Design, fabrication and cold-test of an X-band accelerating structure for linearizer

X-band high gradient accelerating technology is a challenging and important technology in advanced electron linear accelerator facilities. The X-band accelerating structure can provide harmonic compensation to eliminate non-linear energy spread and realize linear compression of bunch in linac. In this paper, a special X-band traveling-wave accelerating structure is designed for linearizer, with accelerating gradient of 20 MV/m under the input power below 5 MW according to the requirement of Dalian Coherent Light Source. The fabrication and cold-test of the structure are successfully completed and the transmission efficiency of power is about 0.38.


Introduction
The X-band accelerating structure can achieve much higher gradient of 120 MV/m than that of S-band and C-band, which is researched by many institutes, meet the requirement of the development of the high energy physics.The X-band accelerating structure is also applied to the X-ray free electron laser (FEL) facilities, used to compensate the non-linear effects from S-band structure in linac [1].The final bunch compression and self-amplified spontaneous emission are extremely limited by non-linear effects which lead to unwanted sharp temporal spikes by coherent synchrotron radiation.Higher harmonic compensation is a valid method to maintain the initial temporal bunch profile and avoid unnecessary amplification of undesired collective effects, which has been proposed at Boeing, DESY, SLAC and SXFEL [1][2][3][4].The necessary harmonic voltage Vx is expressed in theory, where initial energy Ei, initial rms length σz0, final energy E0, final length σz, RF wavelength λs and λx of S-band and X-band, the chicane momentum compaction coefficients R56 and T566.
The group of Shanghai Synchrotron Radiation Facility has developed a set of X-band linearizer in 2017 and it has been working well during the period above four years.Owing to the success of X-band linearizer in SXFEL, the Dalian Institute of Chemical Physics en-trusts Shanghai Synchrotron Radiation Facility to develop an X-band structure for Dalian Coherent Light Source, to realize energy nonlinear compensation.The designed X-band traveling-wave accelerating structure meets the requirement of radio frequency breakdown and energy gain with the input power below 5 MW.

RF design
The X-band accelerating structure is a constant gradient structure, which the energy gain is about 10 MeV below 5 MW of input power and the length of whole structure is below 0.7 m.The designed method of regular cavities adopt the structural optimization by polynomial fitting, with the maximum electric field strength Emax less than 245 MV/m and the new modified Poynting vector Sc below 4.2 MW/mm 2 under consideration for the cavity breakdown rate [5].Compared with the shunt impedance Ra and phase stability, 4π/5 mode is deter-mined to be the more effective and suitable operating mode for high gradient X-band technology.Thus, the cell period length is 10.497 mm, the regular cell number of whole structure is 49, and the gradient is about 20 MV/m.Due to suppressing the multi-pole field components, dual-feed racetrack couplers are adopted to ensure good beam quality.The layout of the whole structure is shown in figure 1(a), including 49 regular cells and two magnetically coupled cavities.Through a series of optimization simulations, the final average iris aperture is about 3.5 mm, the shunt impedance range is 93.8 -115.4MΩ/m, the group velocity range is 2.48% -1.15% of the speed of light, and the filling time is 99 ns.When the gradient is 20 MV/m, the required input power is about 3.7 MW.The electric field distribution on the axial direction is shown in figure 1(b), and the flatness of the field is less than 2%.The figure 1(c) shows the input reflection parameter of the whole structure, and S11 is -41.8 dB at the operating frequency of 11424 MHZ.

Machining and brazing
After the parametric design of the whole structure has been completed, the next step in X-band manufacture is machining, which is mainly divided into conventional cavity processing and coupler processing.The total length of whole structure is 0.66 m.The regular cavities adopt the traditional method of bowl-shaped processing, shown in figure 2(a), which is roughed and reserved for 20 wires, and then milled to the corrected size at one time by using a precision numerically controlled production centre.For different lathes and gem knives, there is a certain error in the bearing, so it is necessary to process several sample cavities to measure before and correct the simulated parameters to obtain the real processing size.The machining accuracy of the CNC is about 5um, so the frequency consistency of the processing is within 6 MHz, which can be corrected by turning the whole structure.The processing way of coupler adopts cover plate and box, shown in figure 2(b), which is processed by integrated molding, including standard waveguide, 3dB power divider and coupling cavity, to ensure the symmetry of the dual-feed coupler.
The welding adopts the form of segment brazed and check the leak rate each time to ensure the high quality of brazing.After the total welding is completed, the leakage is detected less than 10 -10 torr•L/s, which satisfies the requirements of vacuum sealing.

Low-power measurement
The measurement is made throughout the machining and brazing process.In the manufacture, the accelerating structure is subjected to pre-weld measurement, segmental post-weld measurement, coupler pre-weld and post-weld measurement, and the whole pipe splicing measurement and postweld tuning.The measured frequency range of conventional cavities is 11418 -11421 MHz, and the coupling coefficient of couplers are 0.8 and 0.85 respectively.The minimum of S11 parameter can reach -32 dB nearing operating frequency, which refers to the frequency when it is in a vacuum environment and works at a special constant temperature.Considering environmental factors in lowpower microwave measurements, frequency should be corrected from that of operating to measurement platform.It mainly includes two items of pressure and temperature [6].The figure 3(a) gives the measurement platform, consist of test accelerating structure, Labview software, stepper motor, network analyzer, computer and other accessory equipment.The tuning environment is exposed to the atmospheric environment.According to temperature and humidity of room, the corrected frequency is 11424.44MHz.
In the tuning process, the S-parameter and standing wave ratio (SWR) of the whole accelerating structure are measured by vector network analyzer and the electric field distribution is obtained by the bead-pull method, which is a non-resonant perturbation way to revise the frequency of each cell one by one and a non-contact method to reduce friction damage in inner wall [7].The couplers should be adjusted carefully to minimize the reflection from the output and the global S-parameter by tuning the coupling cell and its adjacent cell.The final S11 parameter is shown in figure 3(b).At the corrected frequency of room temperature, S11 is -34.8 dB, corresponding to SWR about 1.05.The bandwidth of less than 1.2 is beyond 4 MHz in input coupler.
Under the condition of the marched input coupler and output coupler, the longitudinal electric field distribution on beam axial line is present in figure 4(a).From shown in the figure 4 (b), the range of phase shift error is about -1.93º -1.87º .The accumulated error of phase advance is 0.69º which is also meet the requirement of less than 2 degree.The S21 value is -4.18 dB at the corrected frequency when it is subtracted the interference from coaxial wave-guide converters, corresponding to the transmission efficiency of power about 0.38.The decay constant of RF power is 0.481 and the filling time is about 105 ns.The final required input power is about 3.9 MW with the accelerating gradient of 20 MV/m, and the effective energy gain is 10.5 MeV.The key results of the X-band traveling-wave accelerating structure are satisfied of design goals, listed in table 1.The accelerating structure maintains very good vacuum tightness after tuning with the leakage rate smaller than 10 -11 torr•L/s.Meanwhile the straightness error of the whole structure is within 0.1 mm.

Conclusion
The X-band traveling wave accelerating structure completes the whole process from design, machining, brazing and tuning.The length of the tested accelerating structure is 0.66 m, and the input power is about 3.7 MW when the energy gain is 10 MeV.Recently the accelerating structure has been shipped to Dalian Coherent Light Source for high-power experiments and beam experiments.

Acknowledgements
Authors are grateful to the help and support of collimation team of Shanghai Synchrotron Radiation Facility, group of Shanghai Accelerator Magnet Co., Ltd., and Dalian Institute of Chemical Physics during the research.Works was supported by the National Natural Science Foundation of China (No. 11975298) and the Alliance of International Science Organizations (No. ANSO-CR-KP-2020-16).

Figure 1 .
Figure 1.The designed X-band structure results: (a) Layout of 3D model diagram, (b) The longitudinal electric field distribution Ez on axial, (c) The S11 distribution.

Figure 2 .
Figure 2. The processing drawings of (a) regular cell and (b) box of coupler.

Figure 3 .
Figure 3.The diagram of (a) measurement platform and (b) S11 distribution.

Figure 4 .
Figure 4.The measured results of the whole structure: (a) The longitudinal electric field distribution, (b) The error of phase shift for each cell.
[1] Emma P 2001 X-band RF harmonic compensation for linear bunch compression in the LCLS Office of Scientific and Technical Information LCLS-TN-01-1 [2] Dowell D H et al 1995 Magnetic pulse compression using a third harmonic RF linearizer Proc. of the 1995 Particle Accelerator Conference pp 992-4 [3] Flottmann K et al 2001 The TESLA X-FEL injector Proc. of the 2001 Particle Accelerator Conference pp 2236-8 [4] Zhao Z T et al 2017 Status of the SXFEL facility APPL SCI-BASEL 7 6 p 607 [5] Huang X X et al 2017 Design of an X-band accelerating structure using a newly developed structural optimization procedure Nucl.Instrum.Meth.A 854 pp 45-52 [6] Zhang Y et al 2021 Radio frequency conditioning of an S-band accelerating structure prototype for compact proton therapy facility Nucl.Sci.Tech.32 64 [7] Fang W C et al 2013 The nonresonant perturbation theory based field measure-ment and tuning of a linac accelerating structure Science China Physics Mechanics and Astronomy 56 pp 2104-9

Table 1 .
Main parameters of the accelerating structure.