7 th Symposium IMEKO T 4, 3 rd Symposium IMEKO T 9 ad 5 th IWAD Workshop Istrumetatio for the IT Era Sept. 8-,, Kosice, Slovakia I-situ calibratio of rotatig coil magetic measuremet systems: a case study o Liac4 magets at EN Pasquale Arpaia,, Marco Buzio, Giacarlo Golluccio,, Ferado Mateo Departmet of Egieerig, Uiversity of Saio, orso Garibaldi 7, 8 Beeveto, Italy. Ph : +39 843584-7, Fax: +39 84 3584, E-mail: arpaia@uisaio.it EN, Europea Orgaizatio for Nuclear esearch Geeva 3, Switzerlad Ph: +4 767 6, E-mail: giacarlo.golluccio@cer.ch; marco.buzio@cer.ch Abstract- A i-situ procedure for calibratig the equivalet radius ad width of the coil trasducer i rotatig mode measuremets for magetic field quality aalysis is proposed. The stadard calibratio procedure is ot suitable whe the coil is loger tha the maget uder test, because a average value of the radius ad of the width alog the legth as a whole is obtaied. This problem icreases for small coils used i small-aperture magets, such as quadrupoles of ew-geeratio liear accelerators. I the paper, the problem of the coil parameter calibratio is highlighted ad the the proposed calibratio method ad the correspodig measuremet statio are illustrated. Experimetal results of a case study o the maget series of the ew liear particle accelerator LINA4, desiged to itesify the proto flux curretly available i the accelerator chai at the Europea Orgaizatio for Nuclear esearch (EN), are reported. I. Itroductio The most accurate techique of field quality measuremet for particle accelerator magets is based o a trasducer coil rotatig ito the maget apertures []. A measuremet of the magetic flux liked to the rotatig coil as a fuctio of the agular positio is delivered. The mai quatities of iterest for field quality characterizatio are the harmoic coiciets of the D field expasio []. Those coiciets deped essetially o the legth, the width ad the rotatio radius of the coils. By meas of mechaical measuremets practically oly the legth ca be obtaied accurately eough (+ -3 ~ -4 ). Magetic measuremets are the best optio because all o-idealities are automatically icluded i the results [3]. The equivalet width ad radius have to be determied by rotatig the coil i a kow uiform dipole field ad i a uiform quadrupolar magetic field respectively. The classical approach to the coil calibratio [4], usig a uiform magetic field over the whole coil legth, gives a average value for the radius ad width which is suitable whe the coil is shorter tha the maget uder test or i the ideal case of perfectly costat width. This procedure fails whe the coil geometry is ot regular, ad the mechaical errors become more ifluet whe the coil size is reduced. At EN, a ew liear accelerator Liac4 is curretly beig built to replace the old Liac. The trasverse focusig to the beam is give by several Permaet Maget Quadrupoles (PMQ) [5] with a aperture mm ad 45 mm legth. The small dimesios of the support used to build up the coil (i this case mm of legth, less tha mm i width ad mm thickess) make the widig process more difficult. Low rigidity i the widig ca easily occur at the ed side ad i the middle of the coil. I this paper, first the theoretical backgroud of the rotatig coil magetic measuremet is illustrated, focusig o the coil sesitivity parameter calculatio. I sectio II, the proposed coil calibratio method is show i the specific case of a quadrupole maget. The last sectio will report about the measuremet statio ad the experimetal results o Liac4 PMQs. II. otatig coil backgroud I the classical D harmoic aalysis, the field harmoic cotet is proportioal to the DFT coiciets Ψ of the flux samples Φ k as a fuctio of the agular positio: Ψ N k Φ k e ( k ) πi( ) From eq. (), the magetic field harmoic coiciets are derived []: ()
7 th Symposium IMEKO T 4, 3 rd Symposium IMEKO T 9 ad 5 th IWAD Workshop Istrumetatio for the IT Era Sept. 8-,, Kosice, Slovakia N κ where is the erece radius (typically the trasverse size of the particle beam), N is the umber of agular poits per tur ad κ are complex geometric calibratio coiciets or coil sesitivity factors. These represet the coil geometry completely, ad they are idepedet of the measured magetic field. For a perfect radial coil, iitially o the horizotal plae (zero iitial phase), with a ifiitesimally thi widig cross-sectio, the factors reduce to a real umber [3]: NT Lc κ W + Ψ + W where is the average radius, L c is the legth of the coil, is the harmoic order, N T is the umber of coil turs ad W is the width of the coil. I other words, the coil sesitivity factors for a radial coil ca be computed from the total equivalet area A c of the coil (give by the legth, the width ad the umber of turs) ad the equivalet radius (average betwee the two coil eds). All κ are proportioal to total coil area A c ad icrease like radius - ad icrease with W. I the stadard case A c is estimated magetically rotatig the coil i a uiform kow erece dipole ad i a erece quadrupole oce fixed the legth of the coil by meas of geometrical measuremets [3]. The harmoic coiciets of eq. (3) are erred to the coil erece axes defied by the zero erece of the agular ecoder []. A traslatio ad a rotatio i the -D complex plae are ecessary to er the harmoic coiciets to the maget erece frame [6]. The distace vector z x + i y betwee the coil erece frame ad the maget erece frame (figure ), which for a quadrupole maget is cetred o the magetic axis where B, ca be calculated from []: () (3) Y z (4) Y z We X X a) b) Figure : a) radial coil rotatig i a quadrupole field. Y-X is the maget frame, Y -X is the coil frame. b) details of the compesatio scheme with two ested radial coils, the ier coil has half of the width W but has the double the umber of turs.
7 th Symposium IMEKO T 4, 3 rd Symposium IMEKO T 9 ad 5 th IWAD Workshop Istrumetatio for the IT Era Sept. 8-,, Kosice, Slovakia II. I-situ coil calibratio method A. alibratio Method Whe the coil width irregularities are importat ad oly a part of the coil is immersed i the magetic field, the geeral method described above must be completed maget uder test istead of the stadard ereces ( isitu calibratio). I priciple, if the maget is moved trasversally by a give distace ad the quadrupole compoet is kow, the radius ad the equivalet width W of the coil ca be recostructed directly. I other words, the two parameters ca be computed by calculatig κ ad κ from eq. (3) ad substitutig them i eq. (): Ψ NNT LcW Ψ3 NN L W T c (5) Assumig for istace a purely horizotal movemet x, from (4) ad (5), if the phase error betwee the coil frame ad the maget frame is egligible, ca be derived: Ψ 3 x e (6) Ψ The maget stregth, correspodig to the itegrated quadrupole gradiet (GdL), is used to calibrate the W : (7) ad: GdL w L c { ψ } e 3 GdL The erece value of the gradiet GdL must be obtaied i this method by a idepedet measuremet. (8) III. Experimetal esults () The coil used to measure this maget is mm log with a exteral diameter of 9 mm. It presets two ested radial widigs o the same plae (figure b). The exteral oe geerates the absolute sigal relative to the mai field of the quadrupole. The ier oe is coected i series oppositio to the exteral coil, i order to geerate a sigal more sesitive to the high order harmoics []. Whe the two coils are coected i electrical oppositio the κ of the series, as well the κ, are zero. This relatio ca be obtaied oly if the two coils have the same equivalet surface, thus the iteral widig, sice it has half of the W, it has twice the umber of turs. A. Measuremet statio architecture I Figure, the equipmet used to calibrate the coil directly o the measuremet system is depicted. The agular erece of the ecoder is prelimiarily aliged to the gravity by meas of a sesor tilt o the shaft. A -D traslatio stage, equipped by a liear ecoder of.3 μm resolutio ad μm repeatability, allows the permaet quadrupole to be moved i the x-y directio. The agular error ad the offset of the axes origis betwee the maget erece frame ad the -D stage were foud by movig the maget first alog the x, the i y directio [7] ad measurig the displacemet z from eq.(4). The agular error of.5 ad the origi displacemet of 3 μm i the x directio ad of 6 μm i y will ot affect the calibratio procedure. The measuremet system is a ew rotatig bech aimed at testig the PMQ magets of the Liac4 drift tube [5].
7 th Symposium IMEKO T 4, 3 rd Symposium IMEKO T 9 ad 5 th IWAD Workshop Istrumetatio for the IT Era Sept. 8-,, Kosice, Slovakia Figure : the rotatig coil ad the calibratio system. B. Measuremet procedure With the help of the D stage, the maget is first cetred with respect to the rotatig coil by miimizig iteratively eq. (5). The coil radius ad the equivalet width ca be measured i 4 steps: i) move the maget alog the x axis to a give positio; ii) make a cotiuous rotatio measuremet of the flux as a fuctio of the agular positio; iii) calculate the FFT obtaiig the d ad the 3 rd harmoic of the measured flux (from (5), a movemet i the x axis correspods to a variatio i the real part of the, ad a movemet i the coordiate y affects the imagiary part of the d harmoic coiciet); iv) calculate the from eq. (7) ad W from eq. (9).. esults The procedure was applied to the Liac4 shaft usig a prototype permaet quadrupole measured with the stretched wire system. The SSW [8] measured a itegrated gradiet of.435 Tm/m for this maget. The logitudial positio was fixed at mm from the left coil edge, where the width variatio is liear ad is far from the coil ed side. The repeatability of the radius ad of the coil area is better tha + µm. The ucertaity of the two parameters calculated propagatig the error from eq. (6) ad (8) is + μm for the radius ad + 6 µm for the equivalet width. The exteral coil is affected i the cetral part by a strog variatio i the width profile. The iteral coil is ested i the exteral oe, thus its width is more uiform. Nevertheless, the radius variatio with respect to the axis rotatio reduces the uiformity of the measuremet (the variatio i the measuremet is about +5 % alog the mm of the exteral coil legth ad of +3 % for iteral coil). The accuracy of the gradiet measuremet is withi the specificatios oly for the calibrated coil regios (better tha.3 %, with respect to the required %). Oce the coils are calibrated i a specific logitudial positio usig the erece maget, the calculated κ are exploited to evaluate the magetic stregth ad harmoic quality of several quadrupoles of the Liac4 drift tube tak. The quadrupole stregth measured is withi the toleraces of +.5% required from the beam optic specificatio, eve if the ucertaity of the rotatig coil measuremet (+.8 Tm/m) is higher tha the oe of the stretched wire (+. Tm/m). II. oclusios I this paper, a ovel procedure to calibrate directly i situ the coil sesitivity geometry parameter is proposed. This procedure represets a improvemet with respect to the stadard oe, which returs a average value of the coil radius ad width alog the whole legth of the coil, is ot accurate eough whe the magetic legth is shorter tha the coil legth ad the coil surface geometry is poor. The ew procedure is applied to the prototype coils developed to measure the field quality of six permaet quadrupoles of the Liac4 drift tube. The MS error of the magetic stregth measuremet, compared to the stretched wire system take as the erece, is improved from 6 % to.%. Sice the tolerace required for the accelerator is %, the ew procedure ca be used with cofidece to avoid systematic measuremets with the stretched wire system. efereces [] A. Jai, Harmoic coils, AS o measuremet ad aligmet of accelerator ad detector magets, EN 3
7 th Symposium IMEKO T 4, 3 rd Symposium IMEKO T 9 ad 5 th IWAD Workshop Istrumetatio for the IT Era Sept. 8-,, Kosice, Slovakia 98-5, August 998. [] L. Bottura, Stadard aalysis procedures for field quality measuremet of the LH magets part I: Harmoics, EN-iteral ote, February. [3] M. Buzio, Maifacturig ad calibratio of search coils, EN Accelerator school, Jue 9, Bruges, Belgium. [4] O. Dukel, oil Maufacture, Assembly ad Magetic alibratio Facility for Warm ad old Magetic Measuremets of LH Supercoductig Magets, 4 th Iteratioal Magetic Measuremet Workshop IMMW4, September 5, Geeva, Switzerlad. [5]. Garoby, G. Bellodi, F. Gerigk, K. Hake, A.M. Lombardi, M. Pasii,. ossi, E.Z. Sargsya, M. Vretear, Liac4, a ew ijector for the EN PS Booster, Proceedigs of Europea Particle Accelerator oferece 6, Ediburgh [6] L. Walckiers, Harmoic oils, EN Accelerator school, Jue 9, Bruges, Belgium. [7] S.. Gottschalk, K. Kagas, D. J. Taylor, W. Thayer, a Air Bearig otatig oil Magetic Measuremet System, Proceedigs of Europea Particle Accelerator oferece 5, Koxville. [8] L. Walckiers, Magetic measuremet with coils ad wires, EN Accelerator school, Jue 9, Bruges, Belgium. 4