Chinese Physics C(HEP NP) Vol.32.No.12.Dec..2008 Studies on high order mode of bell-shaped prototype cavities MA Guang-Ming(马广明)2 ZHAO Zhen-Tang(赵振堂)1 (Shanghai Synchrotron Radiation Facility, Shanghai Institute of Applied CAS, Shanghai 201800, China) 2(Graduate University of Chinese Academy of Sciences, Abstract Aluminium and copper prototype cavities were designed to study higher order modes(HOM). An automatic field mapping system was developed with LabviEW to measure the radiofrequency(RF) charac- teristics, such as resonant frequency, Q-value, shunt impedance and electromagnetic field distribution of the higher-order modes in a model RF cavity. Two kinds of the bell-shaped cavities were measured using the field mapping system, their frequencies are 1.5 GHz and 800 MHz respectively. The fields'distributions of the monopole modes and dipole modes, as well the r/Q values, were measured Key words perturbation method, higher order modes, LabVIEW, superconducting RF PACs29.20.db,29.27.Bd 1 Introduction Here we set up a new system of HOM field map- ping, R/Q measurement, etc. This system is used to The superconducting RF cavity, which is widely study the bell-shaped cavity, the common shape of sed in particle accelerators of the world, has the ad- the superconducting cavities vantages of low RF power consumption on the cav- The prototype shown in Fig. 1(a)is the newly de- ity wall and high cavity shunt impedance. However, veloped 1.5 GHz higher harmonic cavity for the SSRF to ensure stability of the storage ring, Higher Or Some copper prototypes were also der Modes(HOM) of the cavity have to be heavily made to study the RF modes'characteristics.The other one, Fig. 1(b)is an 800 MHz cavity. Previous measurements have been done at Tsinghua Univer sity, including HOM measurement, LHC type HOM coupler 2) and CWct type HOM coupler), etc 2 Field mapping system The measurement system is a computer aided au- omatic system based on a perturbation technique, which is employed to evaluate higher order mode and shunt impedance characteristics of RF cavities. A small object is suspended on a nylon thread down the central beam pipe of the cavity and is drawn along its Fig. 1. Two kinds of prototype cavities. entire length, perturbing the electromagnetic fields (a) The 1.5 GHz single cell copper harmonic cavity shape;(b)800 MHz aluminum cavity then calculated from the resultant shift in resonant frequency. Received 10 March 2008 Supported by Science and Technology Commission of Shanghai Municipality(026505027, 036505011) 1)E-mail: zhaozt@ ssrcac c 1012-1015
Chinese Physics C (HEP & NP) Vol. 32, No. 12, Dec., 2008 Studies on high order mode of bell-shaped prototype cavities * MA Guang-Ming(ê2²) 1,2 ZHAO Zhen-Tang(ë,) 1;1) 1 (Shanghai Synchrotron Radiation Facility, Shanghai Institute of Applied Physics, CAS, Shanghai 201800, China) 2 (Graduate University of Chinese Academy of Sciences, Beijing 100049, China) Abstract Aluminium and copper prototype cavities were designed to study higher order modes (HOM). An automatic field mapping system was developed with LabVIEW to measure the radiofrequency (RF) characteristics, such as resonant frequency, Q-value, shunt impedance and electromagnetic field distribution of the higher-order modes in a model RF cavity. Two kinds of the bell-shaped cavities were measured using the field mapping system, their frequencies are 1.5 GHz and 800 MHz respectively. The fields’ distributions of the monopole modes and dipole modes, as well the R/Q values, were measured. Key words perturbation method, higher order modes, LabVIEW, superconducting RF PACS 29.20.db, 29.27.Bd 1 Introduction The superconducting RF cavity, which is widely used in particle accelerators of the world, has the advantages of low RF power consumption on the cavity wall and high cavity shunt impedance. However, to ensure stability of the storage ring, Higher Order Modes (HOM) of the cavity have to be heavily damped. Fig. 1. Two kinds of prototype cavities. (a) The 1.5 GHz single cell copper harmonic cavity shape; (b) 800 MHz aluminum cavity shape. Here we set up a new system of HOM field mapping, R/Q measurement, etc. This system is used to study the bell-shaped cavity, the common shape of the superconducting cavities. The prototype shown in Fig. 1(a) is the newly developed 1.5 GHz higher harmonic cavity for the SSRF storage ring[1] . Some copper prototypes were also made to study the RF modes’ characteristics. The other one, Fig. 1(b) is an 800 MHz cavity. Previous measurements have been done at Tsinghua University, including HOM measurement, LHC type HOM coupler[2] and CWCT type HOM coupler[3] , etc. 2 Field mapping system The measurement system is a computer aided automatic system based on a perturbation technique, which is employed to evaluate higher order mode and shunt impedance characteristics of RF cavities. A small object is suspended on a nylon thread down the central beam pipe of the cavity and is drawn along its entire length, perturbing the electromagnetic fields. The longitudinal and transverse mode impedances are then calculated from the resultant shift in resonant frequency. Received 10 March 2008 * Supported by Science and Technology Commission of Shanghai Municipality (026505027, 036505011) 1)E-mail: zhaozt@ssrc.ac.cn 1012 — 1015
MA Guang-Ming et al: Studies on high order mode of bell-shaped prototype cavities 1013 2.1 Perturbation method guage. Every module of the software is called a vir- tual Instrument (VI). The VIs are the building blocks Perturbation measurements involve drawing a for every program perturbing object(usually a bead, with radius r, per- ittivity a) through the central beam pipe of th avity, while at the same time monitoring the cav- user interface ty's resonant frequency as the object travels its en- tire length. The bead perturbs the stored energy of the resonant system by a very small amount, which function realisation(dll, VISA) frequency shift is related to the relative E-field and Perturbation measurements are performed on RF cavities to evaluate R/Q, which is a figure for the impedance of an RF cavity at resonance. The equa- tion used to solve R/Q for an RF cavity is derived from Slater's Perturbation theoryl and normal tuned motor driver control GPIB-USB circuit theory as following, 2) R =7(F+) step motor 56BYG network analyser agilent Fig. 2. The signal diagram of the field mapping S(i)√△fcos The coordination between the motion and data S(l)√△f ifor acquisition is tricky. There are two methods of deal- ing with it: one is to probe the position of the per- fo is resonant frequency without perturbation; f, is turbing object and the frequency of the network ana resonant frequency with perturbation; Af; is f; -fol lyzer in a certain time gap, while the motor is running in the i-th interval: S(i) is sign of E, axial electric with a constant speed; the other way is to stop the field in the i-th interval; B is shape factor of the motor while the computer is acquiring data. The for- bead; dz is step of the bead moved along axial di- mer method is faster le the latter one is more ac- rection; A is wavelength corresponding to fo; N is the curate. When the whole path is not total number of the steps to be measured. the latter way is preferred 2.2 Programming 2.3 Perturbing objects The measurement system consists of a network Two perturbing objects are made.“PO1#”isa analyzer which is controlled by a computer via a cylinder(3.8 mm, L=9.9 mm, thickness is 1 mm) GPIB-USB interface using the data acquisition soft- made of copper sheet. It mainly perturbs the ax- ware LabVIEW. The perturbing object(or bead)is ial field;"PO2#" is a copper disk with a diameter suspended on a nylon thread and is drawn through of 20 mm, it is used to probe the electric field com- the center of the cavity. A step-motor controlled by ponent Er. Perturbing object"PO3#", developed computer via 6030 PCI card), drives a roller assem- at Tsinghua University, is like a cage 5,which effec- bly on each side of the cavity. The network analyzer tively perturbs the axial electric field Ex while the feeds the cavity with a narrow bandwidth signal and radial field Er is nearly undisturbed a calibration measurement is made whereby all losses Higher order modes are identified by the field dis are eliminated due to lengths of cable, etc. The struc- tribution on axis. For the monopole modes, we use ture of the system is shown in Fig. 2 perturbing object "Po1#" to perturb their electric The system uses Lab ViEW to integrate the mo- field component on axis, E. For dipole modes, we tion control and data acquisition. LabViEW( is use" PO2* to perturb the electric field component a commercial high level graphical programming lan- along the radius direction, E, 2)Marchand P, Proch D. Higher Order Mode Measurements in a 5-cell Co vity at 1 GHz and Application to a Superconducting Cavity for PETRA, CERN-EF-RF 82-7. 1982 3)Beijing Hollysys Electric Technology Co. Ltd. User's Manual for 6030 Motor Control Card, 2002
No. 12 MA Guang-Ming et alµStudies on high order mode of bell-shaped prototype cavities 1013 2.1 Perturbation method Perturbation measurements involve drawing a perturbing object (usually a bead, with radius r, permittivity ε) through the central beam pipe of the cavity, while at the same time monitoring the cavity’s resonant frequency as the object travels its entire length. The bead perturbs the stored energy of the resonant system by a very small amount, which is a small shift in the resonant frequency (∆f). This frequency shift is related to the relative E-field and H-field strengths in the area of the beam[4] . Perturbation measurements are performed on RF cavities to evaluate R/Q, which is a figure for the impedance of an RF cavity at resonance. The equation used to solve R/Q for an RF cavity is derived from Slater’s Perturbation theory[4] and normal tuned circuit theory as following1,2) R Q = B f0 (I 2 1 +I 2 2 ), (1) where, I1 = XN i=1 S(i) • p ∆fi • cos 2πf0z c •dz; I2 = XN i=1 S(i) • p ∆fi • sin 2πf0z c •dz; f0 is resonant frequency without perturbation; fi is resonant frequency with perturbation; ∆fi is |fi−f0| in the i-th interval; S(i) is sign of Ez axial electric field in the i-th interval; B is shape factor of the bead; dz is step of the bead moved along axial direction; λ is wavelength corresponding to f0; N is the total number of the steps to be measured. 2.2 Programming The measurement system consists of a network analyzer which is controlled by a computer via a GPIB-USB interface using the data acquisition software LabVIEW. The perturbing object (or bead) is suspended on a nylon thread and is drawn through the center of the cavity. A step-motor controlled by computer via 6030 PCI card3) , drives a roller assembly on each side of the cavity. The network analyzer feeds the cavity with a narrow bandwidth signal and a calibration measurement is made whereby all losses are eliminated due to lengths of cable, etc. The structure of the system is shown in Fig. 2. The system uses LabVIEWr to integrate the motion control and data acquisition. LabVIEWr is a commercial high level graphical programming language. Every module of the software is called a Virtual Instrument (VI). The VIs are the building blocks for every program. Fig. 2. The signal diagram of the field mapping system. The coordination between the motion and data acquisition is tricky. There are two methods of dealing with it: one is to probe the position of the perturbing object and the frequency of the network analyzer in a certain time gap, while the motor is running with a constant speed; the other way is to stop the motor while the computer is acquiring data. The former method is faster, while the latter one is more accurate. When the whole path is not immensely large, the latter way is preferred. 2.3 Perturbing objects Two perturbing objects are made. “PO1#” is a cylinder (φ3.8 mm, L=9.9 mm, thickness is 1 mm) made of copper sheet. It mainly perturbs the axial field; “PO2#” is a copper disk with a diameter of 20 mm, it is used to probe the electric field component Er. Perturbing object “PO3#”, developed at Tsinghua University, is like a cage[5] , which effectively perturbs the axial electric field Ez while the radial field Er is nearly undisturbed. Higher order modes are identified by the field distribution on axis. For the monopole modes, we use perturbing object “PO1#” to perturb their electric field component on axis, Ez. For dipole modes, we use “PO2#” to perturb the electric field component along the radius direction, Er. 1) Tong D. Higher Order Mode Measurements on the HERA Superconducting Cavity Modules, DESY-M-87-05. 1987. 2) Marchand P, Proch D. Higher Order Mode Measurements in a 5-cell Copper Cavity at 1 GHz and Application to a Superconducting Cavity for PETRA, CERN-EF-RF 82-7. 1982. 3) Beijing Hollysys Electric Technology Co. Ltd. User’s Manual for 6030 Motor Control Card, 2002
1014 Chinese Physics C(HEP NP) quality factors(Q), and R/Q values, etc. Calcula- 3 Calculation and experiment tions including its on-axis field distribution, R/Q, etc, 3. 1 1.5 GHz single cell higher harmonic were performed using MAFIA before measurements cavity In Fig. 3, the longitudinal monopole modes are calculated by MAFIA, CLANS, etc. The comparison We have investigated the high order modes up to of calculation and experiment shows that most modes Hz in the cavity and measured their frequencies, can be identified, as shown in Fig 3 E(norm)-tmOl 06 0.5 1.5 E(norm)-tm05 E(norm)-tmo6 0 0 0.2 0.15-0050.050.15 z/mm(×10) -1.0 0.15-0.050.050.15 (x102) z/mm Fig. 3. Electric fields distribution of the monopole modes in the single cell 1.5 GHz higher harmonic cavity A 0.4 2哥 4 E03(norm)-disk 0.8 04 0.4 E04(norm)-disk 2-s E05(norm)-disk (×10) Fig. 4. The lowest two dipole modes of the sing cell 1.5 GHz higher harmonic cavity
1014 Chinese Physics C (HEP & NP) Vol. 32 3 Calculation and experiment 3.1 1.5 GHz single cell higher harmonic cavity We have investigated the high order modes up to 3 GHz in the cavity and measured their frequencies, quality factors (Q), and R/Q values, etc. Calculations including its on-axis field distribution, R/Q, etc, were performed using MAFIA before measurements. In Fig. 3, the longitudinal monopole modes are calculated by MAFIA, CLANS, etc. The comparison of calculation and experiment shows that most modes can be identified, as shown in Fig. 3. Fig. 3. Electric fields distribution of the monopole modes in the single cell 1.5 GHz higher harmonic cavity. Fig. 4. The lowest two dipole modes of the sing cell 1.5 GHz higher harmonic cavity
IA Guang-Ming et al: Studies on high order mode of bell-shaped prototype cavities 1015 The problem of the lowest dipole modes is a surement are in Fig. 5. They are as expected, but lemma of the"single-mode" cavity. Because they do not exactly correspond to the calculation result don't propagate out the cell even the beam pipe's ra- The reasons are due to the bead's vibration during the dius is increased. Since the dipole modes may deflect measurement and the errors of positioning the bead. electrons off the synchronous orbit, it's an important The R/Q calculation method needs to be studied fur- Issue In the experiment, we found the two modes, each ne has two degenerate modes. Their electric fields d Er component along the axis are shown in Fig 4 800 MHz bell-shaped HOM These two modes cant propogate along the beam 60 pipe so that they can't be damped by the ferrite HOm calculation O measurement (higher order modes)damper. In order to damp these two modes, special treatment of the beam pipe need 」。。 to be applied, e. g. to enlarge the beam pipe like KeK B cavity, or to flute the beam pipe like CESR cavity 6 frequency/ GHz Fig. 5. Monopole mode results 3.2 800 MHz bell-shaped aluminum cavity We also performed a test of the 80 4 Conclusion and discussion aped aluminum cavity. The following steps were taken to measure the hom characteristics The field mapping system has been a 1)Clean the cavity parts using ethanol and ace- The results of the cavities tests demonstrate that ts main functions have beer 2)Make bead, i.e. perturbation object, and scale kinds of cavities are measured by using this system. the perturbation object's shape factor. The shape The system can be well used to identify the differ factor scaling is performed like this: we use Super- ent modes in the cavities. It roughly provides the Fish or MAFIA to calculate the fundamental mode's monopole modes'R/Q values. More work will be R/Q first, and then adjust the factor until the funda- done to improve the systen mental's measurement results are consistent with the calculation results The authors would like to thank Prof. TONG 3) Perform the "bead-pull "experiment, identify Dechun, as well as TAO Xiaokui, from Tsinghua Uni each mode. see Fig 3: versity for their enthusiastic help. The rF group col 4) Measure the mode's r/Q value. leagues of ssrf are also acknowledged for their sup- The results of 1* bell-shaped cavity R/Q mea- port References 3 LIANG Y Z. Research on HOM Coup monic Cavity. Master thesis, at El partment, Beijing: Tsinghua Univer 1 MA G, ZHAO Z, LIU J. Chinese Physics C, 2008, 32(4): 4 Maier L C, Jr, Slater J C. Journal of Applied Physics, 1952,23:68 2 TAO X K, CHEN H B, TONG D C. Study of HOM Cou- 5 XIAO L, LIANG Y Z, TONG D et al. NIM A, 2001, 463 plers on an 800 MHz Prototype Cavity. In: Proceedings of 8693 he Asian Particle Accelerator Conference. Beijing, China, 6 Padamsee, Barnes P et al. Particle Accelerators, 1992, 40 2001,746-748
No. 12 MA Guang-Ming et alµStudies on high order mode of bell-shaped prototype cavities 1015 The problem of the lowest dipole modes is a dilemma of the “single-mode” cavity. Because they don’t propagate out the cell even the beam pipe’s radius is increased. Since the dipole modes may deflect electrons off the synchronous orbit, it’s an important issue. In the experiment, we found the two modes, each one has two degenerate modes. Their electric fields and Er component along the axis are shown in Fig. 4. These two modes can’t propogate along the beam pipe so that they can’t be damped by the ferrite HOM (higher order modes) damper. In order to damp these two modes, special treatment of the beam pipe need to be applied, e.g. to enlarge the beam pipe like KEKB cavity, or to flute the beam pipe like CESR cavity [6] . 3.2 800 MHz bell-shaped aluminum cavity We also performed a test of the 800 MHz bellshaped aluminum cavity. The following steps were taken to measure the HOM characteristics: 1) Clean the cavity parts using ethanol and acetone; 2) Make bead, i.e. perturbation object, and scale the perturbation object’s shape factor. The shape factor scaling is performed like this: we use SuperFish or MAFIA to calculate the fundamental mode’s R/Q first, and then adjust the factor until the fundamental’s measurement results are consistent with the calculation results. 3) Perform the “bead-pull” experiment, identify each mode, see Fig. 3; 4) Measure the mode’s R/Q value. The results of 1# bell-shaped cavity R/Q measurement are in Fig. 5. They are as expected, but do not exactly correspond to the calculation results. The reasons are due to the bead’s vibration during the measurement and the errors of positioning the bead. The R/Q calculation method needs to be studied further. Fig. 5. Monopole mode results. 4 Conclusion and discussion The field mapping system has been developed. The results of the cavities tests demonstrate that its main functions have been realized. Two different kinds of cavities are measured by using this system. The system can be well used to identify the different modes in the cavities. It roughly provides the monopole modes’ R/Q values. More work will be done to improve the system. The authors would like to thank Prof. TONG Dechun, as well as TAO Xiaokui, from Tsinghua University for their enthusiastic help. The RF group colleagues of SSRF are also acknowledged for their support. References 1 MA G, ZHAO Z, LIU J. Chinese Physics C, 2008, 32(4): 275 2 TAO X K, CHEN H B, TONG D C. Study of HOM Couplers on an 800 MHz Prototype Cavity. In: Proceedings of the Asian Particle Accelerator Conference. Beijing, China, 2001, 746—748 3 LIANG Y Z. Research on HOM Coupler for Higher Harmonic Cavity. Master thesis, at Engineering Physics Department, Beijing: Tsinghua University, 2003 4 Maier L C, Jr., Slater J C. Journal of Applied Physics, 1952, 23: 68 5 XIAO L, LIANG Y Z, TONG D et al. NIM A, 2001, 463: 86—93 6 Padamsee, Barnes P et al. Particle Accelerators, 1992, 40: 17
