BEAM BASED CALIBRATION FOR BEAM POSITION MONITORS

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1 TBA0 Proceedns of IBIC05 Melbourne Austrl BEAM BASE CAIBATION FO BEAM POSITION MONITOS M. Te KEK/J-PAC Tsukub Ibrk Jpn Copyrht 05 CC-BY-.0 nd by the respectve uthors Abstrct Be poston ontorn s one of the ost fundentl dnostc tools n n ccelertor. To et ood perfornce of the BPM syste the be-bsed lnent ethod hs been developed nd used for ore precse BPM lnent nd ntnn the perfornce. The snl fro BPM s trnsferred by coxl cble nd processed by snl processn crcut. The be poston s clculted fro the reltve rtos between the outputs of the BPM hed. The crcut n s clbrted n the bennn on test bench. But ths clbrton chnes wth ech pssn yer. To escpe fro ths proble ethod for clbrton of the n slr to be-bsed lnent s key ssue to ntn the ood perfornce of the BPM syste. For ths propose be-bsed n clbrton ethod hs been developed nd used t KEK. Both be-bsed lnent nd be bsed n clbrton ethods re presented usn concrete exples. INTOCTION For hh enery ccelertors the esureent of the be poston s one of the bsc dnostcs lon wth the be ntensty nd the bettron oscllton frequency. Stblty of the closed orbt s very portnt for stble opertons to ntn ood perfornce n n ccelertor. Therefore we hve prepred BPM t ech qudrupole net. For exple there were 86 BPMs n the J- PAC Mn n. The BPM syste requres hh ccurcy esureent. In order to stsfy the requreent we hve done creful clbrton of the BPM syste n three steps before the cossonn. But n KEKB we found notceble errors lrer thn 0. n lost ll BPM redns. These errors coe fro the lnent error of BPM to ts dcent qudrupole net nd the blnce on output dt of the BPM. Be-bsed lnent (BBA) s ethod for correctn the offset of BPM hed bsed on be esureent []. The center poston of ech BPM should be known n ters of offset fro the netc center of the dcent qudrupole net. The reltve n of the output dt y drft due to unpredctble blnce on output snls fro the pckup electrodes becuse the output snls ust trvel throuh seprte pths such s cbles connectors ttenutors swtches nd then re esured by the snl detectors. For ths reson the ns of every BPM of KEKB hve been clbrted by non-lner lest-squre ethod []. The se process of n clbrton used n KEKB hs been tred wth the BPM syste n J-PAC ISBN Mn n however the fttn result ve ndefnte solutons. A new be-bsed ethod to clbrte the ns of BPMs t the J-PAC Mn n hs been developed usn the Totl est Squre ethod (TS) []. CAIBATION ING INSTAATION The output dt fro BPM syste ws usully clbrted n the follown three steps on the test bench t KEKB [].. Mppn esureent of BPM syste The BPM heds were fbrcted to wthn ± 0. tolernce. However vrtons of frequency response between button electrodes cnnot be nored consdern the ccurcy requreents. All BPMs were pped t test bench wth ovble ntenn to dentfy the electrcl zero poston of ech BPM.. Alnent of eoetrcl offset Most BPMs (~97%) were lned n relton to ther nerest qudrupole net. After nstllton of BPM heds n the rn we esured the eoetrcl offsets of the BPM heds reltve to the qudrupole net. But the esured offsets were not the offset fro the feld center of qudrupole net.. Attenuton rto of trnssson lne We eployed twsted coxl cbles wth foed Polyethylene nsulton between BPMs n the tunnel nd electroncs t locl control roo bove round. To esure snl ttenuton t the detecton frequency the cbles toether wth the electroncs were lso clbrted to 50 µ ccurcy. BEAM BASE AIGNMENT In order to ln BPM to the feld center of qudrupole net the BPM offset s clbrted by fndn the poston of the closed orbt t tht BPM whch s nsenstve to chne of the feld strenth of the dcent qudrupole net. Clbrton dt re tken for dfferent be orbts nd dfferent feld strenths of the qudrupole net. The orbt chne due to the feld rdent chne k of the qudrupole net s proportonl to the closed orbt dsplceent x fro the netc center of the qudrupole net. Fure shows n exple of BPM offset esureent by BBA n the n rn t J-PAC [5]. A correcton col wound on ech pole of qudrupole net ws used to chne the feld strenth. The current on the correcton col I Q ws chned fro - A to A nonlly. To chne the

2 Proceedns of IBIC05 Melbourne Austrl TBA0 orbt bup orbt x ws set to three dfferent orbts of nd 8. When the be orbt s n the vcnty of the center of the qudrupole net even f the current of the correcton col s chned the orbt does not chne snfcntly (F. -() ~ (c)). In the esureent three x / I Q vlues were obtned for the bup orbts s shown F.-(d). The be poston whch ves x / I 0 s the offset of the BPM. Q Fure shows the offset dstrbutons for M BPMs. The BPM Offsets esured by ths ethod were nstlled n the dt bse. x [] x [] 8.88 () Bup y = -0.08x Q I[A] -7.8 (c) Bup y = 0.0x x [] x [](di=0) 0.69 (b) Bup y = x Q I[A] 0 (d) OFFSET y = x Fure : strbuton of BPM offsets obtned wth BBA n J-PAC M. () x-plne (b) y-plne. The effects of the BPM offset correcton cn be seen n the be orbt. Fs. () nd (b) show the closed orbt dstorton (CO) wth nd wthout the offset correcton for the M. The closed orbt ws corrected better thn t ws wthout the correcton especlly the vertcl closed orbt Q I[A] x / IQ Fure : x-co vs. QM current I Q. () bup ~ -8 (b) bup ~ 0 (c) bup ~ +8. () The orbtl chne due to I Q cn be ontored not only the BPM but by ny other BPMs n the rn. Fure shows the offset postons observed by ll BPMs when the feld strenth of qudrupole net s chned. Fure : Offset vlues clculted wth the ll BPM response. y 0 t BPM#0 t J-PAC. The vertcl nd horzontl offsets were obtned for lost ll BPMs n the J-PAC M by ths BBA ethod. (b) Fure : COs lon the M corrected wthout / wth the BBA offset dt (red / blue lnes respectvely). () x-co (b) y-co. Fure 5 show the offset dstrbuton obtned by BBA n the E nd the HE t KEKB. We hve lso set the offset dt n the dt bse of BPM syste. Fure 5: BPM offsets. Blue brs nd red brs show horzontl offsets nd vertcl offsets respectvely. The effects of the BPM offset correcton cn be seen n the be orbt. Fures 6 upper nd lower show the CO ISBN Copyrht 05 CC-BY-.0 nd by the respectve uthors

3 TBA0 Proceedns of IBIC05 Melbourne Austrl before nd fter the be bsed lnent for the E. The orbt s soother especlly n the rc sectons fter the offset correcton s ncluded. Fure 7: BPM odel wth electrodes. Copyrht 05 CC-BY-.0 nd by the respectve uthors Fure 6: CO chne by BBA n the E t KEKB. BEAM BASE GAIN CAIBATION The be bsed n clbrton (BBGC) s very effectve ethod for chevn BPM ccurcy. We ntroduce the two n nlyss ethods tht hve been developed t KEKB nd J-PAC.. BBGC for BPM wth Four Buttons The BPM odel ssues the confurton wth four electrodes s llustrted n F. 7. The output volte of the -th electrode for the be poston nst the BPM center s expressed s: qf x y where s the reltve n fctor F (xy) s the response functon norlzed to F (00)= nd q s the proportonl fctor to the be current. The response functon depends only on the eoetrcl structure of the BPM hed. The be postons re esured tes wth pckup hed by chnn the orbt t the ontor ech te the snl fro the -th electrode t the -th esureent s ven by q F x y ISBN Snce we cn set to wth proper scln fctor for the be chre there exst only unknown ns nd. We esure nd t ech esureent. Snce wll not chne t ech esureent q x nd y re unknown preters. After the -th esureent the nuber of the unknown preters s +. The known preters re. When s lrer thn then exceeds + nd the unknown preters ncludn the ns cn be clbrted usn non-lner lest-squre ethod J q F x y q x y q x y where denotes the rry of fttn preters. The fttn nlyss hs been perfored usn the Mrqurdt ethod [6] whch s ble to obtn the optu vlue wth suffcent ccurcy. Ths BPM odel hs the nce syetry tht ll of the response functons cn be expressed wth only one functon F x y F F x b y x y b xy x x y b xy y x 6x y y b x y xy x y x y F x y F x y F x y F x y The expnson coeffcents nd re deterned by fttn the esured ppn t the clbrton stnd or the clculted ppn by the fnte boundry eleent ethod. Fure 8 shows the exple of the reltve ns of nd of ll BPM pckups n the rn whch were obtned by BBGC t KEKB [6].

4 Proceedns of IBIC05 Melbourne Austrl TBA0 BBGC for BPM wth onl Cut In the J-PAC M we dopted n electrosttc pckup wth donl-cut cylnder type duct s shown n F. 0 where the horzontl nd vertcl be postons re ndependently detected by two prs of pckup electrodes. The sulton ws perfored by usn the ethod n the prevous secton to estte ns of the M BPMs. For these lner response pckups the bove-entoned lest squres (S) ethod nzn the su of the squre of the dfference between ech electrode output nd the odel response functon s not pplcble. The sulton showed the result tht these ns were chned dependn on the ven ntl vlues for q x nd y n the fttn process. The non-lner fttn ethod ws not ble to be used for the n nlyss of such donl cut electrodes. Fure 8: The eltve ns obtned by BBGC n E (upper) nd HE (lower) t KEKB. Here horzontl scle s BPM No. The results of the fure re the frst esureent for BBGC t KEKB where the spred of these ns s -8% ~ +8%. The n dt re used nto the softwre to clculte the be poston to correct the ns of ll BPMs. We converted the esured vlue of BPM n nto BPM offset vlue. We tred to copre the offset wth the offset fro BBA. Fure 9 shows the correlton of both offsets n the E nd the HE t KEKB. Fro these correltons we beleve tht BPM n drft hs cused the offset chne. Fure 9: The correlton of both offsets n the E nd the HE t KEKB. Fure 0: BPM heds wth donl cut electrodes n J- PAC M. The outputs of donl cut electrodes for the be poston (x y) re ven by x x () y y () where s the proper norlzton fctor proportonl to the be current nd re the reltve ns to the electrode nd s norlzed to nd s the rdus of the donl cut electrode. By elntn x y nd n the bove forul we obtn the equton Ths lner equton express three ns n ters of four outputs. When be postons re esured tes the sultneous lner equtons re expressed n trx representton of ISBN Copyrht 05 CC-BY-.0 nd by the respectve uthors

5 TBA0 Proceedns of IBIC05 Melbourne Austrl Ax b where A x b Fure : econstructed ppn dt. ed: (x y) wthout correcton Blck: (x y) wth TS. Then nd denotes the esured output t the -th esureent. The pproxte soluton by lest squres (S) of the lner syste s ven by x S T T A A A b when the coponents of trx A hve no errors. On the other hnd when A hs errors the best pproxted soluton s ven by totl lest squres (TS) ethod [7]. The soluton of TS s ven by By usn rel be we tested both the TS nd the S ethod for donl cut BPMs n the J-PAC M. The poston esureents were done n nne dsplceents of be postons t the BPM s shown n F.. The results of n clbrtons re surzed n Tble. We cn see dfferences n the reltve ns depend on the fttn ethod. The be postons corrected by the new n re overlpped on F.. x TS T T A A I A b n Copyrht 05 CC-BY-.0 nd by the respectve uthors where n s the rnk of A nd σ s the sllest snulr vlue of the trx [A b]. We copre the TS ethod wth the S ethod by usn sultons. In ths sultons the ppn dt were enerted fro odel outputs wth the defned Eq. ()-() 500 ponts t 5 dsplced postons wth 0.% Gussn nose s shown n F. 8. The ns were ven resonble vlues set = =.0 =.005 = Tble : Sulton esult S rton TS rton The results of vlues ven to reltve ns nd vrton fro true ns n both TS nd S sultons re surzed n Tble. The TS ves sller vrtons thn S. Corrected postons by obtned ns re shown s blck ponts n F.. ISBN Fure : Mesured ppn dt nd corrected ppn dt. ed ponts re the esured postons wthout n correcton. Blck ponts re the corrected postons wth TS ethod. Tble : Corrected eltve Gns by TS nd S Methods BPM00 TS S BPM00 G TS S

6 Proceedns of IBIC05 Melbourne Austrl TBA0 We nlyzed the ns usn the dt obtned wth ctul be. In order to obtn the ppn dt of be postons the be orbt ws kcked by steern net. The ns nd re plotted n F. ()(b) nd (c) respectvely s functons of the ddress nuber lon M. The ns for two cses of be ntenstes (low nd hh) re plotted s blue nd red sold crcles respectvely. The be ounts of "ow" nd "Hh" ntenstes re 0 nd 0 -order protons per pulse respectvely. The ns re dfferent by xu of % between the cses of "ow" nd "Hh" ntensty. The ccopned error brs re clculted s follows. F X F Y X Y X Y 0 X Y X XY 5Y X X Y XY Y b0 b X by b X b XY b5y b X b X Y b XY b Y 7 where the coeffcents ( n bn n 9 ) re obtned by fttn of the ppn dt. The be poston s lso obtnble fro the output volte of ny three electrodes chosen out of four electrodes. sn the se dt we lso obtned the norlztons of two electrodes s X Y ( ) X ( ) Y ( ) ( ) Then t ves the four reltons between the be poston nd the norlzton s follows: ABC ABC x y FX X Y FY X Y BC BC x y FX X Y FY X Y AC AC x y FX X Y FY X Y AB AB x y F X Y F X Y X Y Fure : eltve ns clculted by TS ethod. nd re plotted. The ns for low ntensty (blue lne) nd hh ntensty (red lne) re plotted Here horzontl scle s BPM No. EAATION OF GAIN COECTION Exnton of Four Button Pckups t KEKB sully the be poston s clculted fro the output of four electrodes s F.. We obtn the norlzton of the snls (X Y) s X Y. Mppn esureent ws de t ny esh ponts n the centrl re. We ftted thrd order polynonls (F x F Y ) of two vrbles (X Y) for these esh dt to descrbe the relton between (x y) nd (X Y) for ech BPM s follows where X Y y F X Y x F X Y where functons ( F X F ) re thrd order polynonls for Y three electrodes of BPM. If the four outputs hve del correlton these four be postons ((x y ) (x y ) (x y ) (x y )) should concde wth ech other. The softwre procedure for the BPM syste perfors clculton of not only be postons usn four electrodes but lso four be postons usn three electrodes to exne consstency on these postons. The devtons on the four be postons re represented by the stndrd devton forul s follows: X Y X X wth X X Y Y wth Y Y () where x nd y re the stndrd devtons on four be postons clled the consstency error of be poston esureent. Fure shows n exple of the dstrbutons of the consstency error t KEKB. As result of hvn corrected the output volte wth new ns the consstency error bece very sll. ISBN Copyrht 05 CC-BY-.0 nd by the respectve uthors

7 TBA0 Proceedns of IBIC05 Melbourne Austrl CONCSION We should py soe specl ttenton to urntee precse esureent of be postons over lon te. The BBA esureent s useful for correcton of the BPM offset error. The n blnce on four outputs of BPM chnes rdully over lon perod. The blnce on the ns ves offset errors to be poston. The ost probble source of the n drft s the chne n the electrcl chrcterstcs of the trnssson lne of the snl by teperture drft becuse we found sesonl vrton n the n drft t KEKB. We hve cheved hh-ccurcy BPM syste by ontorn the consstency error nd pplyn be-bsed n clbrton [8]. Copyrht 05 CC-BY-.0 nd by the respectve uthors Fure : Consstency before (top) nd fter (botto) n clbrton n E t KEKB horzontl scle s BPM No. Exnton of BPM Gn t J-PAC M To evlute the nlyzed ns we checked the consstences of four postons clculted fro Eqs. () nd () s follown x x y y x y x y where (x y ) s the poston usn two electrodes n the horzontl or vertcl drecton (x y ) s the poston usn four electrodes nd (x y ) nd (x y ) re obtned usn three electrodes. We lso defned the consstency of x nd y s x nd y n Eq. (). Tble shows proveent of consstency error by usn BBGC. Tble : Consstency Before nd fter Gn Clbrton of BPM t J-PAC M Before After σ [] σ [] σ [] σ [] BPM BPM ISBN EFEENCES [] M. Msuzw et l. Proceedns of EPAC 000 enn Austr p.780. [] K. SATOH nd M. TEJIMA Proceedns of the 997 Prtcle Accelertor Conference ncouver 087. [] M. Te et l. Proceedns of IPAC0 Hubur Gerny p. 75. [] M. Te et l. Proceedns of the th Syposu on Accelertor Scence nd Technoloy Sprn-8 Ako Hyoo Jpn fro October [5] T. Toy et l. Be-Bsed lnent of the BPMs t J-PAC M Proc. of Prtcle Accelertor Socety Meetn 0 Aoor Jpn [6]. Mrqurdt An lorth for lest-squres estton of nonlner preters SIAM J. Appl. Mth. 96 ol. pp.. [7] I. Mrkovsky nd S.. Huffel Snl Processn 87 (007) 8. [8] M.Arn et l. Proress n KEKB be nstruentton systes Pro. Theor. Exp. Phys. 0 0A007 ( pes).