- Email: [email protected]
Beam dynamic design of a high intensity injector for proton linac
Nuclear Instruments and Methods in Physics Research A 827 (2016) 145–151
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Beam dynamic design of a high intensity injector for proton linac$ Wei-Ping Dou a,n, Zhi-Jun Wang a, Fang-Jian Jia b, Yuan He a,n, Zhi Wang b, Yuan-Rong Lu b a b
Institute of Modern Physics, The Chinese Academy of Sciences, Lanzhou 73000, China State Key Lab of Nuclear Physics and Technology, Peking University, Beijing 100847, China
art ic l e i nf o Article history: Received 23 August 2015 Received in revised form 25 April 2016 Accepted 29 April 2016 Available online 30 April 2016 Keywords: High intensity KONUS DTL RFQ Compact linac injector
a b s t r a c t A compact room-temperature injector is designed to accelerate 100 mA proton beam from 45 keV to 4.06 MeV for the proposed high intensity proton linac at State Key Lab of Nuclear Physics and Technology in Peking university. The main feature is that the Radio Frequency Quadruple (RFQ) and the Drift Tube linac (DTL) sections are merged in one piece at the total length of 276 cm. The beam is matched in transverse directions with an compact internal doublet instead of an external matching section in between. The design has reached a high average accelerating gradient up to 1.55 MV/m with transmission efficiency of 95.9% at the consideration of high duty factor operation. The operation frequency is chose to be 200 MHz due to the already available RF power source. The injector combines a 150 cm long 4-vanes RFQ internal section from 45 keV to 618 keV with a 126 cm long H-type DTL section to 4.06 MeV. In general the design satisfy the challenges of the project requirements. And the details are presented in this paper. & 2016 Elsevier B.V. All rights reserved.
1. Introduction
doublet as the internal matching cells. The main considerations are:
The compact high gradient injector is a highly desirable choice for modern low energy accelerator projects because of its low cost and limited footprint. The combining of different RF accelerating structures into one single device is a very attractive way to do it. The short-internal cells are usually adopted to match the beam between RF structures. This type of hybrid structure as an ion injector is employed and studied by many laboratories. For example, the cavity for interdigital H-type RFQ-drift tube combination, which accelerate proton beam up to 2 MeV at the length of 230 cm, has been developed at the FRANZ (Frankfurt Neutron Source) [1], where three rebunching gaps and a internal triplet are used as matching cells. A hybrid single cavity (HSC) [2] for interdigital H-type RFQ-drift tube combination has been built as the direct injector for a synchrotron accelerator for cancer therapy by Tokyo institute of Technology, which can accelerate 12C6 þ up to 2 MeV/u at a total length of 180 cm. Therefore, considering the advantages of such injectors, the decision was made to carry out the studies of a compact room-temperature injector with the combination of RFQ and H-type Drift Tube for a proton linac at the State Key Lab of Nuclear Physics and Technology of Peking university. It includes two rebunching gaps and a
(1) Single RF source for both sub-structures in order to save RF cost. (2) The RF is decoupled between these two sub-structures. (3) The different structures phases are adjusted alone by phase shift but at the same operating frequency.
☆ Supported by the National Natural Science Foundation of China (Grant No. 9146303) and National Program on Key Basic Research Project of China (Grant No. 2014CB845503). n Corresponding authors. E-mail addresses: [email protected] (W.-P. Dou), [email protected] (Y. He).
http://dx.doi.org/10.1016/j.nima.2016.04.108 0168-9002/& 2016 Elsevier B.V. All rights reserved.
The designed scheme is shown in Fig. 1. There are total 3 periodic cells inside the DTL, the first cell is a doublet in DTL and the rest of the period cell structures are triplet. Since the injector combines two distinctive sub-structures, each can be designed separately and optimized as a whole later. During the design, the software PAMTEQM [3], LORASR [4] and TraceWin [5] are used as well as for the beam dynamic simulations. Generally, the design process can be divided into four major steps (1) Firstly the RFQ beam dynamic design is finished by using PARMTEQM. (2) Then the DTL design is done by LORASR with input particle distribution from PARMTEQM. At this stage, the transverse and longitudinal envelope are controlled manually, which may not be well optimized. (3) At the third stage, TRACEWIN was used to find the matched Twiss parameters of DTL period structures and to optimize the triplet gradient automatically except the first doublet. (4) Finally with the help of TRACEWIN, the doublet was matched to the Twiss parameters of the rest of the DTL period structures. The
146
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Fig. 1. The designed scheme.
RFQ. The transverse focusing strength can be increased by either reducing the aperture or increasing the inter-vane voltage V and/or using lower frequency. However, a smaller aperture may limit the transverse acceptance, whereas RF frequency and the inter-vane voltage V are limited by the availability and cost. In this case, the RF system is already chosen to be 200 MHz with an inter-vane voltage of 70 kV. Taking account of the space charge effect, the transverse phase advance becomes [8]
σt2 =
B2 Iλ 3(1 − ff )k +δ− , 8π a3bγ 3
where
(2)
δ is RF defocusing parameter expressed as 2
δ=
Fig. 2. The transverse focusing strength B versus cell number in the traditional and optimized design.
beam dynamics studies have been carried out for 100 mA proton beam from 45 keV to 4.06 MeV at the total length of 276 cm. And the details will be discussed in the following sections.
2. RFQ section The traditional RFQ beam dynamics design generally follows the classic Los Alamos National Laboratory (LANL) Four-Section Procedure (FSP) [6], which has been adopted and proven by various RFQ projects in the world during the last three decades. However, a New FourSection Procedure (NFSP) [7] has been employed to design high beam intensity RFQ which subjected to the strict constraints on the beam quality and structure length. Different to the traditional approaches (1) Non-constant transverse focusing strength B along the RFQ according to the different space-charge conditions are adopted. (2) The speed of the beam bunching process is controlled to decrease the number of longitudinal unstable particles. The transverse focusing strength B [6] for a RFQ can be described as
B=
qλ2XV , mc 2a2
(1)
where q is the charge state of ions, λ is the RF wavelength, X is the focusing parameter, V is the inter-vane voltage, m is the relativistic mass of ions, c is the velocity of light, a is the minimum aperture of
qπ AV sin ϕs 2mc 2β 2γ
(3)
where s is the phase advance with space charge effect, I is the ⎛ 3 zq10−6 ⎞ ⎟, where beam current, ff is the ellipsoid form factor, k = ⎜ 8π ⎝ mc 2 ⎠ z¼376.73 Ω. β, γ are the relativistic velocity and gamma, A is the acceleration parameter, ϕs is synchronous phase, a and b are the transverse and longitudinal rms beam radius. From the matched beam envelope equation described in [9], the normalized rms emittance ϵ can be written as
ϵtn =
a2σtγ . λ
(4)
The method is to adjust the transverse phase advance st to limit the variation of beam size and the emittance growth. In the gentle bunching section, the B is increased to balance both the growing RF defocusing effect and space charge effect. When the beam acceleration starts, the increased beam velocity weakens RF defocusing effect, and B should accordingly fall down to allow a large bore aperture and higher acceleration gradient. The maximum value of B is decided by the maximum surface field and the average aperture. Fig. 2 shows the optimized transverse focusing strength B changing smoothly comparing with that of the traditionally almost constant B. Fig. 3 compares the transverse phase advance st and the RMS beam size for the traditional and the optimized design. In the traditional design, the transverse phase advance st reduces rapidly first in shaper section and then increases in acceleration section. Accordingly, the RMS beam size has larger variation. While in the optimized design, the transverse beam size has a small oscillation after the shaper section. The evolution of the synchronous phase and vane modulation factor m should be tuned to improve the bunching stability at the same time. Fig. 4 compares the modulation factor m and synchronous phase ϕs for the traditional and optimized design respectively. In the shaper section, which is up to the first 40 cells, the ϕs is kept at 90° in the optimized design instead of the linear increasing in traditional design. It is aimed to have a maximum longitudinal acceptance for high intensity beam and good bunching. Then the ϕs almost linearly
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147
Fig. 3. Comparison of the transverse phase advance st and the RMS beam size before and after the optimization.
Fig. 4. The modulation factor m and synchronous phase ϕs versus cell number in the traditional and optimized design.
Table 1 Beam dynamics simulation results of the traditional and optimized design. Parameters
Traditional
Optimized
Frequency (MHz) Input (MeV) output energy (MeV) Beam current (mA) Vane voltage (kV)
200 0.045 0.618 100 70 0.2
200 0.045 0.618 100 70 0.2
0.327 1.46 149.2 92.8 0.31
0.365 1.46 150.3 96.5 0.28
y . norm . RMS (π mm mrad) ϵout
0.30
0.28
z . RMS ϵout
0.25
0.13
ϵtrans . norm . RMS (π mm mrad) Minimum apertures (cm) Kilpatrick factor (cm) Cavity length (cm) Beam transmission (%) x . norm . RMS (π mm mrad) ϵout
(MeV deg)
Fig. 5. The RFQ parameters as a function of the cell number in the optimized design.
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Fig. 6. The beam transmission along the RFQ and the beam phase space of the RFQ.
Fig. 7. The normalized RMS emittance variation along the RFQ.
increases until the end smoothly. At the same time, the modulation m goes up smoothly compared with the traditional design. In the end, the modulation m is lower in the main acceleration section which is compensated by the higher synchronous phase ϕs. The overall design results in a higher transmission efficiency and a lower emittance growth in a limited length.
The detailed beam dynamics simulation results of the traditional and optimized design are listed in Table 1. Compared to traditional design, beam quality of the optimized design is better at almost same cavity length and same input parameters and RF. Fig. 5 shows RFQ parameters as a function of the cell number in the optimized design. And Fig. 6(a) shows the beam envelope and Fig. 6(b) shows the phase space distributions at the entrance and exit of RFQ. The FWHM phase spread at the exit is approximately ±35°, which is the required maximum phase spread of KONUS H-DTL. The evolution of the normalized RMS emittances along the RFQ is plotted in Fig. 7, where the transverse normalized RMS emittance curves grow significantly due to very strong space charge force but weak transverse focusing in radial matching section. Then there are some acceptable growth, which is caused by the fast bunching over limited structure length requirement. In the end part of structure, the emittance decreases mainly because of the loss of out-off-bucket particles.
3. DTL section The room temperature H-mode DTL cavity based on KONUS beam dynamics is adopted because of its high shunt impedance
Fig. 8. The effective voltage and the maximum value of axis field in each accelerating gap.
W.-P. Dou et al. / Nuclear Instruments and Methods in Physics Research A 827 (2016) 145–151
Table 2 Quadruple parameters. Lens
DBA1
TBA2
TBA3
Drift. length (mm) Eff. length (mm) Filed gradient (T/m)
20 32/32 88/91
20/20 31/46/31 80.3/88.69/80.3
20/20 32/50/32 64.6/76.3/64.6
Table 3 The main parameters of DTL. Parameters
Value
RF frequency (MHz) 200 Input energy (MeV) 0.618 Input energy (MeV) 4.07 Number of gaps 18 Length (m) 1.26 Acceleration gradient (MV/m) 2.8 Transmission (%) 95.9
149
[10], which is well suited for the short length constraints of this project. KONUS beam dynamics [11,12] can overcome the conflicting requirements of the transverse defocusing, longitudinal bunching and RF accelerating. A KONUS period consists of a quadrupole triplet, a rebuncher section with negative synchronous phase of typically from 25° to 35°, and a multi cell acceleration section with zero degree synchronous phase. In the KONUS beam dynamics, the key parameters are [13] (1) the phase shift in the same cavity at transition from rebunching gaps to 0° gaps, for example at the transition 35° to 0°; (2) the starting conditions δW and δϕ of the first gap of each 0° section (where δW is energy difference between bunch center Wc and synchronous particle Ws and the δϕ is corresponding phase difference). The transition cell from rebunching gap to 0° gap belongs to the same resonator, the geometrical length of the transition cell can be adjusted by mounting a drift tube with the length L following the
Fig. 9. The input particles distribution.
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Fig. 10. The longitudinal and transverse envelope containing 99% particles along the DTL.
Eq. (5) below
L=
(180 + 35) βλ . 180 2
(5)
Fig. 8 shows the effective voltage of each accelerating gap and the maximum field at axis. The maximum axis field is 13.8 MV/m, which is below Kilpatrick breakdown field of 14.7 MV/m at 200 MHz. The parameters of quadrupoles are listed in Table 2. In the longitudinal direction, the quadrupole acts like a drift space and must be made as short as possible. Shorter powerful quadrupole triplet/doublet are needed for sufficient transverse focusing and minimum longitudinal defocusing. The maximum quadrupole field gradient chosen is 91 T/m, which corresponds a pole tip magnetic field of 1.09 T/m at 24 mm of aperture. And it is readily available with conventional technology. Well-balanced ratio of rebunching gap to 0° gap is typically between 1:2 and 1:4. The starting conditions δW and δϕ of the first gap of each 0° section are depend on longitudinal phase space distribution and adjusted to match beam parameters of the following sections.
4. Combined optimization The LORASR is used for the DTL design, where the transverse and longitudinal envelope are tuned by hand traditionally, but it may not be well optimized. The beam loss due to the imperfect longitudinal matching is not an issue for 2.7 m DTL, where the optimization is done by hand. The TRACEWIN is used to do the transverse optimization additionally. There are four steps
(1) Setting transverse phase advance of the last two KONUS periodic cells. (2) Finding the entrance transverse Twiss parameters of KONUS periodic structures corresponding to the optimized triplet gradient convergely. (3) The doublet was used to match the beam from RFQ to the Twiss parameters of the above mentioned KONUS period structures entrance. (4) Finally, TRACEWIN is used for the DTL beam dynamic tracking to confirm the whole design. Table 3 shows the main parameters of the DTL. Fig. 9 shows the input particles distribution coming from the RFQ exit produced by PARMTEQ. Fig. 10 shows the longitudinal and transverse envelope containing 99% particles along the DTL. At 100 mA, 99% beam envelope is smaller than the 10 mm radius of the drift tube. The energy spread is smaller than 0.5% at the DTL exit.
5. Summary The compact room-temperature injector combines a RFQ and a H-type DTL that has two KONUS periods and a doublet as internal matching cells has been designed for the project of the high intensity proton linac at Peking University. The design follows the NFSP philosophy and the KONUS principles, and the results show that it satisfy the beam quality and structure length requirements. The injector has reached a high average accelerating gradient up to 1.55 MV/m and is designed to accelerate 100 mA proton beam from 45 keV to 4 MeV at the length of 276 cm. The future plan is to
W.-P. Dou et al. / Nuclear Instruments and Methods in Physics Research A 827 (2016) 145–151
study error tolerance in details. The mechanic design and RF structure simulations in CST will come later.
Acknowledgments The authors sincerely thank Prof. U. Ratzinger at Frankfurt University and Prof. Zhihui LI at Sichuan University for their kind helps and useful discussions.
References [1] M. Heilmann, C. Claessens, D. Mader, et al., in: Proceedings of IPAC, Shanghai, China, 2013. [2] Liang Lu, Toshiyuki Hattoti, Noriyosu Hayashizaki, Nucl. Instrum. Methods
151
Phys. Res. A 688 (2012) 11–21. [3] K.R. Crandall, T.P. Wangler, L.M. Young, et al., LA-UR-96-1836, 2005. [4] U. Ratzinger, et al., LORASR – a computer code to calculate the longitudinal and radial beam dynamics of a drift tube accelerator, GSI Internal Report 0791. [5] D. Uriot, TraceWin Documentation, 〈http://irfu.cea.fr/Sacm/logiciels/index3〉. php, 2011. [6] K.R. Crandall, R.H. Stokes, T.P. Wangler, in: Proceedings of the 1979 Linear Accelerater Conference, Montauk, NY, USA, pp. 205–216. [7] Chuan Zhang, Alwin Schempp, Nucl. Instrum. Methods Phys. Res. A 586 (2008) 153–159. [8] X.Q. Yan, J.X. Fang, Z.Y. Guo, et al., Nucl. Instrum. Methods Phys. Res. A 554 (2005) 132–137. [9] M. Reiser, Theory and Design of Charged Particle Beams, Wiley, New York, 1994. [10] U. Ratzinger, R. Tiede, Nucl. Instrum. Methods Phys. Res. A 415 (1998) 2229–2235. [11] U. Ratzinger, R. Tiede, Laser Part Beam 20 (2002) 447–450. [12] R. Tiede, U. Ratzinger, in: Proceedings of the Hadrons Beam 2008, Nashville, Tennessee, USA, 2008. [13] R. Tiede, U. Ratzinger, H. Podlech, et al., Hadron Beam, USA, 2008, 1, 2013.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Beam dynamic design of a high intensity injector for proton linac$ Wei-Ping Dou a,n, Zhi-Jun Wang a, Fang-Jian Jia b, Yuan He a,n, Zhi Wang b, Yuan-Rong Lu b a b
Institute of Modern Physics, The Chinese Academy of Sciences, Lanzhou 73000, China State Key Lab of Nuclear Physics and Technology, Peking University, Beijing 100847, China
art ic l e i nf o Article history: Received 23 August 2015 Received in revised form 25 April 2016 Accepted 29 April 2016 Available online 30 April 2016 Keywords: High intensity KONUS DTL RFQ Compact linac injector
a b s t r a c t A compact room-temperature injector is designed to accelerate 100 mA proton beam from 45 keV to 4.06 MeV for the proposed high intensity proton linac at State Key Lab of Nuclear Physics and Technology in Peking university. The main feature is that the Radio Frequency Quadruple (RFQ) and the Drift Tube linac (DTL) sections are merged in one piece at the total length of 276 cm. The beam is matched in transverse directions with an compact internal doublet instead of an external matching section in between. The design has reached a high average accelerating gradient up to 1.55 MV/m with transmission efficiency of 95.9% at the consideration of high duty factor operation. The operation frequency is chose to be 200 MHz due to the already available RF power source. The injector combines a 150 cm long 4-vanes RFQ internal section from 45 keV to 618 keV with a 126 cm long H-type DTL section to 4.06 MeV. In general the design satisfy the challenges of the project requirements. And the details are presented in this paper. & 2016 Elsevier B.V. All rights reserved.
1. Introduction
doublet as the internal matching cells. The main considerations are:
The compact high gradient injector is a highly desirable choice for modern low energy accelerator projects because of its low cost and limited footprint. The combining of different RF accelerating structures into one single device is a very attractive way to do it. The short-internal cells are usually adopted to match the beam between RF structures. This type of hybrid structure as an ion injector is employed and studied by many laboratories. For example, the cavity for interdigital H-type RFQ-drift tube combination, which accelerate proton beam up to 2 MeV at the length of 230 cm, has been developed at the FRANZ (Frankfurt Neutron Source) [1], where three rebunching gaps and a internal triplet are used as matching cells. A hybrid single cavity (HSC) [2] for interdigital H-type RFQ-drift tube combination has been built as the direct injector for a synchrotron accelerator for cancer therapy by Tokyo institute of Technology, which can accelerate 12C6 þ up to 2 MeV/u at a total length of 180 cm. Therefore, considering the advantages of such injectors, the decision was made to carry out the studies of a compact room-temperature injector with the combination of RFQ and H-type Drift Tube for a proton linac at the State Key Lab of Nuclear Physics and Technology of Peking university. It includes two rebunching gaps and a
(1) Single RF source for both sub-structures in order to save RF cost. (2) The RF is decoupled between these two sub-structures. (3) The different structures phases are adjusted alone by phase shift but at the same operating frequency.
☆ Supported by the National Natural Science Foundation of China (Grant No. 9146303) and National Program on Key Basic Research Project of China (Grant No. 2014CB845503). n Corresponding authors. E-mail addresses: [email protected] (W.-P. Dou), [email protected] (Y. He).
http://dx.doi.org/10.1016/j.nima.2016.04.108 0168-9002/& 2016 Elsevier B.V. All rights reserved.
The designed scheme is shown in Fig. 1. There are total 3 periodic cells inside the DTL, the first cell is a doublet in DTL and the rest of the period cell structures are triplet. Since the injector combines two distinctive sub-structures, each can be designed separately and optimized as a whole later. During the design, the software PAMTEQM [3], LORASR [4] and TraceWin [5] are used as well as for the beam dynamic simulations. Generally, the design process can be divided into four major steps (1) Firstly the RFQ beam dynamic design is finished by using PARMTEQM. (2) Then the DTL design is done by LORASR with input particle distribution from PARMTEQM. At this stage, the transverse and longitudinal envelope are controlled manually, which may not be well optimized. (3) At the third stage, TRACEWIN was used to find the matched Twiss parameters of DTL period structures and to optimize the triplet gradient automatically except the first doublet. (4) Finally with the help of TRACEWIN, the doublet was matched to the Twiss parameters of the rest of the DTL period structures. The
146
W.-P. Dou et al. / Nuclear Instruments and Methods in Physics Research A 827 (2016) 145–151
Fig. 1. The designed scheme.
RFQ. The transverse focusing strength can be increased by either reducing the aperture or increasing the inter-vane voltage V and/or using lower frequency. However, a smaller aperture may limit the transverse acceptance, whereas RF frequency and the inter-vane voltage V are limited by the availability and cost. In this case, the RF system is already chosen to be 200 MHz with an inter-vane voltage of 70 kV. Taking account of the space charge effect, the transverse phase advance becomes [8]
σt2 =
B2 Iλ 3(1 − ff )k +δ− , 8π a3bγ 3
where
(2)
δ is RF defocusing parameter expressed as 2
δ=
Fig. 2. The transverse focusing strength B versus cell number in the traditional and optimized design.
beam dynamics studies have been carried out for 100 mA proton beam from 45 keV to 4.06 MeV at the total length of 276 cm. And the details will be discussed in the following sections.
2. RFQ section The traditional RFQ beam dynamics design generally follows the classic Los Alamos National Laboratory (LANL) Four-Section Procedure (FSP) [6], which has been adopted and proven by various RFQ projects in the world during the last three decades. However, a New FourSection Procedure (NFSP) [7] has been employed to design high beam intensity RFQ which subjected to the strict constraints on the beam quality and structure length. Different to the traditional approaches (1) Non-constant transverse focusing strength B along the RFQ according to the different space-charge conditions are adopted. (2) The speed of the beam bunching process is controlled to decrease the number of longitudinal unstable particles. The transverse focusing strength B [6] for a RFQ can be described as
B=
qλ2XV , mc 2a2
(1)
where q is the charge state of ions, λ is the RF wavelength, X is the focusing parameter, V is the inter-vane voltage, m is the relativistic mass of ions, c is the velocity of light, a is the minimum aperture of
qπ AV sin ϕs 2mc 2β 2γ
(3)
where s is the phase advance with space charge effect, I is the ⎛ 3 zq10−6 ⎞ ⎟, where beam current, ff is the ellipsoid form factor, k = ⎜ 8π ⎝ mc 2 ⎠ z¼376.73 Ω. β, γ are the relativistic velocity and gamma, A is the acceleration parameter, ϕs is synchronous phase, a and b are the transverse and longitudinal rms beam radius. From the matched beam envelope equation described in [9], the normalized rms emittance ϵ can be written as
ϵtn =
a2σtγ . λ
(4)
The method is to adjust the transverse phase advance st to limit the variation of beam size and the emittance growth. In the gentle bunching section, the B is increased to balance both the growing RF defocusing effect and space charge effect. When the beam acceleration starts, the increased beam velocity weakens RF defocusing effect, and B should accordingly fall down to allow a large bore aperture and higher acceleration gradient. The maximum value of B is decided by the maximum surface field and the average aperture. Fig. 2 shows the optimized transverse focusing strength B changing smoothly comparing with that of the traditionally almost constant B. Fig. 3 compares the transverse phase advance st and the RMS beam size for the traditional and the optimized design. In the traditional design, the transverse phase advance st reduces rapidly first in shaper section and then increases in acceleration section. Accordingly, the RMS beam size has larger variation. While in the optimized design, the transverse beam size has a small oscillation after the shaper section. The evolution of the synchronous phase and vane modulation factor m should be tuned to improve the bunching stability at the same time. Fig. 4 compares the modulation factor m and synchronous phase ϕs for the traditional and optimized design respectively. In the shaper section, which is up to the first 40 cells, the ϕs is kept at 90° in the optimized design instead of the linear increasing in traditional design. It is aimed to have a maximum longitudinal acceptance for high intensity beam and good bunching. Then the ϕs almost linearly
W.-P. Dou et al. / Nuclear Instruments and Methods in Physics Research A 827 (2016) 145–151
147
Fig. 3. Comparison of the transverse phase advance st and the RMS beam size before and after the optimization.
Fig. 4. The modulation factor m and synchronous phase ϕs versus cell number in the traditional and optimized design.
Table 1 Beam dynamics simulation results of the traditional and optimized design. Parameters
Traditional
Optimized
Frequency (MHz) Input (MeV) output energy (MeV) Beam current (mA) Vane voltage (kV)
200 0.045 0.618 100 70 0.2
200 0.045 0.618 100 70 0.2
0.327 1.46 149.2 92.8 0.31
0.365 1.46 150.3 96.5 0.28
y . norm . RMS (π mm mrad) ϵout
0.30
0.28
z . RMS ϵout
0.25
0.13
ϵtrans . norm . RMS (π mm mrad) Minimum apertures (cm) Kilpatrick factor (cm) Cavity length (cm) Beam transmission (%) x . norm . RMS (π mm mrad) ϵout
(MeV deg)
Fig. 5. The RFQ parameters as a function of the cell number in the optimized design.
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Fig. 6. The beam transmission along the RFQ and the beam phase space of the RFQ.
Fig. 7. The normalized RMS emittance variation along the RFQ.
increases until the end smoothly. At the same time, the modulation m goes up smoothly compared with the traditional design. In the end, the modulation m is lower in the main acceleration section which is compensated by the higher synchronous phase ϕs. The overall design results in a higher transmission efficiency and a lower emittance growth in a limited length.
The detailed beam dynamics simulation results of the traditional and optimized design are listed in Table 1. Compared to traditional design, beam quality of the optimized design is better at almost same cavity length and same input parameters and RF. Fig. 5 shows RFQ parameters as a function of the cell number in the optimized design. And Fig. 6(a) shows the beam envelope and Fig. 6(b) shows the phase space distributions at the entrance and exit of RFQ. The FWHM phase spread at the exit is approximately ±35°, which is the required maximum phase spread of KONUS H-DTL. The evolution of the normalized RMS emittances along the RFQ is plotted in Fig. 7, where the transverse normalized RMS emittance curves grow significantly due to very strong space charge force but weak transverse focusing in radial matching section. Then there are some acceptable growth, which is caused by the fast bunching over limited structure length requirement. In the end part of structure, the emittance decreases mainly because of the loss of out-off-bucket particles.
3. DTL section The room temperature H-mode DTL cavity based on KONUS beam dynamics is adopted because of its high shunt impedance
Fig. 8. The effective voltage and the maximum value of axis field in each accelerating gap.
W.-P. Dou et al. / Nuclear Instruments and Methods in Physics Research A 827 (2016) 145–151
Table 2 Quadruple parameters. Lens
DBA1
TBA2
TBA3
Drift. length (mm) Eff. length (mm) Filed gradient (T/m)
20 32/32 88/91
20/20 31/46/31 80.3/88.69/80.3
20/20 32/50/32 64.6/76.3/64.6
Table 3 The main parameters of DTL. Parameters
Value
RF frequency (MHz) 200 Input energy (MeV) 0.618 Input energy (MeV) 4.07 Number of gaps 18 Length (m) 1.26 Acceleration gradient (MV/m) 2.8 Transmission (%) 95.9
149
[10], which is well suited for the short length constraints of this project. KONUS beam dynamics [11,12] can overcome the conflicting requirements of the transverse defocusing, longitudinal bunching and RF accelerating. A KONUS period consists of a quadrupole triplet, a rebuncher section with negative synchronous phase of typically from 25° to 35°, and a multi cell acceleration section with zero degree synchronous phase. In the KONUS beam dynamics, the key parameters are [13] (1) the phase shift in the same cavity at transition from rebunching gaps to 0° gaps, for example at the transition 35° to 0°; (2) the starting conditions δW and δϕ of the first gap of each 0° section (where δW is energy difference between bunch center Wc and synchronous particle Ws and the δϕ is corresponding phase difference). The transition cell from rebunching gap to 0° gap belongs to the same resonator, the geometrical length of the transition cell can be adjusted by mounting a drift tube with the length L following the
Fig. 9. The input particles distribution.
150
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Fig. 10. The longitudinal and transverse envelope containing 99% particles along the DTL.
Eq. (5) below
L=
(180 + 35) βλ . 180 2
(5)
Fig. 8 shows the effective voltage of each accelerating gap and the maximum field at axis. The maximum axis field is 13.8 MV/m, which is below Kilpatrick breakdown field of 14.7 MV/m at 200 MHz. The parameters of quadrupoles are listed in Table 2. In the longitudinal direction, the quadrupole acts like a drift space and must be made as short as possible. Shorter powerful quadrupole triplet/doublet are needed for sufficient transverse focusing and minimum longitudinal defocusing. The maximum quadrupole field gradient chosen is 91 T/m, which corresponds a pole tip magnetic field of 1.09 T/m at 24 mm of aperture. And it is readily available with conventional technology. Well-balanced ratio of rebunching gap to 0° gap is typically between 1:2 and 1:4. The starting conditions δW and δϕ of the first gap of each 0° section are depend on longitudinal phase space distribution and adjusted to match beam parameters of the following sections.
4. Combined optimization The LORASR is used for the DTL design, where the transverse and longitudinal envelope are tuned by hand traditionally, but it may not be well optimized. The beam loss due to the imperfect longitudinal matching is not an issue for 2.7 m DTL, where the optimization is done by hand. The TRACEWIN is used to do the transverse optimization additionally. There are four steps
(1) Setting transverse phase advance of the last two KONUS periodic cells. (2) Finding the entrance transverse Twiss parameters of KONUS periodic structures corresponding to the optimized triplet gradient convergely. (3) The doublet was used to match the beam from RFQ to the Twiss parameters of the above mentioned KONUS period structures entrance. (4) Finally, TRACEWIN is used for the DTL beam dynamic tracking to confirm the whole design. Table 3 shows the main parameters of the DTL. Fig. 9 shows the input particles distribution coming from the RFQ exit produced by PARMTEQ. Fig. 10 shows the longitudinal and transverse envelope containing 99% particles along the DTL. At 100 mA, 99% beam envelope is smaller than the 10 mm radius of the drift tube. The energy spread is smaller than 0.5% at the DTL exit.
5. Summary The compact room-temperature injector combines a RFQ and a H-type DTL that has two KONUS periods and a doublet as internal matching cells has been designed for the project of the high intensity proton linac at Peking University. The design follows the NFSP philosophy and the KONUS principles, and the results show that it satisfy the beam quality and structure length requirements. The injector has reached a high average accelerating gradient up to 1.55 MV/m and is designed to accelerate 100 mA proton beam from 45 keV to 4 MeV at the length of 276 cm. The future plan is to
W.-P. Dou et al. / Nuclear Instruments and Methods in Physics Research A 827 (2016) 145–151
study error tolerance in details. The mechanic design and RF structure simulations in CST will come later.
Acknowledgments The authors sincerely thank Prof. U. Ratzinger at Frankfurt University and Prof. Zhihui LI at Sichuan University for their kind helps and useful discussions.
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