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, 2002No. 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, per￾mittivity ε) through the central beam pipe of the cavity, while at the same time monitoring the cav￾ity’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 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 equa￾tion 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 di￾rection; 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 soft￾ware 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 assem￾bly 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 struc￾ture of the system is shown in Fig. 2. The system uses LabVIEWr to integrate the mo￾tion control and data acquisition. LabVIEWr is a commercial high level graphical programming lan￾guage. Every module of the software is called a Vir￾tual 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 deal￾ing with it: one is to probe the position of the per￾turbing object and the frequency of the network ana￾lyzer 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 for￾mer method is faster, while the latter one is more ac￾curate. 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 ax￾ial field; “PO2#” is a copper disk with a diameter of 20 mm, it is used to probe the electric field com￾ponent Er. Perturbing object “PO3#”, developed at Tsinghua University, is like a cage[5] , which effec￾tively perturbs the axial electric field Ez while the radial field Er is nearly undisturbed. Higher order modes are identified by the field dis￾tribution 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