EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH European Laboratory for Particle Physics

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1 EUROPEAN ORGANIZATION FOR NUCEAR RESEARCH European aboratory for Particle Physics shc Projects shc Project Report 47 EDDY CURRENT MODEING AND MEASURING IN FAST-PUSED RESISTIVE MAGNETS P. Arpaia,2, M. Buzio 2, G. Gollucio,2, G. Montenero,2 Departent of Engineering, University of Sannio, Benevento, Italy 2 CERN, Geneva, Switzerland Abstract shc-project-report /08/200 A ethod for odeling and easuring electroagnetic transients due to eddy currents in fast-pulsed resistive agnets is proposed. In particular, an equivalent-circuit odel and a ethod for tie-doain easureents of eddy currents are presented. The easureents are needed for an accurate control of the agnetic field quality to ensure adequate stability and perforance of the particle bea in particle accelerators in dynaic conditions (field raps up to about 700 T/s). In the second part, the results of experients for odel definition, identification, and validation are discussed. The tests were carried out on a quadrupole of inac4, a new linear particle accelerator under construction at CERN (European Organization for Nuclear Research). inac4 CERN CH - 2 Geneva 23 Switzerland August 200 Presented at the 200 IEEE Instruentation & Measureent Technology Conference (I2TMC) 3-6 May 200, Austin, USA

2 Eddy Current Modeling and Measuring in Fast-Pulsed Resistive Magnets Pasquale Arpaia,2, Marco Buzio 2, Giancarlo Golluccio,2, Giuseppe Montenero,2 ) Departent of Engineering, University of Sannio, Corso Garibaldi 07, 8200 Benevento, Italy. Ph : , Fax: , E-ail: arpaia@unisannio.it 2) CERN, European Organization for Nuclear Research 2 Geneva 23, Switzerland. Ph: , E-ail: giancarlo.golluccio@cern.ch; arco.buzio@cern.ch; giuseppe.ontenero@cern.ch Abstract A ethod for odeling and easuring electroagnetic transients due to eddy currents in fast-pulsed resistive agnets is proposed. In particular, an equivalent-circuit odel and a ethod for tie-doain easureents of eddy currents are presented. The easureents are needed for an accurate control of the agnetic field quality to ensure adequate stability and perforance of the particle bea in particle accelerators in dynaic conditions (field raps up to about 700 T/s). In the second part, the results of experients for odel definition, identification, and validation are discussed. The tests were carried out on a quadrupole of inac4, a new linear particle accelerator under construction at CERN (European Organization for Nuclear Research). Keywords- Accelerator agnets, Eddy currents, oad odeling. I. INTRODUCTION inac2, the injector of the CERN Proton Synchrotron Booster (PSB), liits the perforance of the proton accelerator coplex owing to its low output energy (50 MeV). This bottleneck is going to be reoved by eans of a higherenergy linear accelerator under developent (inac4), which will double the brightness and the intensity of the bea delivered by the PSB and will ensure the ultiate bea needed for the arge Hadron Collider []. The bea is focused by eans of several narrow-aperture quadrupole electroagnets along the acceleration path. The agnet coils are air-cooled, thus only pulsed operation at Hz is allowed. Consequently, the field is switched on and off in synchronization with the passage of particle bunches. A difficult easureent proble arises fro the dynaic requireents for the field quality inside such a agnet. The present work focuses on a so-called Type III quadrupole, installed in the Chopper line of inac4 [2]. This 60 long, 29 aperture agnet is powered by the current cycle of Figure. The current rap-up lasts 200 s and is followed by a flat-top of 600 s at a noinal current of 200 A, where the field is required to be stable within 0-3. The flat top stability is deterined essentially by the decay of the eddy currents induced during the rap, as well as by other parasitic effects [3]. In general, the ain effects of eddy currents are: (i) to screen flux changes, (ii) to delay the achieveent of noinal DC field, (iii) to introduce high haronic content perturbing the field [4]. An equivalent circuit odel is necessary to fully understand the eddy currents effects, as well as to plan possible corrective actions [5]-[6]. Eddy current effects are hard to predict accurately because they depend on a nuber of uncertain paraeters, such as the agnetic properties of the iron yoke, its teperature, the surface resistivity of the lainations [7], the echanical tolerances leading to unwanted air gaps in the agnetic circuit, etc. As a consequence, an experiental approach is necessary to validate both design calculations and anufacturing quality [3]. In this paper, a ethod for odeling and easuring electroagnetic transients due to eddy currents in fast-pulsed resistive agnets is proposed. In particular, in Sections 2 and 3, an equivalent-circuit odel and a easureent ethod of eddy currents are respectively proposed. In Section 4, the experiental results related to odel definition, identification and validation carried out on a quadrupole of inac4 are discussed. Figure : current excitation wavefor for the lainated iron-core agnet Type III quadrupole.

3 2 II. THE PROPOSED MODE The eddy currents are generated by electric fields arising fro variable agnetic fluxes [7]. They build up during the current pulse rap-up and decay during the constant portion. In the proposed odel, their effect is considered as a bypass current, flowing through a chain of R/ circuits connected in parallel to the ain coil (Figure 2). III. THE PROPOSED MEASUREMENT METHOD The e..f. V C induced in the coil has to be integrated in order to obtain the linked flux. Assuing that the quadrupole is excited starting fro a deagnetized state at t=t 0, the flux seen by a search coil with N t turns inserted in the agnet is calculated as: t ( t) VC ( t) dt (3) N t0 t In the ideal (linear) case, this flux would be siply proportional to the excitation current via the utual inductance CM, depending on the geoetry and on the agnetic pereability of the iron core [0]: (t)= CM I(t) (4) Figure 2: equivalent odel circuit of eddy current effect For a short agnet such as a Type III, the contribution of the fringe field ay be doinant [8]-[9], thus two R/ chains are considered in order to take into account: (i) the eddy currents parallel to the ain coils (i.e. across the lainations), which have a short tie constant, and (ii) the eddy current circuit, in the plane of the end lainations (i.e. perpendicular to the agnet axis) due to the fringe field. The odel also takes into account the parasitic capacitance of the agnet coil that could influence the ain field at high frequency (about MHz or above). The bypass eddy currents (I and I 2 ) are negligible with respect to the ain current, thus can be considered as utually independent and the analysis can be siplified [8]. The current I flowing through the ain coil of the agnet is given by: I I 0 exp exp 2 R R 2 I p 2 where I 0 is the current source, the ain coil inductance, R, R 2,, and 2 are the equivalent resistance and inductance of the eddy current circuits, respectively. The current I p flowing through the parasitic capacitor will introduce sall ripples in the flux. Assuing the static field B to be siply proportional to the agnet current, the ain field coponent can be described by: B t t B 0 exp exp 2 where B 0 is the ain field at the end of the double exponential decay and B ac is the high-frequency ripple introduced by I p ; α and β are the aplitudes of the exponential decays, and and 2 are the tie constants delaying the field response. B ac In actual conditions, a current difference I can be defined as: ( t) I I( t) (5) CM The current difference (5) includes contributions fro all nonideal effects, builds up during the rap and decays over the flat-top. Assuing that the transient has copletely died out at the end of the flat top, i.e. I(t S )=0, one can derive: NtI ( ts) (6) t s CM V ( t) dt t0 C By considering that the easured signals are affected by electrical noise, ains hu, power supply ripple and so on, the accuracy of the ratio (6) can be increased by averaging both the ters, the current excitation and the voltage coil integral over a short tie interval t S -t t t S. IV. EXPERIMENTA RESUTS In the following, the experiental results related to (i) the odel definition, (ii) the odel identification, and (iii) the odel validation carried out on a Type III quadrupole are illustrated. A. Model Definition In the odel definition, the ain proble is to take into account both the eddy current circuit in the iron yoke laination and the other circuit created by the fringe field in the plane perpendicular to the agnet axis. To understand how the different eddy current circuits influence the tie doain integral easureents a sall coil of 4.5 diaeter was used to scan the field inside the aperture in different positions with a 5 longitudinal step. The observed variation of the eddy current decay is function of the position inside the agnet aperture []. The decay includes two contributions: a slow one which tends to disappear when the coil is in the iddle of the agnet

4 3 aperture, and a fast one which is present along the whole agnet length. B. Model Identification The equivalent agnet ipedance was easured in order to deterine the values of the odel paraeters fro 500 Hz up to MHz. A gain phase analyzer (Powertek GP02) was used to easure the phase and the aplitude of the ipedance. The easureent was perfored at low current (200 A), thus the odel does not take into account the effects due to the nonlinearity of the pereability (saturation effects of the iron yoke) that ight affect the easureents. The obtained data were validated through a crosscheck with a CERN-built syste, the PROMIT [2], capable of analyzing gain and phase up to 20 khz by forcing a sinusoidal current up to 5 A. In Figure 3, the results of two typical easureents in the frequency doain at 0.2 and 3.0 A are reported as an aplitude bode diagra. In the range fro 500 Hz to 20 khz, the two curves overlap. This confirs that in this range the agnet has a linear behavior not related to the excitation current (fro independent easureents, iron yoke saturation is expected at current values well above 00 A). Figure 3: aplitude Bode diagra of the agnet. Table : eddy currents paraeter calculation Paraeter value R () 0 (µh) 957 R 2 (k).42 2 (µh) 583 C p (pf) 280 C. Model Validation The odel was validated according to the following procedure: easure the agnet ipedance vs. frequency; evaluate the unknown odel paraeters R, R 2,, 2 and C p with a non linear coplex fitting ethod [3]; copare the easureent data in the tie doain [] with the DC odel siulation results; calculate the residual between the odel and the easureents. The results of the frequency-doain easureent were used to deterine the five unknown odel circuit paraeters. The ain coil inductance was obtained fro design specifications, while the resistance R was calculated by considering the winding wire cross section and length and cross-checked by four-wire easureent. A non linear least square ethod was used to estiate R, R 2,, 2 and C p (see Table ). In Figures 4-5, the results of the fitting are shown. The odel fits the ipedance easureent with a residual less than 0 % for the absolute value of the ipedance up to 750 khz, and less than 0 % of error between the easured value and the siulated ipedance phase. The axiu difference between the odel and the easureent curves occurs for frequency higher than 600 khz. In any case, in the range of interest (fro 500 Hz to 450 khz) the odel is able to replicate the agnet behavior. Figure 4: odeled and easured aplitude Bode diagra of the ipedance (up) and residual (down). In Figure 6, the coplete odel for the transient analysis is shown. The circuit reproduces the tie doain easureent schee proposed in []. It siulates the flux linked to the pick up coil used to easure the field inside the agnet aperture. The excitation current wavefor (Figure ) is applied as input to the odel in order to understand the behavior of the tie integral of the voltage generated at the ends of the transforer secondary winding (Figure 6) representing the pick-up coil. The resistance of 0 G is the acquisition syste resistance. In Figure 7, the tie response of the equivalent circuit to the excitation current is shown. The flux siulated at the end of the acquisition chain, and the acquired actual flux expressed as described in (5), are shown. The circuit is able to replicate the decay effect due to the eddy currents but is still issing the contribution of the utual

5 4 coupling of the parasitic circuits with the pick-up coil in the flux easureents. The difference between easureent and siulation in the tie doain still evidences a very sallaplitude slow decay during the flat-top. In the future work all the utual couplings between the coil and the circuits will be taken into account. V. CONCUSIONS A odel-based ethod is proposed for easuring electroagnetic transients due to eddy currents in a short quadrupole agnet in tie and frequency doain. The effects of eddy currents in the pole laination and in the plane perpendicular to the agnet axis are odeled by two R/ chains. The residual between equivalent ipedance easureents and odel predictions below 750 khz is less than 0% for both the aplitude and phase. The odel describes the decay effect in the tie doain easureents by using an actual excitation current curve. In this case, the residual presents a slow decay effect during the current flat-top probably due to direct coupling between the coil and the two parasitic circuits. ACKNOWEDGMENTS Authors thank Ricardo Beltron Mercadillo, ucette Gaborit and Olaf Dunkel for their work and Alessandra obardi and Felice Cennao for their useful suggestions. Figure 5: odeled and actual ipedance: phase diagra (up) and percentage residual error (down). Figure 6: coplete circuital odel of the eddy current and of the easureent syste. Figure 7: easured and odeled flux scaled by the utual inductance : tie doain transients (up), and residual (down). REFERENCES [] R. Garoby, G. Bellodi, F. Gerigk, K. Hanke, A.M. obardi, M. Pasini, C. Rossi, E.Z. Sargsyan, M. Vretenar, inac4, a new injector for the CERN PS Booster, Proceedings of European Particle Accelerator Conference 2006, Edinburgh. [2] R.K. ittlewood, Magnetic properties of the new linac quadrupoles, CERN PS/SM/77-5, 977 [3] T. Zickler et al, MAGNETS, internal note, October [4] S. Igarashi, T. Adachi, H. Soeya, N. Tani, and Y. Watanabe, Eddy Current effects on the J-Parc RCS sextupole Magnets, IEEE Transactions on Applied Superconductivity, vol. 8, N. 2, June [5] S. Fang, W. Chou Analysis and Measureents of Eddy Current Effects of A Bea Tube in a Pulsed Magnet, Proceedings of European Particle Accelerator, 997, Vol. 3, 2-6 May, pp: [6] N. Tani, T. Adachi, H. Soeya, Y. Watanabe, H. Sato, and J. Kishiro, Eddy Current Effect of Magnets for J-Parc 3 GeV Synchroton, IEEE transactions on Applied Superconductivity, vol. 4, N. 2, June [7] M. Negrazus, D. George, V. Vrankovic, and M. Werner, Eddy Current Reduction in a Fast Raped Bending Magnet, IEEE transactions on applied superconductivity, vol. 6, N. 2, June [8] K. Fan,I. Sakai, Y. Arakaki, Modeling of eddy current effects in an opposite-field septu, Nuclear Instruents and Methods in Physics Research A,vol 597,pp 42-48, [9] K. Koseki, M. Tawada, H. Nakayaa, H. Kobayasi, M. Shirkata and J. Okaura, Pulsed bending agnet of the J-PARC MR, Proceedings of European Particle Accelerator Conference 2006, Edinburgh. [0] J. J. Feeley, A Siple Dynaic Model for Eddy Currents in a Magnetic Actuator, IEEE Transaction on Magnetics, vol. 32, nº. 2, pp , March 996 [] P. Arpaia, M. Buzio, G. Golluccio, Measureent of eddy current transients in a fast cycled INAC quadrupole agnet at CERN, XIX IMEKO World Congress Fundaental and Applied Metrology, isbon, Septeber [2] G. Deferne, A novel diagnostic syste for the electrical properties of superconducting agnets, International Magnetic Measureent Workshop- IMMW6, Bad Zurzach, October [3] R. Mcdonald, J. Schoonan, A. P. ehenen, The applicability and Power of Nonlinear east square for the analysis of Ipedance and Aitance data, Journal of electroanalytical cheistry, vol. 3, pp 77-95, January 982.