Beam dynamics, RF measurement and commissioning of a CW heavy ion IH-DTL

Beam dynamics, RF measurement and commissioning of a CW heavy ion IH-DTL 1 2 first-author 1 1 2 1 1 1 2 1 1 2 1 2 1 1 1 1 corresp Corresponding author, yinxj@impcas.ac.cn Corresponding author, yinxj@impcas.ac.cn yinxj@impcas.ac.cn Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China University of Chinese Academy of Sciences, Beijing 100049, China University of Chinese Academy of Sciences, Beijing 100049, China A 53.667 MHz CW (continuous-wave) heavy ion IH-DTL has been designed for the SSC-LINAC injector of HIRFL-CSR (Heavy Ions Research Facility at Lanzhou-Cooling Storage Ring). It accelerates ions with maximum mass to charge ratio of 7.0 from 143 keV/u to 295 keV/u. Low power RF measurement of the IH-DTL1 has been carried out to investigate the RF performance and the quality of the electric field distribution on the beam axis. The measured Q 0 value and the shunt impedance are 10400 and 198 M Ω /m, respectively. The electric field distributions on and around the beam axis were evaluated and compared with the design value. By a new approach, the dipole field component is also estimated. The beam dynamics simulation using measured field distribution was presented in this paper. Based on the dynamics analysis both in transverse and longitudinal phase space, the field distribution can meet the design requirement. Finally, the RF conditioning and very first beam commissioning on the IH-DTL1 were finished. The beam test results agree well with the simulation results, what’s more, the property of the variable output beam energy about the separated functions DTL was verified. Linac RF measurement Beam dynamic simulation Commissioning 1 Introduction 1 In HIRFL-CSR [ 1 1 ], the SFC (Sector Focusing Cyclotron) as the only injector can provide heavy ion beams for CSR or SSC (Separated Sector Cyclotron) respectively, as shown in Fig. 1 Fig. 1 . Such a structure restricts the annual operation time. Moreover, the extraction beam current of the SFC is only 0.1puA for very heavy ions or 1puA for lighter heavy ions [ 2 2 ], which limits the overall performance of HIRFL-CSR. So a new CW high current heavy ion linac injector named SSC-LINAC has been designed to improve the operation efficiency for HIRFL [ 3 3 ]. This linac mainly consists of an ECRIS (Electron Cyclotron Resonance Ion Source), a 4-rod RFQ [ 4 4 ], and 4 IH-DTLs, as shown in Fig. 2 Fig. 2 . The actual normalized horizontal acceptance of the SSC is very small, only 0.42 π mm.mrad [ 2 2 ]. With the SSC-LINAC, the injection beam current of the SSC can be increased more than 10 times compared to the old injector SFC. By the way, the vertical normalized acceptance of the SSC is 6 times that of the horizontal one, which is big enough for the beam injection. Considering the performance enhancement of the ECR ion source, and the efficiency improvement of SSC [ 5 5 ], the designed normalized acceptance of SSC-LINAC is 1.0 π mm.mrad. The first IH-DTL cavity which can accelerate the 238 U 34+ ion from 143 keV/u to 295 keV/u has been designed and fabricated. The parameters of the IH-DTL1 including 10 accelerating gaps are listed in Table 1 Table 1 . The low level RF measurement of the IH-DTL1 was performed to get the RF performance of the cavity, such as resonant frequency, Q 0 value, power coupler property at low level status, and frequency tuning range, then to evaluate the field distribution of the IH-DTL1. The key point of this paper is the analysis of the field distribution. The measurement procedure and results are introduced firstly. Furthermore, the beam dynamic simulation using the measurement results is described in detail. After the RF conditioning of the IH-DTL1, the first beam commissioning of the mixed heavy ion beam with 12 C 3+ and 16 O 4+ was performed to check the performance of the IH-DTL1. The beam transmission efficiency and the beam transverse emittance values were good for the first beam commissioning. 1 1 Parameters 1 1 Values 1 1 Frequency (MHz) 1 1 53.667 1 1 Design ion 1 1 238 U 34+ 1 1 Ratio of mass to charge 1 1 3-7 1 1 Beam current (emA) 1 1 0.5 1 1 Input energy (keV/u) 1 1 143 1 1 Output energy (keV/u) 1 1 295 1 1 Duty factor (%) 1 1 100 1 1 Transverse normalized acceptance ( π mm.mrad) 1 1 1.0 1 1 Gap number 1 1 10 1 1 Average gap length (mm) 1 1 25 1 1 Gap voltage (kV) 1 1 165 1 1 Kp factor 1 1 1.5 1 1 Drift tube inner radii (mm) 1 1 17.00 1 1 Cavity length (inner wall) (mm) 1 1 588.82 1 1 Cavity diameter (inner wall) (mm) 1 1 1060.00 2 Design and fabrication of the IH-DTL1 1 Compared with the conventional βλ type DTL for the desire energy and frequency range, the IH type DTL is much more superior about RF power efficiency. The IH structure has been chosen because of its high shunt impedance at several tens MHz [ 6 6 ]. For the 53.667 MHz IH-DTL cavity, the effective shunt impedances are about 200 M Ω /m for the 238 U 34+ ion with the relativity factor, β , range of 0.02-0.05. LINREV code [ 7 7 ] was used for preliminary dynamic design of the DTL section. The synchronous phases of the first 8 cells are 0° mainly for accelerating, and in the last 2 cells they are -45° to provide longitudinal focusing. This design strategy is similar to the KONUS [ 8 8 , 9 9 ] beam dynamic technique. Meanwhile, the utilization of the separated functions characteristic makes the enough field error tolerance. Figure 3 Figure 3 shows the phase space distributions at the exit of the RFQ[ 4 4 ]. The corresponding emittance and twiss parameters are listed in Table 2 Table 2 . Between the RFQ and the IH-DTL1, there is a medium energy beam transport (MEBT) line, which consists of 6 quadrupole magnets for beam matching in transverse phase space and a spiral stem buncher with 4 gaps for beam matching in longitudinal phase space. The results of beam dynamic design about the MEBT and the IH-DTL1 are shown in Fig. 4 Fig. 4 . The beam phase space distributions of the entrance and exit of the IH-DTL1 are shown in Fig. 5 Fig. 5 . The transverse emittance growth is about 7%. 1 1 Parameters 1 1 Values 1 1 є x , n ,rms ( π mm mrad) 1 1 0.2 1 1 α x 1 1 -1.57 1 1 β x (mm/mrad) 1 1 0.20 1 1 є y , n ,rms ( π mm mrad) 1 1 0.2 1 1 α y 1 1 1.55 1 1 β y (mm/mrad) 1 1 0.24 1 1 ϵ z ( π Deg keV/u) 1 1 90 1 1 α z 1 1 0 1 1 β z (Deg/(keV/u)) 1 1 13.6 RF design and optimization of the IH-DTL1 by CST-MWS has been discussed in previous paper [ 10 10 , 11 11 ]. Manufacturing of the first IH-DTL cavity has been finished. Fig. 6 Fig. 6 shows the CST model and the IH-DTL1 cavity. In this cavity, 9 drift tubes are supported by 9 stems which are alternately located on both sides of a T shape bridge and all stems contain a water cooling channel. All the structures were fabricated from 99.97% OFE copper except the cavity shell structure. Vacuum brazing technology was adopted for welding the stems and the T shape bridge to keep the performance in vacuum, machine accuracy, and surface roughness. The shell was made of high carbon steel and the inner surface was copper electroplated with the thickness of approximately 0.2 mm. All the surface was polished to make the roughness batter than 1 μM. Two half drift tubes were mounted on the end walls. All the gap and tube's lengths were carefully optimized to match the TTF of the dynamic design. The machining accuracy of the tubes is better than 0.02 mm. Fine installation of the drift tubes was carried out by some purposed-made tools for controlling the axiality and gap length of the tubes. During the process of the tubes installation, a Leica AT401 laser tracker and a purpose-made optical target which can be held on the tube were used to make the transverse and longitudinal installation accuracy better than 60 μM, as shown in Fig. 7 Fig. 7 . The position errors can be negligible comparing with the average cell length of 58.6mm. By the way, moving the optical target on the whole surfaces of the tube and then processing all the data recorded by the laser tracker in the subsidiary software, the position and angle information in 3 dimensional space can be obtained. A magnetic loop power coupler has been designed and manufactured, which can deliver RF power of up to 20 kW through the RF coaxial transmission to the cavity, as shown in Fig. 8 Fig. 8 . Considering the aluminum oxide ceramics and the water cooling channel, this power coupler was welded by a 4-step decreased temperature vacuum brazing technology. The size of the coupler ring was exactly computed and left the proper allowance. One fine tuner which compensates for frequency shift during operation is driven by a servo motor. And a fixed coarse tuner is installed opposite of the fine tuner in the DTL cavity to bring the resonant frequency near to the designed value 53.667 MHz. 3 RF measurement and data analysis 1 3.1 Device and method of the RF measurement 2 Agilent E5061B VNA (Vector Network Analyzer) was used as the main measure instrument. The signal cables connected to the coupler and the pickup were attached to the port 1 and port 2 of the VNA, respectively. In the measurement of the electric field of the IH-DTL1, the perturbation method [ 12 12 , 13 13 ] was adopted. According to the perturbation theory, the phase shift, ΔΦ, indicates the electric field, <math id="M1"><mover accent="true"><mi>E</mi><mo>¯</mo></mover></math> , by: <math display="block" id="M2"><mrow><mover accent="true"><mi>E</mi><mo>¯</mo></mover><mo>=</mo><msqrt><mrow><mfrac><mrow><mn>4</mn><mi>P</mi><mi>Δ</mi><mi>ϕ</mi></mrow><mrow><mn>3</mn><msub><mi>ω</mi><mn>0</mn></msub><mi>Δ</mi><mi>V</mi></mrow></mfrac><mtext> </mtext><mfrac><mrow><msub><mi>ϵ</mi><mtext>r</mtext></msub><mo>+</mo><mn>2</mn></mrow><mrow><mo stretchy="false">(</mo><msub><mi>ϵ</mi><mtext>r</mtext></msub><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><msub><mi>ϵ</mi><mn>0</mn></msub></mrow></mfrac></mrow></msqrt><mn>,</mn></mrow></math> where P =1 mW is the average output power of the VNA, and ω 0 is the output circular frequency. Then if the size of the bead Δ V is small enough, we can approximately consider <math id="M3"><mrow><mi>E</mi><mo>=</mo><mover accent="true"><mi>E</mi><mo>¯</mo></mover></mrow></math> , where E is the electric field at the center of the bead. Several PTFE (polytetrafluoroethylene) cylinder beads were considered, and towed by a high strength Nomex line with the diameter of 0.3 mm. This measurement system is driven by a step motor. The VNA records one phase datum in 0.02 s and the tempo of the bead is 21.42±0.02 mm/s. So we can transform the achieved data of equal time intervals into equal distance intervals. The time of VNA recording and the bead moving are both 32 s, and the two devices should be triggered at same time. Throughout the process of measurement, the temperature and humidity of the environment fluctuate in the range of 10.0∼11.5 ℃ and 50∼60% respectively. During the field distribution measurement, the electromagnetic interference and mechanical vibration should be avoided. By perturbation method, usually the phase shift below 5 can ensure the precision of the measurement. Finally, we choose a 5mm bead in length with Φ 4.00 mm and the maximum phase shift is 3.5°. 3.2 RF performance of DTL1 cavity 2 The S 11 parameter of the power coupler has been tuned to better than -40 dB and the S 21 parameters of the two pickups are both about -50 dB finally. The frequency range of the cavity with coarse tuner is 1.02 MHz, as shown in Fig. 9 Fig. 9 , and completely covers the operation frequency, 53.667 MHz. The fine tuner can tune the resonant frequency about 140 kHz in 100 mm moving distance with no effect on field distribution along the beam axis. The measured Q 0 value of this cavity is 10400 at operation frequency finally, which is 85% of the simulation result by CST-MWS. Then the shunt impedance of the DTL cavity is 198 MΩ/m which was found by the measured Q 0 and the simulated R/Q value. Then we can evaluate that 18.4 kW RF power should be required if the U 34+ beam was accelerated successfully in our case. 3.3 Data analysis and beam dynamics benchmarks 2 In the measurement, background noise of the phase shift is less than ±0.04°. For the whole sets of the measured data, we used the Fourier transform filter high frequency noise. Because the bead is not infinitely small, the measurement accuracy in the low field strength area is not as good as the high field strength area. Lastly the data are averaged and compared with the designed field in the beam dynamic. For the benchmarking, the measured field and the designed field on the central axis are both normalized by the maximum value of E-field on the beam axis, as shown in Fig. 10 Fig. 10 . As can be seen, the measured fields match the simulation field very well. Figure 11 Figure 11 shows the normalized cell voltage differences between measured and designed value. These voltage values can be imported into BEAMPATH code [ 14 14 ] for beam tracking. The beam dynamics simulation of 238 U 34+ with 0.5 emA beam current was performed using the designed and measured field distribution respectively, and the beam phase space distributions at the exit of the IH-DTL1 were almost the same. So the field distribution of the IH-DTL1 can meet the beam dynamic design requirements. 3.4 The dynamics effects of off-axis fields analyze 2 Since the structure of the IH-DTL is symmetry in horizontal direction and asymmetry in vertical, it is hard to remove the vertical dipole field. In the RF design, the vertical dipole field has been optimized lower than 3.0% of the longitudinal field. As shown in Fig. 12 Fig. 12 , in the vertical center plane, the electric field distribution is asymmetrical about the centerline, and the longitudinal position of the field peak is variant with different vertical positions. The slope of the line formed by the peak field position can be used as the evidence of the dipole field quantity. So the fields on the vertical center plane were measured and the peak positions of the measurement data relative to the each gap center are compared with the CST-MWS simulation results, which are shown in Figs. 13 Figs. 13 and 14 14 . The dislocations of the peaks match the CST-MWS simulation results except those in the 9th gap. However, the dislocations in the 9th gap are smaller than the simulation data, which indicates the actual dipole field is not larger than the simulation result in the 9th gap. So the 3D simulation fields can represent the actual field in this IH-DTL for investigating the beam dynamics effects of the dipole field. This dipole field would cause the particle motion offset in the transverse plane for the average value of the vertical component of the E-field being not equal to 0 and should be investigated carefully for stable operation. The particle tracking of the beam center was performed using a 3D electromagnetic field and the transverse position offset is shown in Fig. 15 Fig. 15 . It can be found clearly that the position offset in the vertical direction is 0.27 mm, which is much larger than that of the horizontal plane, and the deflection angle is about 0.5 mrad in vertical direction. The beam phase space distribution at the exit of the IH-DTL1 is shown in Fig. 16 Fig. 16 . Because the dipole field component only exists in the vertical direction, the beam emittance of vertical direction is about 5% bigger than it in horizontal. By the vertical steering magnet at the entrance of the IH-DTL1, the correction of 0.3 mrad on the inject beam can make the beam center be close to the beam axis in the vertical, as shown in Fig. 17 Fig. 17 . But the beam emittance in the vertical is still bigger than it in the horizontal. Anyhow, to satisfy the operating requirement, the sets of correcting magnets need to be installed both at the entrance and exit of the IH-DTL1. 3.5 Acceptance and output beam energy study 2 The energy acceptance range of the DTL1 must be studied carefully because the output energy of the RFQ may be a little higher or lower than the design value [ 15 15 ]. We set ±2% errors about the input energy of the IH-DTL1 in this study. Generally, when the input energy of the DTL is changed, the beam parameters at the exit should be different from the desired value. But for the separated function DTL, the RF phase and power can be tuned easily to rematch the requirement of the following acceleration structure. As shown in Fig. 18 Fig. 18 , when the center energy of the IH-DTL1 inject beam is 140 keV/u and the beam inject phase at the original design value which corresponds the green square dot, the extraction beam’s energy is a little higher than the desired value, and the longitudinal phase space distribution of the extraction beam is shown in the left of Fig. 20 Fig. 20 . The transverse beam envelope is very small because the shortage of the inject energy lead to the beam phase in the acceleration gap slipping backward and the transverse RF focusing strength enhancing. The enhancing of the transverse RF focusing strength means the fading of the longitudinal constraint of the RF field. So the longitudinal emittance and bunch length are larger than the desired value. By tuning the inject phase forward and keeping the inject energy 140 keV/u, the energy, longitudinal emittance, and bunch length of the extraction beam become smaller and smaller, at the same time, the transverse envelope is growing. When the inject phase is tuned to -9, which corresponds the red square dot in the Fig. 18 Fig. 18 , the transverse envelope, longitudinal emittance, and bunch length of the extraction beam become acceptable and the beam energy can ensure the injection requirement of the following accelerators, as shown in the right side of Fig. 20 Fig. 20 . Same as above, Fig. 19 Fig. 19 shows that when the injection beam’s energy is 146 keV/u, the the transverse envelope, longitudinal emittance, and bunch length of the extraction beam vary with the different inject phase, and the longitudinal phase space distributions of the extraction beam correspond the green and red square dots, which represent that the injection phase is the original value and the optimized one respectively. These are shown in Fig. 21 Fig. 21 . In brief, the energy acceptance of the IH-DTL is enough to overcome the ±2% error of output energy in RFQ. Moreover, it is easier to inject into the post accelerators if the output beam energy of the IH-DTL1 can be adjusted in a certain range. This can be realized by tuning the phase and global gap voltage. The output energy of the IH-DTL1 can be adjusted from 260 to 300 keV/u, with the longitudinal emittance and transmission efficiency in a acceptable range, for U 34+ as shown in Fig. 22 Fig. 22 . For the inject phase being -0.2 rad, the output beam energy can be tuned from 260 keV/u to 280 keV/u with the cavity power from 10 kW to 15 kW, and the corresponding longitudinal emittance and the transmission efficiency are both very good. In the same way, setting the inject phase to be 0.3 rad, the extraction beam’s energy can be larger than 300 keV/u and the corresponding longitudinal emittance and the transmission efficiency are both acceptable if the cavity power is above 20 kW. Moreover, keeping the injection phase and increasing the cavity power up to a value higher than desired, the output beam’s energy changes little if the cavity power continue increasing. This rule can be used for distinguishing whether the cavity power is too high for the design value. Considering the beam commissioning, the RF power can be decided distinctly for each kind of ion from above RF measurement result, but the accurate cavity phase must be tuned by manual work. Thus the simulation results can give the guide for the beam commissioning based on the beam energy spread and bunch length signal obtained by the beam diagnostics system. 4 The first beam commissioning 1 4.1 IH-DTL1 RF conditioning 2 The RF conditioning was started from pulse mode at the duty 1% when the DTL cavity vacuum was 1.0×10 -5 Pa. When we turned on the RF power at the level from 0.1 kW to 1 kW, the RF power unstable of the IH-DTL1 cavity began and the power reflection appeared, which indicated some discharge phenomenon occurring. In addition, the operating stability of the solid-state 40kW power amplifier of IH-DTL1 was poor in the begining. After about a half month of conditioning, the stability of the RF amplifier was improved. One month later, the RF power up to 18 kW with duty 20% was transmitted into the cavity. The cavity vacuum is continuously improving and after 2 months of pumping, the pressure is better than 1.0×10 -5 Pa. After then the IH-DTL1’s RF conditioning shifted to CW mode from lower power. It should be noted that the water cooling design was not perfect on the cavity wall and the highest temperature of the cavity wall became 67 ℃ in the up and bottom flanges where the magnetic fields were high, which was much higher than expected when the cavity power was 15 kW with CW mode. So we decided to suspend the higher power conditioning, and to design 4 additional cooling plates on the cavity wall. At the same time, we began to prepare the first beam commissioning of the IH-DTL1. 4.2 Experimental setup 2 The experimental setup used for the beam commissioning of the IH-DTL1 is shown in Fig. 23 Fig. 23 . It consists of an ECRIS, a low energy beam transport (LEBT) line, and a CW 4-rods RFQ. The LEBT system includes 90 bending magnets, 4 matching quadrupoles, and two solenoids for the injection matching of the RFQ. A beam diagnostic system including wire scanners and a Faraday cup was installed in the LEBT. The LEBT and the RFQ were used in our previous research work and had been described in Ref. [ 15 15 ]. The IH-DTL1 was connected to the RFQ through the medium energy beam transport (MEBT)line. A spiral stem rebuncher with 4 gaps was successuflly developed and installed in the MEBT. A beam diagnostic platform was installed after the IH-DTL1, which includes a Faraday cup, two slit-wire type transverse emittance measurement devices, and a silicon detector for energy spread measurement. A Low Level Radio Frequency (LLRF) control system was developed to operate the RF cavity in a self-constant mode including the frequency, phase, and power. 4.3 Beam commissioning results 2 When the beam was injected into the IH-DTL1, the power of the rebuncher and IH-DTL1 were fixed at the design values which were obtained by calculating through the RF measurement values. The operating phases were scanned carefully and fixed to insure the signals of the BPM behind the IH-DTL1 where most clear, as shown in Fig. 24 Fig. 24 . It should be noted that the combined beam with 12 C 3+ and 16 O 4+ ions were firstly used in the beam commissioning. The reason for accelerating the combined beam is to make preparations of the future energy spread detector’s calibration. The front end section including ECR, LEBT, and RFQ were tuned to transport approximately 78 euA this combined ions to the IH-DTL1 entrance, and the beam current was 63 euA on the Faraday cup at a distance of 1.2 m from the exit of the IH-DTL1, which correspond to the 80% transmission efficiency. The particle energy was measured with the time of flight method using two Beam Position Monitors (BPM), separated by a distance of 563 mm. By manually tuning the phase of IH-DTL1, the time of flight of beam between the two BPMs changed from 73.5 ns to 75.6 ns, which correspond the beam energy of 304.2 keV/u and 287.5 keV/u by calculating. Energy spectrums of C 3+ and O 4+ were measured, as shown in Fig. 25 Fig. 25 . With different RF power of IH-DTL1, output beam energy of the IH-DTL1 can be adjusted conspicuously. By tuning the RF phase of the IH-DTL1, the output beam energy can be changed slightly. The measured HWHM energy spread values of the IH-DTL1 is approximately 5%. Figure 26 Figure 26 shows emittance measurement results of the combined beam. The measured values of the normalized RMS emittance in the horizontal and vertical plane were 0.139 π .mm.mrad and 0.157 π .mm.mrad, respectively. The vertical emittance is a little larger than the horizontal one, because of the vertical dipole field component in the IH-DTL1 and the beam and lens alignment of the last lens. The detail information and result analysis of the beam commissioning will be published in the near future. 5 Conclusion 1 The low power RF test of the SSC-LINAC DTL1 has been finished. The frequency of the cavity without any tuning is 54.135 MHz, which is 470 kHz higher than our operation frequency, 53.667MHz. But such frequency disparity is easily tuned by the coarse tuner plunges. Based on the measured shunt impedance, 18.4 kW RF power will be required for U 34+ beam. Beam dynamic simulations using the measured results show that the real field distribution can match the dynamics requirement. Acceptances in transverse and longitudinal plane are both large enough. And the output energy of the DTL1 can be adjusted in a some ranges around the design 295keV/u by the beam dynamic simulation. This is the superiority of the separate function DTL. The CW mode high power RF conditioning of the IH-DTL1 is partially achieved, and some problems about the cavity are found out and handing. The first beam commissioning of the IH-DTL1 in CW mode was performed with an acceptable result. References J.W. Xia , W.L. Zhan , B.W. Wei , et al . The heavy ion cooler-storage-ring project (HIRFL-CSR) at Lanzhou[J] . Nucl. Instrum. Meth. A 488 , 11 ( 2002 ). doi: 10.1016/S0168-9002(02)00475-8 http://doi.org/10.1016/S0168-9002(02)00475-8 The heavy ion cooler-storage-ring project (HIRFL-CSR) at Lanzhou[J] X.N. Li , Y.J. Yuan , C. Xiao , et al ., Beam dynamics simulation of HEBT for the SSC-linac injector . Chinese Phy. C 36 , 11 ( 2012 ). doi: 10.1088/1674-1137/36/11/016 http://doi.org/10.1088/1674-1137/36/11/016 Beam dynamics simulation of HEBT for the SSC-linac injector Y. He , Z.J. Wang , C. Xiao , et al ., Conceptual design of linear injector for SSC of hirfl . in Proceedings of the 25th International Linear Accelerator Conference, LINAC-2010, Tsukuba, Japan ( KEK , Tsukuba, Japan , 2010 ), p. 482 . Conceptual design of linear injector for SSC of hirfl G. Liu , Y.R. Lu , Z. Wang , et al . Design of a CW high charge state heavy ion RFQ for SSC-LINAC . Nucl. Instrum. Meth. A 701 , 186 ( 2013 ). doi: 10.1016/j.nima.2012.11.017 http://doi.org/10.1016/j.nima.2012.11.017 Design of a CW high charge state heavy ion RFQ for SSC-LINAC Y.J. Yuan , J.W. Xia . Present status of storage rings at HIRFL . In: 8th International Conference on Nuclear Physics at Storage Rings (Stori11)Laboratori Nazionali di Frascati dell INFN . Frascati : CERN , ( 2011 ) Present status of storage rings at HIRFL U. Ratzinger , in CERN Accelerator School 2000 ( CERN , Geneva, Switzerland , 2005 ), ( CERN Yellow Report No. 2005-003 ). CERN Accelerator School 2000 O. Kamigaito , M. Kase , N. Sakamoto , et al ., Construction of a booster linac for the RIKEN heavy-ion linac . Rev. Sci. Instrum . 76 , 013306 ( 2005 ). doi: 10.1063/1.1834708 http://doi.org/10.1063/1.1834708 Construction of a booster linac for the RIKEN heavy-ion linac U. Ratzinger , in Proceedings of the 1991 Particle Accelerator Conference, San Francisco, CA, 1991 ( IEEE , New York , 1991 ). T.P. Wangler , Principles of RF linear Accelerators ( 2ed Completely Revised and Enlarged Edition ) ( John Wiley & Sons, Inc. , New York , 1998 ), p. 197 . Principles of RF linear Accelerators Computer Simulation Technology (CST) , Micro Wave Studio https://www.cst.com/ https://www.cst.com/ . X.N. Du , Y. He , Y.J. Yuan , et al . Optimization of the three-dimensional electric field in IH-DTL . Chinese Phy. C , 36 , 5 ( 2012 ). doi: 10.1088/1674-1137/36/5/013 http://doi.org/10.1088/1674-1137/36/5/013 Optimization of the three-dimensional electric field in IH-DTL G. Liu , Y.R. Lu , X.J. Yin , et al . Sci . China Phys. Mech . 57 , 1311 - 1317 ( 2014 ). doi: 10.1007/s11433-014-5418-0 http://doi.org/10.1007/s11433-014-5418-0 Sci H. Klein . Basic concept I . In: Proceeding of CERN Accelerator School (CERN 92-933) . Geneve : CERN , 1992 . 97 - 124 . Basic concept I Y.K. Batygin , Particle-in-cell code BEAMPATH for beam dynamics simulations in linear accelerators and beamlines . Nucl. Instrum. Meth. A 539 , 455 ( 2005 ). doi: 10.1016/j.nima.2004.10.029 http://doi.org/10.1016/j.nima.2004.10.029 Particle-in-cell code BEAMPATH for beam dynamics simulations in linear accelerators and beamlines X.J. Yin , Y.J. Yuan , J.W. Xia , et al . Design, fabrication, and beam commissioning of a continuous-wave four-rod rf quadrupole . Phys. Rev. Accel. Beams 19 , 010402 ( 2016 ). doi: 10.1103/PhysRevAccelBeams.19.010402 http://doi.org/10.1103/PhysRevAccelBeams.19.010402 Design, fabrication, and beam commissioning of a continuous-wave four-rod rf quadrupole 10.1007/s41365-018-0373-5 This work was supported by the National Natural Science Foundation of China (Nos. 11375243 and 11405237) and the Guangdong Innovative and Entrepreneurial Research Team Program (No. 2016 ZT06G373). 2017-05-13 2017-07-11 2017-07-14 2018-02-26 2018-03-01 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2018 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-018-0373-5 http://dx.doi.org/10.1007/s41365-018-0373-5 . 2018 Nuclear Science and Techniques 03 29