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Design of RF chopper system for improving beam quality in FEL injector with thermionic gun
Nuclear Instruments and Methods in Physics Research A ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Design of RF chopper system for improving beam quality in FEL injector with thermionic gun$ Q. Chen a, B. Qin a,n, P. Tan a, T. Hu a, Y. Pei b, F. Zhang b a State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China b National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, China
art ic l e i nf o
a b s t r a c t
Article history: Received 21 March 2014 Received in revised form 11 April 2014 Accepted 17 April 2014
For a linac-based Free Electron Laser (FEL), good beam quality largely contributes to the success of the final radiation. An imperfection confronted with the HUST THz-FEL facility is the long beam tail that emerges in the electron gun and exists through the whole beam line. This paper proposes to deploy a chopper system after the electron gun to truncate the beam tails before they enter into the linac. Physical dimensions of the chopper cavity are discussed in detail and we have developed and derived new analytical expressions applying to all frequencies for the optimal design. Also, technical issues of the cavity are considered. Beam dynamic simulation is performed to examine the truncation effect and the results show that more than 78% of the beam tail can be removed effectively, while preserving the emittance and energy spread in acceptable level. & 2014 Published by Elsevier B.V.
Keywords: RF chopper High intensive beams FEL Linac
1. Introduction As free electron laser (FEL) is the most prominent candidate for producing high average power and continuously tunable terahertz radiation, a linac-based THz-FEL facility has been planned to be built in Huazhong University of Science and Technology (HUST). Preliminary design of the whole system is finished and engineering parameters of some key components have been obtained [1–3]. The HUST FEL facility mainly consists of an independently tunable cell (ITC) RF gun, a normal temperature S-band linac, a planar undulator and an optical cavity. The FEL injector includes the ITC-RF gun and the S-band linac, both of which are designed to operate at 2856 MHz. For successful operation, the injector must provide the oscillator with high quality beams delivered by the transport line. Beam requirements at the exit of the injector are listed in Table 1. A common drawback of a thermal RF gun is its imperfect performance in longitudinal bunching. According to the analysis in Ref. [4], with present scheme the linac would undergo undesirably intensive beam current, which might result in difficulties or failure in low energy operation. This is due to the compromise between
☆ This work was supported by National Natural Science Foundation of China (11375068), and 2011 project – Hubei collaborative Innovation Center of Nonpower Nuclear Technology. n Corresponding author. Tel.: þ 86 27 87557634. E-mail addresses: [email protected] (B. Qin), [email protected] (Y. Pei).
performance and compactness demanded of the electron gun. The charge of one micro-bunch accelerated by the linac is around 500 pC while the useful portion for radiation, about 15 ps in the head, is only 200 pC. The major portion, located in the tail, will increase the feeded RF power due to beam loading effect, and may cause radiation in the waveguide of the optical cavity. A simple and economical solution is to fix a slit after the first bend magnet, because particles with different energies will follow different trajectories. Then by reasonably designing the transverse position and width of the slit, it is possible to cut off the tail portion of one bunch. However, the solution just eliminates the risk in the waveguide while doing nothing for the linac. In low energy operation, e.g. 6 MeV, the undesirably intensive beams will drain out RF power before they come to the end of the linac. If this is the case, the beams will induce electromagnetic field (wake field) in the vacant power accelerating cells and the energy spread of latter coming bunches will largely increase [5]. So, it is very meaningful to develop a chopper system located before the linac to select only the head portion without changing the initial injector layout much. An attractive proposal, on which our work is based, suggests replacing the short lens with a chopper cavity as shown in Fig. 1, for the self-bunching effect of electrons generated by the ITC-RF gun indicates dispensability in short lens usage. In the rest context, we will refer the initial structure as Scheme 1 and the new structure as Scheme 2. A chopper is usually a magnetic deflector, which can be used for measurement of beam dose [6] and suppression or selection of
http://dx.doi.org/10.1016/j.nima.2014.04.048 0168-9002/& 2014 Published by Elsevier B.V.
Please cite this article as: Q. Chen, et al., Nuclear Instruments & Methods in Physics Research A (2014), http://dx.doi.org/10.1016/j. nima.2014.04.048i
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charged particle beams [7–10]. In Ref. [11], Haimson developed systematic and detailed optimization methods for designing chopper cavities and some specific designs have been reported [12–15]. Recently choppers have found extensive applications in proton linacs, which need choppers to produce precise gaps in bunched linac beams [16–18]. In our project, the chopper is utilized to generate pulses with predefined width, cutting off the tail portion after the electron gun and improving power efficiency in the linac. Nevertheless, the input beams of the chopper are not continuous as the previous cases, which makes it possible to develop some new characteristics of the chopper cavity. For example, in our design the chopper cavity shares power source with the gun and the linac. Besides, the centroid particle will undergo zero deflection force and no extra bias field is required, so the whole structure will be compact.
2.1. Theory and model We choose rectangular resonator as the chopper cavity and the preferable resonant mode is TM120 or TE102, both of which can offer symmetrical magnetic field gradient and the field components of the two modes are exactly the same except for a negative sign caused by the rotation of reference axis. Fig. 3 illustrates the chopper model adopted in the following analysis. The target of
2. Optimization of RF chopper for pulsed electron beams In heavy ion cases, it is popular to use electrostatic fields to create gaps between beam pulses. In order to make the whole system compact and the timing scheme easy to operate, we prefer a RF chopper cavity excited by the same power source of the gun and the linac. The RF chopper system is mainly composed of a resonator and a beam scraper (Fig. 1). Electrons in a micro-bunch will get transverse deflection determined by their longitudinal position and energy when traveling through the resonator and then the tail portion will be retarded by the scraper after drifting some distance. Fig. 2 shows the electron density distribution in longitudinal phase plane at the exit of the ITC-RF gun, explicitly verifying the long beam tail.
Fig. 2. Electron density distribution in longitudinal phase plane at the exit of the RF gun (18,000 macro particles involved).
Table 1 Beam requirements at the exit of the injector. Beam energy Energy spread (FWHM) Normalized emittance (RMS) Micro-pulse charge Micro-pulse length (FWHM) Micro-pulse repetition rate Macro-pulse length Macro-pulse repetition rate
6–14 MeV o 0:3% o 15 μm rad 4 200 pC 5–10 ps 2856 MHz 4–6 μs 10–50 pps Fig. 3. Model of the chopper system.
ITC-RF gun Resonator Alternative design with the lens removed
Lens
Scraper
TW accelerator & Solenoid
Initial design
Fig. 1. Layout of the initial and alternative design of the injector. The resonator and the lens may share some longitudinal space as the latter one is removed in the alternative design, while for clear illustration they are separated from each other.
Please cite this article as: Q. Chen, et al., Nuclear Instruments & Methods in Physics Research A (2014), http://dx.doi.org/10.1016/j. nima.2014.04.048i
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optimization is to construct a chopper cavity providing maximum deflection efficiency with an acceptable Q value and a minimized size. More issues on Q will be addressed latter and now physical dimensions are pursued. In rectangular coordinates, the field components of TM120 mode can be expressed as [19] π 2π y Ez ¼ E0 sin x sin a b π ωϵ 2π 2π Hx ¼ j 2 E0 sin x cos y a b Kc b π ωϵπ 2π E0 cos x sin y ð1Þ Hy ¼ j 2 a b Kc a
which makes it rational to inject the reference particle at the right angle to the RF magnetic field (undergo zero deflection) and no need for the solenoid. In the paraxial area, Hx deflects electrons in the y-direction and it is reasonable to neglect the change in electron energy or velocity. Then the transverse velocity of one particle at the exit of the cavity is Z h=v0 eμ0 v0 H mx vy ¼ sin ðωt þ ϕ0 Þ dt m0 γ 0 0 2eμ0 v0 H mx ωh ωh sin ð7Þ sin þ ϕ0 ¼ 2v0 2v0 ωm0 γ 0
where “a”, “b” and “h” are the dimensions in x, y and z direction respectively, E0 is the reference magnitude of Ez, Kc is the cut off wave number and in TM120 mode we have K c ¼ k ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðπ=aÞ2 þ ð2π=bÞ2 . The resonant frequency is calculated as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 c π 2 2π f¼ þ ð2Þ 2π a b
where v0 is the injection velocity, e and m0 are the charge and the mass of an electron respectively, μ0 is the permeability of free space and γ0 is the relativity factor corresponding to v0. After drifting a distance of L, the transverse displacement is
where c is the velocity of light in free space. The time-averaged energy density corresponding to the three field components is 1 2 π 2 2π x sin y ωEz ¼ ϵE20 sin 4 a b 1 ϵ 2π 2 2 2π 2 π x cos 2 y ωH x ¼ 2 E0 sin 4k b a b 1 ϵ π 2 2 2 2π 2 π ωH y ¼ 2 x sin y ð3Þ E0 cos 4k a a b So energy stored in the resonator with an electrical reference magnitude of E0 is Z hZ bZ a 1 U¼ ðωEz þ ωHx þ ωHy Þ dx dy dz ¼ ϵVE20 ð4Þ 8 0 0 0 where V is the volume of the resonator and V ¼ abh. For specific wall loss power PL, the field strength is determined according to rffiffiffiffiffiffiffiffiffiffiffi 8QP L E0 ¼ ð5Þ ωϵV On the centerline of the cavity, which is also the beam line, the only remained field component is rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffi 4π 2ωϵP L Q 1 sin ðωt þ ϕ0 Þ ð6Þ H x ¼ H mx sin ðωt þ ϕ0 Þ ¼ 2 3 h k ab where ϕ0 is the injection angle of one particle. Then we can optimize the resonator dimension to achieve maximum deflection force. From Eq. (2), it is obvious that the resonant frequency is only dependent on “a” and “b”, leaving the longitudinal dimension “h” to be determined otherwise. 2.2. Optimization methods 2.2.1. Dynamic calculation and optimization of “h” The optimization criteria of “h” can be revealed by analyzing the beam deflection in the cavity, with the aim of obtaining maximum deflection sensitivity. Many previous works have proposed a scheme called the “peak operation”, in which the reference particle injects the cavity at the peak of one RF circle and the cavity is immersed in a solenoid magnetic field offering fixed transverse bias to compensate unwanted deflection force [13,20]. For continuous beams, i.e. beams occupy a whole RF circle, the “peak operation” is necessary, otherwise the pulse repetition rate would be doubled. However, in the HUST FEL injector, Scheme 2 will deploy the chopper cavity after the buncher of ITC-RF gun and its input pulse length is less than a half RF cycle,
Δy ¼ L tan θ
ð8Þ
where θ is the deflection angle and is defined as tan θ ¼ vy =v0 . So, for electrons in a micro-pulse, longitudinal position determines ϕ0 that one particle experiences and then the transverse velocity and displacement of it. To gain maximum deflection efficiency, it comes to optimize “h” to maximize the magnitude of vy (item in the bracket of Eq. (7)). The optimization criteria reported in this paper are slightly different from that of Ref. [20] and a more reasonable result is obtained. According to (Eqs. (6) and 7), for a given particle energy and any specified “a” and “b”, we have rffiffiffi 1 ωh jvy jp sin ð9Þ h 2v0 where jvy j is the magnitude of vy. After some mathematical processing, the optimum value of “h” is subjected to the following transcendental equation: ωh ω 1 ¼ ð10Þ h tan 2v0 v0 With a reference particle energy of 2.6 MeV for example, the optimal value of “h” is found to be 38.42 mm while Ref. [20] would give a value of 51.79 mm. An interesting phenomenon is that the energy of electrons in the tail portion is lower, which makes them get larger deflection and so the sensitivity is enhanced further. Fig. 4 shows the transverse displacement of an electron bunch at 6 Ke=1.4MeV Ke=1.7MeV Ke=2.0MeV Ke=2.3MeV Ke=2.6MeV
5
Displacement at the scraper/mm
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3
4
3
2
1
0 0
20
40
60
80
100
Longitudinal position/degree Fig. 4. Transverse displacement of one bunch at the scraper versus longitudinal position (5 cases involved).
Please cite this article as: Q. Chen, et al., Nuclear Instruments & Methods in Physics Research A (2014), http://dx.doi.org/10.1016/j. nima.2014.04.048i
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the scraper after a drift distance of 100 mm, assuming that the energy of particles in one bunch is the same and Hmx has been normalized to a feasible value of 104 A/m. 2.2.2. Optimization of “a” and “b” From the knowledge in linear algebra, the determination of “a” and “b” needs two criteria coming from the resonant frequency and the deflection efficiency. The former criterion has been illustrated in Eq. (2) and we will mostly focus on the latter one. When the resonator is in steady state operation, the coupled power will be exactly equal to the wall loss required to establish a given electrical field strength. Then Eq. (6) points out the optimization criteria for “a” and “b”. It should be emphasized that the Q value is mainly controlled by the microwave absorbing material coated on the inner wall of the resonator, leaving the optimization 3 of “a ” and “b” subjected to minimizing the value of “a b ” under the constraint of Eq. (2). Eq. (11) gives the analytical expression of “a” and “b” and Fig. 5 confirms the result: 8 < a ¼ λ pffiffiffi 2 3 ð11Þ :b¼ λ 3 where λ is the wavelength corresponding to the resonant frequency. So, theoretically an efficient rectangular chopper working in TM120 mode of 2856 MHz should have transverse dimension of
“105 mm 121 mm”, ignoring the essential correction caused by the coating of absorbing material and the coupler slit. Now the optimal dimensions of the rectangular chopper cavity have been obtained and (Eqs. (10) and 11) apply to any frequency operated in TM120 mode. 2.3. Consideration of Q-value Q value is most important for bringing the resonator into practice. A high Q value requires highly stable frequency and temperature control systems, as well as insupportably long excitation time. According to Ref. [11], the transient field of a circuit follows EðtÞ ¼ Ef ð1 e ωt=2Q L Þ
t exc ¼
6
180
5.5
170
5
160
4.5
150
4
140
3.5
130
3
120
For a coppery resonator with the optimal dimension, eigenmode computation shows a Q-value of 18,600 and the corresponding excitation time is 2.4 μs, much larger than that of the linac. So a reasonable design should make the excitation time less than
3
change in emittance change in energy spread change in scraper efficiency
3
2.5
2.5
b versus a a*b versus a
2
1.5
2
110 100
ð13Þ
Ratio
190
2Q L ln 10 ω
3.5
a*b3
200
x 10 6.5
ð12Þ
where Ef is the steady state field, QL is the loaded Q-value and is equal to Q 0 =2 in load matched case. If we define the excitation time as the time needed to build up 90% level of the steady state field, we can get
8
b/mm
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0
100
200
300
400
500
1.5 600
a/mm Fig. 5. Optimization result of “a” and “b”. The solid line indicates the (a,b) pairs satisfying the resonant frequency; the dash line indicates the reciprocal of the deflection efficiency versus “a”.
1 0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Input power/MW Fig. 7. Influence on the beam quality of the head portion at different input powers. All data are normalized to that of Scheme 1.
Fig. 6. Snapshot of beam profile at the scraper.
Please cite this article as: Q. Chen, et al., Nuclear Instruments & Methods in Physics Research A (2014), http://dx.doi.org/10.1016/j. nima.2014.04.048i
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0.3 μs, indicating the Q-value less than 2340. A popular method to achieve this is coating the inner wall with high resistance material [21–23]. For our group has extensive experience in the use of FeSiAl, this kind of alloy is adopted as the absorbing material to control the Q value. The relative electromagnetic parameters of the FeSiAl alloy used in our project have been measured as ϵ ¼ 13:23 0:25i and μ ¼ 1:77 1:41i at 2856 MHz. Simulation results show that the Table 2 Parameters of the chopper system. Resonant frequency Resonator dimension (x; y; z) Unloaded quality factor Excitation time Input power Drift length Scraper dimension (x; y) Maximum deflection voltage
2856 MHz 105 mm 121.2 mm 38.4 mm 2000 0.25 μs 0.2 MW 100 mm 4 mm 3.6 mm 0.12 MV
5
volume of the coated material has linear relationship with the frequency error, which can be corrected by modifying the transverse dimension. To get the desired Q value of 2000, the volume of the coated material should be 35 mm3 and the corresponding frequency error can be compensated if “b” decreased by 16 μm.
3. Beam dynamic simulation and analysis To checkout the effect of the chopper system on electron beams, beam dynamic simulation is carried out from the exit of the ITC-RF gun down to the entrance of the lianc. The initial distribution of electrons comes from the output file related to the simulation of the ITC-RF gun. The bunch charge and the bunch length at the entrance of the linac between the two schemes are the key points to judge the new design system. Parmela code [24] is used to complete the beam dynamic simulation. And following the optimized dimensions discussed in the previous section, the cavity model is constructed with the help
Fig. 8. Evolution of phase spectrum, energy spectrum and transverse profile of the electron beam in Scheme 2: (left: A) z¼ 0 (exit of the gun); (middle: B) z ¼ 20.8 cm (just before the scraper); (right: C) z ¼ 31.7 cm (entrance of the linac).
Please cite this article as: Q. Chen, et al., Nuclear Instruments & Methods in Physics Research A (2014), http://dx.doi.org/10.1016/j. nima.2014.04.048i
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beam profile, the scraper is set to have a size of “4 mmðxÞ 3:6 mmðyÞ” and with a 0.8 mm offset in the positive y-direction. Snapshot of beam profile at the scraper clearly illustrates this decision (Fig. 6). Now all the intrinsic parameters of the chopper system have been settled. To evaluate the performance, a new assessment index, scrape efficiency, is proposed and defined as the ratio of the scraped particle number of Scheme 2 to that of Scheme 1 (assume that the scraper is also included in Scheme 1 for justice). Apart from the scrape efficiency, it is also required to minimize the chopper deterioration of the quality of the head portion. So emittance and energy spread of the head portion at the entrance of the linac are compared between the two schemes in different input power cases (Fig. 7). For vivid contrast, all data are normalized to that of Scheme 1. The results in Fig. 7 show that while variation of the input power does not affect energy spread, it obviously has great influence on the emittance. Larger input power will get more useless particles removed, manifested by the black line in Fig. 7, but will also result in worse emittance, which indicates that compromise must be made between the two indices. To allow for acceptable emittance increase in the linac, the input power is set to be 0.2 MW. Table 2 displays the final design parameters of the chopper system. Based on the optimized parameters, it is found that 78.2% of the tail portion is removed, at the same time the bunch length reduces from 100 ps to 30 ps and the bunch charge reduces from 525 pC to 282 pC. Snaps of the simulation results shown in Fig. 8 demonstrate the evolution of beam status and beam qualities under the two schemes are listed in Table 3. With the chopped beams, post-calculation shows that the beam load current in the linac is reduced from 1.05 A to 0.79 A and input power of 13 MW is enough to achieve beam energy of 14 MeV while in Scheme 1 the input power should be 16.5 MW. For further comparison, phase space at the exit of the linac under the two schemes (Fig. 9) confirms that the chopper system has effectively removed the tail portion which is also the low energy
of CST to calculate the resonant field. After rearranging and normalizing the data file produced by CST, Parmela code can utilize it to track every macro particle's state at each user defined time step. More consideration should be taken on the injection phase at the entrance of the chopper cavity. Eq. (7) and Fig. 4 have demonstrated the relationship between the injection phase and the transverse displacement at the scraper, implying that the reference particle should undergo zero deflection. With this constraint, the phase setting of the CELL line in Parmela code should satisfy ϕ¼
ωh π Φ 2v0 2
ð14Þ
where Φ is the master clock phase at which the reference particle arrives at the chopper cavity and the π=2 is induced by the phase difference between E-field and H-field. Before launching the simulation, it is still required to figure out the dimension and the transverse position of the scraper, which should not retard the head portion but remove the tail portion efficiently. After a lot of trial and error involving statistical analysis of
Table 3 Beam qualities of the head portion at the entrance of the linac. Scheme 1
Scheme 2
Reference energy (MeV) Energy spread (FWHM) (%) Norm. emittance (x) (μm rad) Norm. emittance (y) (μm rad) Charge (pC)
2.6 0.67 8.319 8.633 210
2.6 0.69 8.326 13.385 210
Bunch lengtha (ps) Bunch chargea (pC)
100 525
30 282
a Refer to qualities of a whole bunch, and bunch length is defined as the width during which more than 95% particles are contained.
Number of particles
Phase spctrum 600
600
500
500
400
400
300
300
200
200
100
100
0 −20
0
20
40
60
0 −20
0
20
40
60
Phase/degree
Phase/degree Energy spectrum Number of particles
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Q3 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66
3000
3000
2000
2000
1000
1000
0 13
13.5
Energy/MeV
14
0 13
13.5
14
Energy/MeV
Fig. 9. Phase spectrum and energy spectrum at the exit of the linac under (left: A) Scheme 1 and (right: B) Scheme 2.
Please cite this article as: Q. Chen, et al., Nuclear Instruments & Methods in Physics Research A (2014), http://dx.doi.org/10.1016/j. nima.2014.04.048i
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portion, while scarcely deteriorating the longitudinal phase space of the head portion.
7
system will not change the longitudinal dimension of the whole facility but exhibits good performance, indicating that the proposal is a promising alternative for future upgrade.
4. Discussion and conclusion The major issue of the beam tails is that it will increase the feed-in RF power significantly due to the beam loading effect, furthermore it might bring instability of the FEL injector. For this consideration in HUST FEL injector, a RF chopper system, which consists of a resonator and a scraper, is proposed to remove the useless portion of the bunched beam before the linac. Originated from the microwave theory, the resonant field is analyzed and the physical dimensions are optimized accordingly to make the resonator get maximum deflection efficiency. One important result is that we developed and derived new analytical expressions applying to all frequency for the optimal design. For practical consideration, magnetic loss material FeSiAl is coated on the inner wall of the resonator to lower the Q value and shorten the excitation time. In the simulation part, scrape efficiency, emittance variation and energy spread variation are selected to assess the performance of the chopper system. It is found that only the former two indices are sensitive to the resonator field and compromise must be made to get relatively high scrape efficiency and acceptable emittance. So, the input power is finally set to be 0.2 MW. Simulation results show that more than 78% of the tail portion is scraped and the corresponding emittance and energy spread are 13.385 μm rad (y direction) and 0.69%, implying very good performance. With the scraped electron bunches, it is certain that the beam loading effect in the linac will be largely relieved. As a result, the power efficiency is enhanced and the success of low energy operation is guaranteed. To be noted, the longitudinal beam profile is only shown through the injector. Since the chopper only removes beam tails located at the lower energy region, the same beam head is contained compared to the original scheme, even after the transport line including the double bend achromat (DBA). So the contribution on FEL gain of two schemes will maintain at the same level. In further works, start-to-end simulation on beam dynamics, and the study on the FEL gain with/without beam tails are expected to evaluate more realistic beam tail effect. Now the HUST FEL facility is under construction and the overall layout has been settled. However, the insertion of the chopper
References [1] Xiong Yong-Qian, Qin Bin, Feng Guan-Yao, et al., Chinese Physics C (March) (2008) 32 (supplement I). [2] B. Qin, P. Tan, L. Yang, et al., Nuclear Instruments and Methods in Physics Research Section A 727 (2013) 90. [3] H. Tong-Ning, C. Qu-Shan, P. Yuan-Ji, et al., Chinese Physics C 38 (2014) 018101. [4] C. Qu-Shan, P. Yuan-Ji, H. Tong-Ning, et al., Chinese Physics Letters 31 (2014) 012902. [5] N.I. Aizatsky. Disk-loaded waveguides for acceleration high intensity short pulse electron beams, in: Proceedings of PAC, vol. 5, 1995, pp. 3229–3231. [6] L. Bartha, I. Uzonyi, Nuclear Instruments and Methods in Physics Research Section B 161–163 (2000) 339. [7] P. Sperr, W. Egger, et al., Applied Surface Science 255 (2008) 35. [8] S. Fu, T. Kato, Nuclear Instruments and Methods in Physics Research Section A 440 (2000) 296. [9] S. Wang, S. Fu, T. Kato, Nuclear Instruments and Methods in Physics Research Section A 547 (2005) 302. [10] T. Houck, F. Deadrick, et al., IEEE Transactions on Plasma Science 24 (1996) 938. [11] J. Haimson. Optimization criteria for standing wave transverse magnetic deflection cavities, in: Proceedings of LINAC, 1966, pp. 303–331. [12] A. Faltens, C. Kerns, IEEE Transactions on Nuclear Science NS-16 (1969) 1059. [13] J. Haimson, B. Mecklenburg. Design and construction of a chopper driven 11.4 GHz traveling wave RF generator, in: Proceedings of PAC, vol. 1, 1989, pp. 243–245. [14] J. Haimson, IEEE Transactions on Nuclear Science NS-12 (1965) 499. [15] M.A. Wilson, R.I. Culter, D.L. Mohr, et al., IEEE Transactions on Nuclear Science NS-32 (1985) 3089. [16] M.A. Clarke-Gayther, et al., The development of a fast beam chopper for next generation high power proton drivers, in: Proceedings of EPAC, 2008, pp. 3584–3586. [17] R. Saethre, et al., Development and operation of the SNS fast chopper systems, in: Proceedings of PAC, 2013, pp. 1473–1477. [18] S. Mishra, et al., Thermal design of the FETS chopper beam dump, in: Proceedings of PAC, 2013, pp. 303–305. [19] R.Q. Yan, Fundamental Theory on Microwave Technology, third edition, Beijing Institute of Technology Press, Beijing (2004) 243–247. [20] C.G. Yao, Electron Linear Accelerator, Science Press, Beijing (1989) 111–117. [21] K. Jin, Y.J. Pei, D.M. Jiang, et al., Nuclear Instruments and Methods in Physics Research Section A 488 (2002) 473. [22] Y. Sun, L. Shen, X. Wang, et al., Nuclear Instruments and Methods in Physics Research Section A 623 (2010) 883. [23] Fang Zhang, Lianguan Shen, Yuanji Pei. Design of a 4-cavities collinear load coated with FeSiAl alloy for 14 MeV linac, in: Proceedings of IPAC, 2013, pp. 3370–3372. [24] L.M. Young, J.H. Billen, Parmela Documentation, LA-UR-96-1835, 2003.
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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Design of RF chopper system for improving beam quality in FEL injector with thermionic gun$ Q. Chen a, B. Qin a,n, P. Tan a, T. Hu a, Y. Pei b, F. Zhang b a State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China b National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, China
art ic l e i nf o
a b s t r a c t
Article history: Received 21 March 2014 Received in revised form 11 April 2014 Accepted 17 April 2014
For a linac-based Free Electron Laser (FEL), good beam quality largely contributes to the success of the final radiation. An imperfection confronted with the HUST THz-FEL facility is the long beam tail that emerges in the electron gun and exists through the whole beam line. This paper proposes to deploy a chopper system after the electron gun to truncate the beam tails before they enter into the linac. Physical dimensions of the chopper cavity are discussed in detail and we have developed and derived new analytical expressions applying to all frequencies for the optimal design. Also, technical issues of the cavity are considered. Beam dynamic simulation is performed to examine the truncation effect and the results show that more than 78% of the beam tail can be removed effectively, while preserving the emittance and energy spread in acceptable level. & 2014 Published by Elsevier B.V.
Keywords: RF chopper High intensive beams FEL Linac
1. Introduction As free electron laser (FEL) is the most prominent candidate for producing high average power and continuously tunable terahertz radiation, a linac-based THz-FEL facility has been planned to be built in Huazhong University of Science and Technology (HUST). Preliminary design of the whole system is finished and engineering parameters of some key components have been obtained [1–3]. The HUST FEL facility mainly consists of an independently tunable cell (ITC) RF gun, a normal temperature S-band linac, a planar undulator and an optical cavity. The FEL injector includes the ITC-RF gun and the S-band linac, both of which are designed to operate at 2856 MHz. For successful operation, the injector must provide the oscillator with high quality beams delivered by the transport line. Beam requirements at the exit of the injector are listed in Table 1. A common drawback of a thermal RF gun is its imperfect performance in longitudinal bunching. According to the analysis in Ref. [4], with present scheme the linac would undergo undesirably intensive beam current, which might result in difficulties or failure in low energy operation. This is due to the compromise between
☆ This work was supported by National Natural Science Foundation of China (11375068), and 2011 project – Hubei collaborative Innovation Center of Nonpower Nuclear Technology. n Corresponding author. Tel.: þ 86 27 87557634. E-mail addresses: [email protected] (B. Qin), [email protected] (Y. Pei).
performance and compactness demanded of the electron gun. The charge of one micro-bunch accelerated by the linac is around 500 pC while the useful portion for radiation, about 15 ps in the head, is only 200 pC. The major portion, located in the tail, will increase the feeded RF power due to beam loading effect, and may cause radiation in the waveguide of the optical cavity. A simple and economical solution is to fix a slit after the first bend magnet, because particles with different energies will follow different trajectories. Then by reasonably designing the transverse position and width of the slit, it is possible to cut off the tail portion of one bunch. However, the solution just eliminates the risk in the waveguide while doing nothing for the linac. In low energy operation, e.g. 6 MeV, the undesirably intensive beams will drain out RF power before they come to the end of the linac. If this is the case, the beams will induce electromagnetic field (wake field) in the vacant power accelerating cells and the energy spread of latter coming bunches will largely increase [5]. So, it is very meaningful to develop a chopper system located before the linac to select only the head portion without changing the initial injector layout much. An attractive proposal, on which our work is based, suggests replacing the short lens with a chopper cavity as shown in Fig. 1, for the self-bunching effect of electrons generated by the ITC-RF gun indicates dispensability in short lens usage. In the rest context, we will refer the initial structure as Scheme 1 and the new structure as Scheme 2. A chopper is usually a magnetic deflector, which can be used for measurement of beam dose [6] and suppression or selection of
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charged particle beams [7–10]. In Ref. [11], Haimson developed systematic and detailed optimization methods for designing chopper cavities and some specific designs have been reported [12–15]. Recently choppers have found extensive applications in proton linacs, which need choppers to produce precise gaps in bunched linac beams [16–18]. In our project, the chopper is utilized to generate pulses with predefined width, cutting off the tail portion after the electron gun and improving power efficiency in the linac. Nevertheless, the input beams of the chopper are not continuous as the previous cases, which makes it possible to develop some new characteristics of the chopper cavity. For example, in our design the chopper cavity shares power source with the gun and the linac. Besides, the centroid particle will undergo zero deflection force and no extra bias field is required, so the whole structure will be compact.
2.1. Theory and model We choose rectangular resonator as the chopper cavity and the preferable resonant mode is TM120 or TE102, both of which can offer symmetrical magnetic field gradient and the field components of the two modes are exactly the same except for a negative sign caused by the rotation of reference axis. Fig. 3 illustrates the chopper model adopted in the following analysis. The target of
2. Optimization of RF chopper for pulsed electron beams In heavy ion cases, it is popular to use electrostatic fields to create gaps between beam pulses. In order to make the whole system compact and the timing scheme easy to operate, we prefer a RF chopper cavity excited by the same power source of the gun and the linac. The RF chopper system is mainly composed of a resonator and a beam scraper (Fig. 1). Electrons in a micro-bunch will get transverse deflection determined by their longitudinal position and energy when traveling through the resonator and then the tail portion will be retarded by the scraper after drifting some distance. Fig. 2 shows the electron density distribution in longitudinal phase plane at the exit of the ITC-RF gun, explicitly verifying the long beam tail.
Fig. 2. Electron density distribution in longitudinal phase plane at the exit of the RF gun (18,000 macro particles involved).
Table 1 Beam requirements at the exit of the injector. Beam energy Energy spread (FWHM) Normalized emittance (RMS) Micro-pulse charge Micro-pulse length (FWHM) Micro-pulse repetition rate Macro-pulse length Macro-pulse repetition rate
6–14 MeV o 0:3% o 15 μm rad 4 200 pC 5–10 ps 2856 MHz 4–6 μs 10–50 pps Fig. 3. Model of the chopper system.
ITC-RF gun Resonator Alternative design with the lens removed
Lens
Scraper
TW accelerator & Solenoid
Initial design
Fig. 1. Layout of the initial and alternative design of the injector. The resonator and the lens may share some longitudinal space as the latter one is removed in the alternative design, while for clear illustration they are separated from each other.
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optimization is to construct a chopper cavity providing maximum deflection efficiency with an acceptable Q value and a minimized size. More issues on Q will be addressed latter and now physical dimensions are pursued. In rectangular coordinates, the field components of TM120 mode can be expressed as [19] π 2π y Ez ¼ E0 sin x sin a b π ωϵ 2π 2π Hx ¼ j 2 E0 sin x cos y a b Kc b π ωϵπ 2π E0 cos x sin y ð1Þ Hy ¼ j 2 a b Kc a
which makes it rational to inject the reference particle at the right angle to the RF magnetic field (undergo zero deflection) and no need for the solenoid. In the paraxial area, Hx deflects electrons in the y-direction and it is reasonable to neglect the change in electron energy or velocity. Then the transverse velocity of one particle at the exit of the cavity is Z h=v0 eμ0 v0 H mx vy ¼ sin ðωt þ ϕ0 Þ dt m0 γ 0 0 2eμ0 v0 H mx ωh ωh sin ð7Þ sin þ ϕ0 ¼ 2v0 2v0 ωm0 γ 0
where “a”, “b” and “h” are the dimensions in x, y and z direction respectively, E0 is the reference magnitude of Ez, Kc is the cut off wave number and in TM120 mode we have K c ¼ k ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðπ=aÞ2 þ ð2π=bÞ2 . The resonant frequency is calculated as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 c π 2 2π f¼ þ ð2Þ 2π a b
where v0 is the injection velocity, e and m0 are the charge and the mass of an electron respectively, μ0 is the permeability of free space and γ0 is the relativity factor corresponding to v0. After drifting a distance of L, the transverse displacement is
where c is the velocity of light in free space. The time-averaged energy density corresponding to the three field components is 1 2 π 2 2π x sin y ωEz ¼ ϵE20 sin 4 a b 1 ϵ 2π 2 2 2π 2 π x cos 2 y ωH x ¼ 2 E0 sin 4k b a b 1 ϵ π 2 2 2 2π 2 π ωH y ¼ 2 x sin y ð3Þ E0 cos 4k a a b So energy stored in the resonator with an electrical reference magnitude of E0 is Z hZ bZ a 1 U¼ ðωEz þ ωHx þ ωHy Þ dx dy dz ¼ ϵVE20 ð4Þ 8 0 0 0 where V is the volume of the resonator and V ¼ abh. For specific wall loss power PL, the field strength is determined according to rffiffiffiffiffiffiffiffiffiffiffi 8QP L E0 ¼ ð5Þ ωϵV On the centerline of the cavity, which is also the beam line, the only remained field component is rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffi 4π 2ωϵP L Q 1 sin ðωt þ ϕ0 Þ ð6Þ H x ¼ H mx sin ðωt þ ϕ0 Þ ¼ 2 3 h k ab where ϕ0 is the injection angle of one particle. Then we can optimize the resonator dimension to achieve maximum deflection force. From Eq. (2), it is obvious that the resonant frequency is only dependent on “a” and “b”, leaving the longitudinal dimension “h” to be determined otherwise. 2.2. Optimization methods 2.2.1. Dynamic calculation and optimization of “h” The optimization criteria of “h” can be revealed by analyzing the beam deflection in the cavity, with the aim of obtaining maximum deflection sensitivity. Many previous works have proposed a scheme called the “peak operation”, in which the reference particle injects the cavity at the peak of one RF circle and the cavity is immersed in a solenoid magnetic field offering fixed transverse bias to compensate unwanted deflection force [13,20]. For continuous beams, i.e. beams occupy a whole RF circle, the “peak operation” is necessary, otherwise the pulse repetition rate would be doubled. However, in the HUST FEL injector, Scheme 2 will deploy the chopper cavity after the buncher of ITC-RF gun and its input pulse length is less than a half RF cycle,
Δy ¼ L tan θ
ð8Þ
where θ is the deflection angle and is defined as tan θ ¼ vy =v0 . So, for electrons in a micro-pulse, longitudinal position determines ϕ0 that one particle experiences and then the transverse velocity and displacement of it. To gain maximum deflection efficiency, it comes to optimize “h” to maximize the magnitude of vy (item in the bracket of Eq. (7)). The optimization criteria reported in this paper are slightly different from that of Ref. [20] and a more reasonable result is obtained. According to (Eqs. (6) and 7), for a given particle energy and any specified “a” and “b”, we have rffiffiffi 1 ωh jvy jp sin ð9Þ h 2v0 where jvy j is the magnitude of vy. After some mathematical processing, the optimum value of “h” is subjected to the following transcendental equation: ωh ω 1 ¼ ð10Þ h tan 2v0 v0 With a reference particle energy of 2.6 MeV for example, the optimal value of “h” is found to be 38.42 mm while Ref. [20] would give a value of 51.79 mm. An interesting phenomenon is that the energy of electrons in the tail portion is lower, which makes them get larger deflection and so the sensitivity is enhanced further. Fig. 4 shows the transverse displacement of an electron bunch at 6 Ke=1.4MeV Ke=1.7MeV Ke=2.0MeV Ke=2.3MeV Ke=2.6MeV
5
Displacement at the scraper/mm
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3
4
3
2
1
0 0
20
40
60
80
100
Longitudinal position/degree Fig. 4. Transverse displacement of one bunch at the scraper versus longitudinal position (5 cases involved).
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the scraper after a drift distance of 100 mm, assuming that the energy of particles in one bunch is the same and Hmx has been normalized to a feasible value of 104 A/m. 2.2.2. Optimization of “a” and “b” From the knowledge in linear algebra, the determination of “a” and “b” needs two criteria coming from the resonant frequency and the deflection efficiency. The former criterion has been illustrated in Eq. (2) and we will mostly focus on the latter one. When the resonator is in steady state operation, the coupled power will be exactly equal to the wall loss required to establish a given electrical field strength. Then Eq. (6) points out the optimization criteria for “a” and “b”. It should be emphasized that the Q value is mainly controlled by the microwave absorbing material coated on the inner wall of the resonator, leaving the optimization 3 of “a ” and “b” subjected to minimizing the value of “a b ” under the constraint of Eq. (2). Eq. (11) gives the analytical expression of “a” and “b” and Fig. 5 confirms the result: 8 < a ¼ λ pffiffiffi 2 3 ð11Þ :b¼ λ 3 where λ is the wavelength corresponding to the resonant frequency. So, theoretically an efficient rectangular chopper working in TM120 mode of 2856 MHz should have transverse dimension of
“105 mm 121 mm”, ignoring the essential correction caused by the coating of absorbing material and the coupler slit. Now the optimal dimensions of the rectangular chopper cavity have been obtained and (Eqs. (10) and 11) apply to any frequency operated in TM120 mode. 2.3. Consideration of Q-value Q value is most important for bringing the resonator into practice. A high Q value requires highly stable frequency and temperature control systems, as well as insupportably long excitation time. According to Ref. [11], the transient field of a circuit follows EðtÞ ¼ Ef ð1 e ωt=2Q L Þ
t exc ¼
6
180
5.5
170
5
160
4.5
150
4
140
3.5
130
3
120
For a coppery resonator with the optimal dimension, eigenmode computation shows a Q-value of 18,600 and the corresponding excitation time is 2.4 μs, much larger than that of the linac. So a reasonable design should make the excitation time less than
3
change in emittance change in energy spread change in scraper efficiency
3
2.5
2.5
b versus a a*b versus a
2
1.5
2
110 100
ð13Þ
Ratio
190
2Q L ln 10 ω
3.5
a*b3
200
x 10 6.5
ð12Þ
where Ef is the steady state field, QL is the loaded Q-value and is equal to Q 0 =2 in load matched case. If we define the excitation time as the time needed to build up 90% level of the steady state field, we can get
8
b/mm
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0
100
200
300
400
500
1.5 600
a/mm Fig. 5. Optimization result of “a” and “b”. The solid line indicates the (a,b) pairs satisfying the resonant frequency; the dash line indicates the reciprocal of the deflection efficiency versus “a”.
1 0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Input power/MW Fig. 7. Influence on the beam quality of the head portion at different input powers. All data are normalized to that of Scheme 1.
Fig. 6. Snapshot of beam profile at the scraper.
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0.3 μs, indicating the Q-value less than 2340. A popular method to achieve this is coating the inner wall with high resistance material [21–23]. For our group has extensive experience in the use of FeSiAl, this kind of alloy is adopted as the absorbing material to control the Q value. The relative electromagnetic parameters of the FeSiAl alloy used in our project have been measured as ϵ ¼ 13:23 0:25i and μ ¼ 1:77 1:41i at 2856 MHz. Simulation results show that the Table 2 Parameters of the chopper system. Resonant frequency Resonator dimension (x; y; z) Unloaded quality factor Excitation time Input power Drift length Scraper dimension (x; y) Maximum deflection voltage
2856 MHz 105 mm 121.2 mm 38.4 mm 2000 0.25 μs 0.2 MW 100 mm 4 mm 3.6 mm 0.12 MV
5
volume of the coated material has linear relationship with the frequency error, which can be corrected by modifying the transverse dimension. To get the desired Q value of 2000, the volume of the coated material should be 35 mm3 and the corresponding frequency error can be compensated if “b” decreased by 16 μm.
3. Beam dynamic simulation and analysis To checkout the effect of the chopper system on electron beams, beam dynamic simulation is carried out from the exit of the ITC-RF gun down to the entrance of the lianc. The initial distribution of electrons comes from the output file related to the simulation of the ITC-RF gun. The bunch charge and the bunch length at the entrance of the linac between the two schemes are the key points to judge the new design system. Parmela code [24] is used to complete the beam dynamic simulation. And following the optimized dimensions discussed in the previous section, the cavity model is constructed with the help
Fig. 8. Evolution of phase spectrum, energy spectrum and transverse profile of the electron beam in Scheme 2: (left: A) z¼ 0 (exit of the gun); (middle: B) z ¼ 20.8 cm (just before the scraper); (right: C) z ¼ 31.7 cm (entrance of the linac).
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beam profile, the scraper is set to have a size of “4 mmðxÞ 3:6 mmðyÞ” and with a 0.8 mm offset in the positive y-direction. Snapshot of beam profile at the scraper clearly illustrates this decision (Fig. 6). Now all the intrinsic parameters of the chopper system have been settled. To evaluate the performance, a new assessment index, scrape efficiency, is proposed and defined as the ratio of the scraped particle number of Scheme 2 to that of Scheme 1 (assume that the scraper is also included in Scheme 1 for justice). Apart from the scrape efficiency, it is also required to minimize the chopper deterioration of the quality of the head portion. So emittance and energy spread of the head portion at the entrance of the linac are compared between the two schemes in different input power cases (Fig. 7). For vivid contrast, all data are normalized to that of Scheme 1. The results in Fig. 7 show that while variation of the input power does not affect energy spread, it obviously has great influence on the emittance. Larger input power will get more useless particles removed, manifested by the black line in Fig. 7, but will also result in worse emittance, which indicates that compromise must be made between the two indices. To allow for acceptable emittance increase in the linac, the input power is set to be 0.2 MW. Table 2 displays the final design parameters of the chopper system. Based on the optimized parameters, it is found that 78.2% of the tail portion is removed, at the same time the bunch length reduces from 100 ps to 30 ps and the bunch charge reduces from 525 pC to 282 pC. Snaps of the simulation results shown in Fig. 8 demonstrate the evolution of beam status and beam qualities under the two schemes are listed in Table 3. With the chopped beams, post-calculation shows that the beam load current in the linac is reduced from 1.05 A to 0.79 A and input power of 13 MW is enough to achieve beam energy of 14 MeV while in Scheme 1 the input power should be 16.5 MW. For further comparison, phase space at the exit of the linac under the two schemes (Fig. 9) confirms that the chopper system has effectively removed the tail portion which is also the low energy
of CST to calculate the resonant field. After rearranging and normalizing the data file produced by CST, Parmela code can utilize it to track every macro particle's state at each user defined time step. More consideration should be taken on the injection phase at the entrance of the chopper cavity. Eq. (7) and Fig. 4 have demonstrated the relationship between the injection phase and the transverse displacement at the scraper, implying that the reference particle should undergo zero deflection. With this constraint, the phase setting of the CELL line in Parmela code should satisfy ϕ¼
ωh π Φ 2v0 2
ð14Þ
where Φ is the master clock phase at which the reference particle arrives at the chopper cavity and the π=2 is induced by the phase difference between E-field and H-field. Before launching the simulation, it is still required to figure out the dimension and the transverse position of the scraper, which should not retard the head portion but remove the tail portion efficiently. After a lot of trial and error involving statistical analysis of
Table 3 Beam qualities of the head portion at the entrance of the linac. Scheme 1
Scheme 2
Reference energy (MeV) Energy spread (FWHM) (%) Norm. emittance (x) (μm rad) Norm. emittance (y) (μm rad) Charge (pC)
2.6 0.67 8.319 8.633 210
2.6 0.69 8.326 13.385 210
Bunch lengtha (ps) Bunch chargea (pC)
100 525
30 282
a Refer to qualities of a whole bunch, and bunch length is defined as the width during which more than 95% particles are contained.
Number of particles
Phase spctrum 600
600
500
500
400
400
300
300
200
200
100
100
0 −20
0
20
40
60
0 −20
0
20
40
60
Phase/degree
Phase/degree Energy spectrum Number of particles
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Q3 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66
3000
3000
2000
2000
1000
1000
0 13
13.5
Energy/MeV
14
0 13
13.5
14
Energy/MeV
Fig. 9. Phase spectrum and energy spectrum at the exit of the linac under (left: A) Scheme 1 and (right: B) Scheme 2.
Please cite this article as: Q. Chen, et al., Nuclear Instruments & Methods in Physics Research A (2014), http://dx.doi.org/10.1016/j. nima.2014.04.048i
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portion, while scarcely deteriorating the longitudinal phase space of the head portion.
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system will not change the longitudinal dimension of the whole facility but exhibits good performance, indicating that the proposal is a promising alternative for future upgrade.
4. Discussion and conclusion The major issue of the beam tails is that it will increase the feed-in RF power significantly due to the beam loading effect, furthermore it might bring instability of the FEL injector. For this consideration in HUST FEL injector, a RF chopper system, which consists of a resonator and a scraper, is proposed to remove the useless portion of the bunched beam before the linac. Originated from the microwave theory, the resonant field is analyzed and the physical dimensions are optimized accordingly to make the resonator get maximum deflection efficiency. One important result is that we developed and derived new analytical expressions applying to all frequency for the optimal design. For practical consideration, magnetic loss material FeSiAl is coated on the inner wall of the resonator to lower the Q value and shorten the excitation time. In the simulation part, scrape efficiency, emittance variation and energy spread variation are selected to assess the performance of the chopper system. It is found that only the former two indices are sensitive to the resonator field and compromise must be made to get relatively high scrape efficiency and acceptable emittance. So, the input power is finally set to be 0.2 MW. Simulation results show that more than 78% of the tail portion is scraped and the corresponding emittance and energy spread are 13.385 μm rad (y direction) and 0.69%, implying very good performance. With the scraped electron bunches, it is certain that the beam loading effect in the linac will be largely relieved. As a result, the power efficiency is enhanced and the success of low energy operation is guaranteed. To be noted, the longitudinal beam profile is only shown through the injector. Since the chopper only removes beam tails located at the lower energy region, the same beam head is contained compared to the original scheme, even after the transport line including the double bend achromat (DBA). So the contribution on FEL gain of two schemes will maintain at the same level. In further works, start-to-end simulation on beam dynamics, and the study on the FEL gain with/without beam tails are expected to evaluate more realistic beam tail effect. Now the HUST FEL facility is under construction and the overall layout has been settled. However, the insertion of the chopper
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Please cite this article as: Q. Chen, et al., Nuclear Instruments & Methods in Physics Research A (2014), http://dx.doi.org/10.1016/j. nima.2014.04.048i
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