A new measurement method of electrode gains for orthogonal symmetric type beam position monitor*

Transcription

1 Sumitted to Chiese Physics C A ew measuremet method of electrode gais for orthogoal symmetric type eam positio moitor* ZOU Ju-Yig( 邹俊颖 ) 1) WU Fag-Fag( 吴芳芳 ) YANG Yog-Liag( 杨永良 ) SUN Bao-Ge( 孙葆根 ) ) Zhou Ze-Ra( 周泽然 ) Luo Qig( 罗箐 ) LU Pig( 卢平 ) XU Hog-Liag( 徐宏亮 ) NSRL, School of Nuclear Sciece ad Techology, Uiversity of Sciece ad Techology of Chia, Hefei 3009, P. R. Chia Astract: The ew eam positio moitor (BPM) system of the ijector at the upgrade project of Hefei Light Source (HLS II) has 19 striplie eam positio moitors. Most cosist of four orthogoal symmetric striplie electrodes. The differeces i electroic gai ad mismachiig tolerace ca cause the chage of the eam respose of the BPM electrodes. This variatio will couple the two measured horizotal positios i order to rig the measurig error. To alleviate this effect, a ew techique to measure the relative respose of the four electrodes has ee developed. It is irrelevat to the eam charge ad the related coefficiet ca e theoretical calculated. The effect of electrodes couplig o this techique is aalyzed. The caliratio data is used to fit the gai for all 19 ijector eam positio moitors. The results show the stadard deviatio of the distriutio of measured gais is aout 5%. Key words: eam positio moitor, electrode gai, caliratio, orthogoal symmetric PACS: 9.0.Ej, r 1 Itroductio Recetly, Hefei Light Source (HLS) is eig upgraded to HLS II. The ijector eam positio moitorig (BPM) system is composed of 19 eam positio moitors, mostly are regular striplie type BPM. They are precisely calirated ad carefully istalled i place [1]. We have developed a ew techique that provides a measure of the relative gai of the four striplie electrodes. The method we developed is similar to the techique of D.L. Rui [] et al. It also ased o the fact that, i a four electrodes eam positio moitor, the positio of the eam is overdetermied. The relative gais of the electrodes ca e calculated y measurig the electrode sigal at may differet eam positios. The method of Rui is ased o the image theory, which requires the geometry of the four BPM electrodes e diagoal symmetric. The geometry of a typical HLS II eam positio moitor is as i Fig. 1. The four electrodes are orthogoal symmetric, which does ot apply to Rui s method, so we develop a ew techique to measure the relative gais of this type of four electrodes eam positio moitor. Through the aalysis of the theoretical electrode sigal iduced y the eam, we fid a ew expressio oly related to the electrode sigal. This expressio ca e used to fit the electrode gai errors, withi each fittig procedure, four ukow parameters are fitted: three utto gais ad a geometry scalig factor. T electrode L 5 R B Fig. 1. HLS II ijector eam positio moitor * Supported y the Natural Sciece Foudatio of Chia ( , , ) 1) zoujyyl@mail.ustc.edu.c ) gsu@ustc.edu.c

2 Derivatio of ew expressio As Fig. 1 show, the four electrodes of a HLS II typical BPM are 90 degrees away from each other. By igorig the ifluece of uch size, the electrode sigal of this type of BPM ca e represeted y [3] Ieam VR 1 Z1x Z Z3x Z... Ieam VL 1 Z1x Z Z3x Z... Ieam VT 1 Z1y Z Z3y Z... Ieam VB 1 Z1y Z Z3y Z... Which, I eam is the eam charge, is the electrodes opeig agle, is the distace from ceter of the eam positio moitor to the electrodes. Z 1x, Z 1y, Z, Z 3x, Z 3y ad Z are itroduced i order to simplify the expressios si( / ) x0 si( / ) y0 Z1x, Z1y, / / si x0 y0 Z, si(3 / ) x0 3y0 x0 Z3x, () 3 / si(3 / ) 3x0 y0 y0 Z3 y, 3 / si( ) 3x 0 y0 x0 y0 Z. Which, x 0 ad y 0 are the positios of the eam. Whe the eam is ear the ceter of the eam pipe, x 0 ad y 0 are small compared to. I this case, the third order ad up ca e igored, so the electrode sigals ca e approximated as a quadratic polyomial expasio Ieam VR (1 Z1x Z) Ieam VT (1 Z1y Z) (3) Ieam VL (1 Z1x Z) Ieam VB (1 Z1y Z) Takig sums ad differeces of Eq. (3) gives (1) VR VL VT VB Z VR VL VT VB VR VL VT VB m VR VL VT VB Z Z Z Z Z Z 1 ZZ VR VL VT VB VR VL VT VB Z Z Z Z Z Z 1 ZZ 1x 1y 1x 1y 1x 1y 1x 1y Also, igore the third order ad up we ca simply get Z Z Z Z Z m 1x 1y 1x 1y Comiig Eq. () ad Eq. (5) to elimiate x 0 ad y 0 gives a expressio that simply relates the electrode sigals kmm (6) kmm ta / I this case, k is a costat oly determied y the electrodes opeig agle of BPM. To the regular ijector striplie BPM of HLS II, is 5 degree, so we ca simply calculate that k is 7. Eq. (6) ot oly shows that Σ is proportioal to the product Σ m Σ, more importatly, the equatio is irrelevat to the eam charge, which is useful whe fit the gai errors usig real eam. 3 Simulatio To simulate the coectio etwee Σ ad Σ m Σ, we used a fiite elemet code to create a map of each electrode respose as a fuctio of eam positio []. The simulated eam was moved i a 5 mm 5 mm square area with a step of 0.5 mm. Σ ad Σ m Σ was calculated with the exact respose of electrodes at every eam positios. The product Σ m Σ is plotted versus Σ i Fig.. I Fig., the poits deviatio from the straight lie oly slightly appears at large amplitudes, shows the extet to which the higher tha secod order terms ca e igored. We see that our quadratic term approximatio is good, the product Σ m Σ approximated to Σ, which fits the form () (5)

3 of Eq. (5) with slightly deviatio at large amplitudes m Fig.. Σ m Σ vs Σ for poits o a 5 mm 5 mm grid with simulated electrodes sigal vs eam positio. I practice, the four electrodes do ot have the same gai, the the coectio etwee electrodes defied y Eq. (6) will fail. We simulate the effect of gai errors y reducig the sigal o electrodes y 10%, that is, the gais (1:) = 1.0, 1.0, 1.0, 0.9. Fig. 3 shows the Σ m Σ vs Σ with the data uder this coditio, idicates the coordiate (0,0). The data is o loger liear ad it is offset from zero. 0. m electrodes sigals are give y V V KV KV KV V KV V KV KV V K V K V V KV V K V K V KV V R R 1 L T B L 1 R L T B T R L T 1 B T R L 1 T B I this case, we calculate Eq. () y igorig the third order ad up V V V V 1K K1 Z V 1 R V L V T V B K K1 V V V V 1K1Z1 1 x Z y m (8) V V V V 1K K1 V V V V 1K1Z1 1 x Z y V V V V 1K K1 So the Eq. (6) ca e modified to k m 1 k 1 K1 K 1 K ta / (7) (9) k is a coefficiet determied y the electrodes couplig effect ad the electrodes opeig agle. We calculate the couplig coefficiets through the aalysis of the simulatio BPM model usig CST-Microwave Studio software. A simulated Gaussia sigal is geerated at oe electrode. By itegratig the origial sigal ad the iduced sigal at other electrodes, we ca get K 1 is 1.8%, -0. K is 5.5%. Fially we get k is aout Fig. 3. Σ m Σ vs Σ for poits o a 5 mm 5 mm grid with electrode itesity computed with the oliear map. Electrodes couplig effect Eq. (6) is ased o the assumptio that the four electrodes are idepedet to each other. I fact, there is couplig effect etwee the electrodes. Each electrode ca e iduced to sigals from other electrodes. We set K 1 as the couplig coefficiet of opposite electrode, K as the couplig coefficiet of adjacet electrode. So the four 5 Electrode gai fit with ew expressio We assume the deviatios from Eq. (9) are determied y the gai variatios etwee differet electrodes. We use a oliear least squares fit to get the electrode gais (g R, g L, g T ad g B ). The merit fuctio to e miimized is gv R R gv L L gv T T gv gv R R gv L L gv T T gv gv gv gv gv gv R R gv L L gv T T gv gv R R gv L L gv T T gv R R L L T T k i 1 gv R R gv L L gv T T gv (10)

4 g B ) ad has a miimum for the est fit gais (g R, g L, g T ad k. To make sure the value of the deomiator is ot zero, we fit the same data four times, each time we set oe of the electrode gais to 1, ad the average the results. 6 Fittig the caliratio data All the 19 HLS II ijector striplie BPMs are calirated at test ech, usig a tugste filamet to simulate the eam [1]. The filamet was moved i a 5 mm 5 mm square area with a step of 0.5 mm. We collect the electrodes sigal data o each simulated eam positio usig Liera Brilliace Sigle Pass [5]. A example of fitted data ased o Eq. (10) at oe BPM (LA-BD-BPM03) is show i Fig.. I Fig., the ope circles are the raw electrode data, the crosses are the electrode data corrected with the fitted gais, the idicates the coordiate (0,0). The fitted gais(g R, g L, g T ad g B ) respectively are 0.88, 1.1, 0.93 ad 1.1. The result shows the data has etter liearity ad passes through zero after gai fittig. Tale 1. The chage of caliratio parameters efore ad after gai fittig efore gai fittig after gai fittig Positio x y x y Offset/mm Geometric coefficiet /mm Gais for 19 BPMs are show i Fig. 5. The distriutio of fitted gais is show i Fig. 6. We ca see most electrodes gai errors are etwee 0.9 ad 1.1. Note that the average value of parameter is a little it larger tha the theoretical value. fitted coeffciet k is 0.530, which electrode 1 electrode electrode 3 electrode k m -0.1 Raw data data after gai fit zero poit BPM umer Fig. 5. Fitted gais ad parameter for all 19 ijector eam positio moitors. k from caliratio data Fig.. vs for a caliratio data at LA-BD-BPM03. To verify the effectiveess aove method, the tale 1 shows the mai geometric caliratio parameters chage of the LA-BD-BPM03 efore ad after gai fittig. Compared to the geometric coefficiet efore gai fittig, the geometric coefficiet are closer to the theoretical value 7.55mm after gai fittig. Thus, the aove method is effective. Couts Fitted gai Fig. 6. Distriutio of fitted gais for the data plotted i Fig. 5.

5 7 Coclusio We have derived a relatioship amog the itesities of the four electrodes of orthogoal symmetrical type eam positio moitor. The relatioship is etter tha the previous study ecause it is irrelevat to the eam charge ad the related coefficiet ca e theoretical calculated. We aalyze the effect of electrodes couplig o the relatioship. We show how the relatioship ca e used to make a eam ased measuremet of the relative gais of the four electrodes. We have used the caliratio data to fit the gai for all 19 ijector eam positio moitors. The stadard deviatio of the distriutio of measured gais is aout 5%, cosistet with the specificatios of the system electroics. We will use the real eam data of HLS II ijector to fit the electrodes gai, this ca e implemeted as a part of the stadard measuremets of the HLS II ijector BPM system. Refereces 1. ZOU Ju-Yig, YANG Yog-Liag, SUN Bao-Ge, et al. Caliratio of Beam Positio Moitors i the Ijector of HLS II. Proceedigs of IPAC013, Shaghai, Chia, 013, Rui D L, Billig M, Meller R, et al. Beam Based Measuremet of Beam Positio Moitor Electrode Gais. Phys. Rev. ST Accel. Beams, 010, 13(9): ~ LI Peg, SUN Bao-ge, LUO Qig, et al. New Methods of Beam Positio Moitors for Measuremet of Quadrupole Compoet. High Power Laser ad Particle Beams, 008, 0(): Olmos A, Pérez F, Rehm G. Matla Code for BPM Butto Geometry Computatio. Proceedigs of DIPAC 007, Veice, Itally, 007, ZOU Ju-Yig, FANG Jia, SUN Bao-Ge, et al. Applicatio of Liera Brilliace Sigle Pass at NSRL Liac BPM System. Proceedigs of IPAC011, Sa Seastiá, Spai, 013,