam transportation.


Introduction
A linear accelerator at the Photo Injector Test Facility at DESY in Zeuthen (PITZ) has been developed as a prototype for generating high-power, tunable THz radiation for THz-pump and X-ray-probe experiments at the European XFEL [1].At PITZ, we aim to produce the THz radiation by using a Self-Amplified Spontaneous Emission (SASE) FEL, seeding FEL and super-radiant undulator radiation techniques.The PITZ linear accelerator can generate and accelerate electron bunches from a photocathode L-band 1.6-cell RF gun to have a small transverse emittance [2] and an average beam momentum of about 6.3 MeV/c.Then, the electron bunches are further accelerated by using the RF electric field from the booster cavity to have the maximum beam momentum of up to 22 MeV/c.A THz beamline has been designed and installed as an extension at the PITZ facility.The recently extended beamline consists of two main devices, including a THz undulator and a magnetic Bunch Compressor (BC) [3].A 3.4 mlong planar LCLS-I permanent undulator magnet (module L143-112000-26 on-loan from SLAC) with a period length (λ u ) of 30 mm has been installed in the second PITZ tunnel [4].Meanwhile, the BC was installed at the end of the PITZ beamline in the first PITZ tunnel.In order to produce the FEL radiation at a central wavelength of 100 µm (3 THz).The electron beam with a momentum of about 17 MeV/c is required for the parameters of the LCLS-I undulator.The Start-to-End simulations based on SASE FEL [5,6] was performed.The simulations suggest a possibility to generate a 100 µm THz pulse with a pulse energy of 0.5 mJ by using an electron bunch with a bunch charge of up to 4 nC (a peak current of 180 A).
In this paper, we describe details of the PITZ BC.Then, we present beam dynamics simulatios for the approach to find the constraints parameters for sending electron beams to have a minimum dispersion after the BC.

PITZ Bunch Compressor
The PITZ BC has been developed to improve the radiation quality during the FEL generation process [7].There are three kinds of invesment techniques to use the BC.Firstly, it can be used to compress an 2-4 nC electron bunch to have a full width at half maximum (FWHM) length longer than >5 ps and to have a peak current of up to 400 A, which is suitable for SASE FEL production [8].Secondly, it can be used to compress an electron bunch with a bunch charges lower than 400 pC to have a bunch length shorter than 1 ps FWHM for a super-radiant radiation [9].Lastly, it can be used to manipulate the longitudinal phase space for getting high radiation energy in the case of seeding FEL production [10].This section presents the geometric specification and the calculated dispersion function along the designed trajectory of the PITZ BC.The PITZ BC, also called a chicane, consists of four dipole magnets.The magnets are the corrector magnets obsoleted from the Hadron-Electron Ring Accelerator (HERA) [11].The first designed of the PITZ chicane was reported in [7].Then, the pole shoes of the magnets were modified to improve uniformities of the magnetic fields.The drawing of the PITZ chicane is shown in figure 1. Simulations using CST-EM studio software [12] were performed in order to provide the identical effective lengths for all dipole magnets .The results show that the positions of the pole plate center of each dipole magnet must be shifted from the z-y axes crossing points (as represent as the red dots in Fig. 1).The shifts of the magnets in (z, y) coordinates in a millimeter unit are as follows: CHICANE.D1 (-4.2, +25), CHICANE.D2 (+4.2, -25), CHICANE.D3 (-4.2, -25), and CHICANE.D4 (+4.2, +25).These shifts deriver an effective length of 327 mm for each dipole magnet [9].The designed parameters including geometric parameters and magnet specifications are listed in table 1.
An electron beam with a momentum deviation, i.e. particles with ∆p/p ̸ = 0, generally travels along the path of the dispersive trajectory.This trajectory is so-called a dispersion function D(s).In our chicane, the electron beam is bent in the vertical direction.Hence, the vertical dispersion along the designed trajectory (s) of our chicane was considered.
As can be seen in figure 2, the dispersion value increases to 0.32 m after the 2 nd dipole magnet, then it is relaxed to zero after passing through the 3 rd and 4 th dipole magnets.In order  to compress and transport a high-charge electron beam (up to 4 nC) with an energy spread of up to 1 % without losing the electron beam, we have to transport the electron beam along the ideal dispersive trajectory.

Beam Dynamics Simulation of BC
The electron beam dynamics simulation throughout the chicane involved finding the constraints parameters of electron beam to transport electrons throughout the chicane and analysing the data in order to find a method that can be used to transport electrons in the experiment.It was performed by using ASTRA [13].A 3-dimensional (3-D) magnetic field distribution (B x , B y , B z ) obtained from CST-EM Studio software was utilized and used in the simulation.As illustrated in figure 1, there are three screens, including HIGH2.SCR2, CHICANE.SCR1, and HIGH2.SCR3 and two beam position monitors (BPM) including, CHICANE.BPM1 and HIGH2.BPM1.Positions of these screens and BPMs were utilized in the simulation in order to optimize the vertical offset positions and the dispersion fuction along the chicane, which can be applied practically in experiments.

Trajectory tracking simulation
A trajectory tracking simulation was performed to scope the range of dipole currents for electron beam transportation.The electron bunch with a mean momentum of 17 MeV/c was represented by nine reference macro-particles in ASTRA simulation.By applying the identical current to all dipole magnets with the 10 mA steps, the dispersion function along the designed trajectory was calculated.The simulation results of beam offsets (left) and dispersions (right) along chicane are plotted in figure 3.This indicates that the zero dispersion after chicane can be achieved when the currents were applied in the range between 1.16 and 1.18 A, while the beam offset positions between 2 nd dipole and 3 rd dipole magnets (the chicane arm) strongly increasing to 17 mm.This suggests that we can't achieve the zero beam offset along the chicane and also the zero dispersion after the chicane (at HIGH2.SCR3) simultaneously.Therefore, we have to set the beam to the positive offset at the chicane arm to reach the minimum dispersion at HIGH2.SCR3.To achieve a compromise between a small dispersion of an electron beam at the HIHG2.SCR3 and a small beam offset at the chicane arm, the applied current for all dipole magnets were tunned and optimized separately with a step of 1 mA.The step size corresponds to the precision of the magnet power supply.The range of the initial current was obtained from the previous study.The constraints considering from the vacuum pipe radius at the chicane arm (NW63CF type: 30 mm) including the beam position offsets at the chicane arm and the dispersions at HIGH2.SCR3 were limitted to 10 mm and 0.02 m, respectively.The simulation results are given in figure 4. The optimum currents of all dipole magnets were found at 1.163, 1.159, 1.163, and 1.163A for D1, D2, D3, and, D4, respectively.These applied currents provide the beam offsets at the chicane arm and the dispersion after the chicane that are smaller than 10 mm and 0.02 m, respectively.These optimum currents were used as initial currents for further bunch compression simulations.zP

Compression case simulation
A relation between R 56 of a bunch compressor and the slope of the longitudinal phase-space (h i ) is C = (1 + h i R 56 ) −1 .In case of a full compression condition C → ∞.Hence, R 56 = − 1/h i .In order to investigate a compression case with the constraints from the previous study, an electron beam dynamics simulation was performed.The 200 pC electron bunch was used, while the booster phase was optimized to match with the full compression condition which is about −20 deg off-crest from a Maximum Mean Momentum Gain (MMMG) phase.This acceleration phase introduces the energy spread of about 0.6 %.The optimized longitudinal phase space is shown in figure 5.It has a positive energy chirp of 4.831 m −1 which is suitable for the calculated R 56 of the chicane.zPP δ p Figure 5. Longitudinal phase-space of an electron-bunch of −20 degrees from MMMG phase where the buch head is at z < 0 and the dash line is the linear fitted.
The compression case simulation was performed by applying the initial dipole currents from the previous study.As can be seen in figure 6, the centroid position offsets (purple color) corresponds to the position offsets from the trajectory tracking in figure 4. The transverse beam size increases after D2 dipole.This phenomena occurs when we transport the 0.6 % energy spread to the dispersive path with a maximum dispersion of 0.36 m.Meanwhile, the electron beam was focused horizontally due to the edge focusing of rectangular dipole magnets.

Conclusion
The magnetic bunch compressor has been installed at the PITZ facility to compress electronbunch to have a peak current up to 400 A for 1.5-2.5 nC bunch charge for enhancement of the radiation energy from the THz FEL production.The calculated dispersion at the chicane arm is equal to 0.32 m.To transport a 17 MeV/c electron beam passing through the chicane, the numerical electron beam simulation throughout the chicane was implemented.The trajectory simulation results given the optimum dispersion at the center between CHICANE.D2 and CHICANE.D3 of 0.37 m.It suggests that it is possible to achieve the minimum dispersion after the chicane with a value of 0.02 m, while the maximum beam offset at the chicane arm is lower than 10 mm.Electron beam dynamics simulation by using the 200 pC with 0.6 % of energy spread and −20 deg off-crest MMMG phase represent the rms transverse beam size of electron-bunch at the chicane arm increasing with a factor of 4. In case of high charge e.g., 2.5 nC transportation, the space charge has an affect to the transverse beam sizes of an electron bunch in the dispersive arm (between CHICANE.D2 and CHICANE.D3).It became lager when the charge is increasing.However, the centroid of the electron beam remains the same as the low charge and the dispersions along the chicane have been calculated by using the centroid position of an electron bunch.Therefore, it is possible to use low charge (200 pC) to find the best path (zero-dispersion after chicane) for beam transportation throughout the chicane.By using the constraints as mentioned earlier, there is space between the dispersive path and the inner pipe of about 20 mm which is enough to transport the electron beam with a high charge of up to 2.5 nC to the chicane.The results of this study are used as a guidline for the developement of trajectory tool to transport electron beam throughout the chicane in the experiment at PITZ.

Figure 1 .
Figure1.The two-dimensional (2D) drawing (up to scale) of the PITZ chicane and its dimensions, the red dots represent the axis-crossing of vacuum pipe.

Figure 2 .
Figure 2. A calculated dispersion function along the designed trajectory of PITZ BC.

Figure 3 .
Figure 3.A simulation results of the offset positions from the center of vacuum tube (left) and a normalize dispersion function (right) along the chicane section.

Figure 4 .
Figure 4.The offset positions and the dispersions for optimum applied electron current along the chicane.

Figure 6 .
Figure 6.Centroid positions offset from the center pipe in the vertical direction and rms beam size of the electron beam along chicane.