Beam-based alignment at the Cooler Synchrotron COSY as a prerequisite for an electric dipole moment measurement
T. Wagner, A. Nass, J. Pretz, F. Abusaif, A. Aggarwal, A. Andres, I. Bekman, N. Canale, I. Ciepal, G. Ciullo, F. Dahmen, S. Dymov, C. Ehrlich, R. Gebel, K. Grigoryev, D. Grzonka, V. Hejny, J. Hetzel, A. Kacharava, V. Kamerdzhiev, S. Karanth, I. Keshelashvili, A. Kononov, A. Kulikov, K. Laiham, A. Lehrach, P. Lenisa, N. Lomidze, A. Magiera, D. Mchedlishvili, F. Müller, N.N. Nikolaev, A. Pesce, V. Poncza, F. Rathmann, M. Retzlaff, A. Saleev, M. Schmühl, D. Shergelashvili, V. Shmakova, J. Slim, A. Stahl, E. Stephenson, H. Ströher, M. Tabidze, G. Tagliente, R. Talman, Yu. Uzikov, Yu. Valdau, A. Wrońska
BBeam-based alignment at the Cooler Synchrotron COSY as a prerequisite for anelectric dipole moment measurement
T. Wagner,
1, 2, ∗ A. Nass, J. Pretz,
1, 2, 3
F. Abusaif,
1, 2
A. Aggarwal, A. Andres,
1, 2
I. Bekman, N. Canale, I. Ciepal, G. Ciullo, F. Dahmen, S. Dymov,
5, 7
C. Ehrlich, R. Gebel, K. Grigoryev,
1, 2
D. Grzonka, V. Hejny, J. Hetzel, A. Kacharava, V. Kamerdzhiev, S. Karanth, I. Keshelashvili, A. Kononov, A. Kulikov, K. Laiham, A. Lehrach,
2, 3
P. Lenisa, N. Lomidze, A. Magiera, D. Mchedlishvili, F. M¨uller,
1, 2
N.N. Nikolaev,
9, 10
A. Pesce, V. Poncza,
1, 2
F. Rathmann, M. Retzlaff, A. Saleev, M. Schm¨uhl, D. Shergelashvili, V. Shmakova,
2, 7
J. Slim, A. Stahl, E. Stephenson, H. Str¨oher,
2, 3
M. Tabidze, G. Tagliente, R. Talman, Yu. Uzikov,
7, 15, 16
Yu. Valdau, and A. Wro´nska (JEDI collaboration) III. Physikalisches Institut B, RWTH Aachen University, 52056 Aachen, Germany Institut f¨ur Kernphysik, Forschungszentrum J¨ulich, 52425 J¨ulich, Germany JARA–FAME (Forces and Matter Experiments),Forschungszentrum J¨ulich and RWTH Aachen University, Germany Marian Smoluchowski Institute of Physics, Jagiellonian University, 30348 Cracow, Poland University of Ferrara and INFN, 44100 Ferrara, Italy Institute of Nuclear Physics, Polish Academy of Sciences, 31342 Crakow, Poland Laboratory of Nuclear Problems, Joint Institute for Nuclear Research, 141980 Dubna, Russia High-Energy Physics Institute, Tbilisi State University, 0186 Tbilisi, Georgia L.D. Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia Moscow Institute for Physics and Technology, 141700 Dolgoprudny, Russia Institut f¨ur Hochfrequenztechnik, RWTH Aachen University, 52056 Aachen, Germany Indiana University Center for Spacetime Symmetries, Bloomington, Indiana 47405, USA Istituto Nazionale di Fisica Nucleare, 70125 Bari, Italy Cornell University, Ithaca, New York 14850, USA Dubna State University, 141980 Dubna, Russia Department of Physics, M.V. Lomonosov Moscow State University, 119991 Moscow, Russia
The J¨ulich Electric Dipole moment Investigation (JEDI) collaboration aims at a direct measure-ment of the Electric Dipole Moment (EDM) of protons and deuterons using a storage ring. Themeasurement is based on a polarization measurement. In order to reach highest accuracy, one hasto know the exact trajectory through the magnets, especially the quadrupoles, to avoid the influ-ence of magnetic fields on the polarization vector. In this paper, the development of a beam-basedalignment technique is described that was developed and implemented at the COoler SYnchrotron(COSY) at Forschungszentrum J¨ulich. Well aligned quadrupoles permit one to absolutely calibratethe Beam Position Monitors (BPMs). The method is based on the fact that a particle beam whichdoes not pass through the center of a quadrupole experiences a deflection. The precision reachedby the method is approximately 40 µ m. I. INTRODUCTION AND MOTIVATION
The observed matter-antimatter asymmetry in the uni-verse cannot be explained by the Standard Model of par-ticle physics and cosmology alone. Additional CP vio-lating mechanisms beyond the already known effects areneeded [1]. Evidence for additional CP violating effectsis accessible from a measurement of permanent ElectricDipole Moments (EDMs) of subatomic particles. TheEDMs violate both parity and time reversal symmetry,and are also violating CP symmetry if the CPT-theoremholds. However, the EDMs predicted by the StandardModel are orders of magnitudes too small to explain thedominance of matter over antimatter in the universe.The discovery of a large EDM would hint towards physics ∗ corresponding author: [email protected] beyond the Standard Model and contribute to the expla-nation for the dominance of matter over antimatter inthe universe.The observation of EDMs of subatomic particles is pos-sible by observing their interaction with electric fields.For neutral particles (e.g., the neutron [2]) this can bedone in small volumes. Because of their accelerationin electric fields, for charged particles this constitutes amore difficult task. The J¨ulich Electric Dipole momentInvestigation (JEDI) Collaboration aims to measure theEDM of the proton and the deuteron in a storage ring.The control of systematic uncertainties is of paramountimportance, making the design of a dedicated EDM stor-age ring, and in particular the alignment of the ring ele-ments [3] and the correction of the closed-orbit [4] a verydemanding task. At the Cooler Synchrotron (COSY)(see Fig. 1) of Forschungszentrum J¨ulich, a first stor-age ring EDM measurement is presently being carriedout for deuterons [5] and being planned for protons. In a r X i v : . [ phy s i c s . acc - ph ] S e p order to improve the precision of the machine, a beam-based alignment method is applied to align the magneticcenters of the quadrupole magnets and the BPMs. Thisbeam-based alignment method has been applied at elec-tron [6] and hadron [7] machines before. This proce-dure requires the quadrupoles to be mechanically aligned.This was achieved by a surveying procedure to a preci-sion of 200 µ m. The detailed alignment data are listedin Tab. III and Tab. IV in the appendix. Several testswere performed to determine the effect of a full beam-based alignment survey of all quadrupoles in the accel-erator. The first two tests [8, 9] showed that the offsetbetween the quadrupoles and BPMs amounts to severalmm. Thus the beam-based alignment measurement hasto be performed for all quadrupoles in the accelerator inorder to have all BPMs properly calibrated.The full measurement campaign for the beam-basedalignment has been performed at COSY for all 56quadrupoles in the ring. With the use of the 31BPMs it was possible to determine the center of the 56quadrupoles in COSY and with that calculate the offsetbetween the BPMs and quadrupoles to get a better cali-bration of the BPMs. In addition this measurement alsoallowed to check the alignment of the quadrupoles in thestraight sections of the accelerator with respect to eachother, where it was found out that some magnets are noton axis with the other quadrupoles (in contrast to thealignment survey results).This paper is organized as follows. In section II a shortintroduction is given, in which the method is described.Section III describes the measurement at COSY and theanalysis of the data followed by section IV discussing theresults. II. THEORETICAL DESCRIPTION OFBEAM-BASED ALIGNMENT
In order to determine whether a particle beam passesthrough the center of a quadrupole, one can use the effectthat an off-center beam experiences a dipole componentleading to a kick of the particle beam. By varying thequadrupole strength, one simultaneously varies the mag-nitude of the dipole component of the field, which theoff-center beam experiences. This results in a measur-able closed-orbit change that depends on the offset ofthe beam inside the quadrupole whose strength was var-ied. The orbit change in one plane (here horizontal, x)can be described by [6]∆ x ( s ) = ∆ k · x ( s ) (cid:96)Bρ − k (cid:96)β ( s )2 Bρ tan πν × (cid:112) β ( s ) (cid:112) β ( s )2 sin πν cos[ φ ( s ) − φ ( s ) − πν ] , (1) Vermessungsb¨uro Stollenwerk & Burghof, 50126 Bergheim where the parameters are explained in Tab. I.
Table I. Explanation of the parameters in Eq. (1)Parameter Meaning∆ x Orbit change s Measurement position s Position of quadrupole∆ k Change in quadrupole strength x ( s ) Position of the beam with re-spect to the magnetic center of thequadrupole (cid:96) Length of quadrupole Bρ = pq Magnetic rigidity of the beam k Quadrupole strength β Beta function ν Betatron tune φ Betatron phase
From Eq. (1) one can see that the orbit change ∆ x ( s )at a given position s is proportional to the beam posi-tion inside the quadrupole x ( s ). As not all parameters inEq. (1) are perfectly known all along the accelerator, theproportionality is quite useful. This permits one to con-struct a merit function to extract the optimal position ofthe beam inside the quadrupole from the measured data.The merit function that was used for this measurementis f ( x ( s ) , y ( s )) = 1 N BPM N BPM (cid:88) i =1 (cid:2) (∆ x i ) + (∆ y i ) (cid:3) (2)∆ x i = x i ( x ( s ); +∆ k ) − x i ( x ( s ); − ∆ k )∆ y i = y i ( y ( s ); +∆ k ) − y i ( y ( s ); − ∆ k )In order to determine the merit function f ( x ( s ) , y ( s )), one has to take two measurements foreach beam position inside the quadrupole. One measure-ment with slightly increased (+∆ k ) quadrupole strengthand another one with slightly reduced ( − ∆ k ) quadrupolestrength. The differences of the beam positions x i and y i at the i -th beam position monitor are summed up inquadrature for all beam position monitors (see Eq. (2)).It is easy to conclude that the merit function is propor-tional to the offset of the beam inside the quadrupolesquared f ∝ (cid:80) i (∆ x i ) + (∆ y i ) ∝ a ( x ( s )) + b ( y ( s )) ,where the factors a and b are introduced because thesensitivity to the strength change of the quadrupole isdifferent in horizontal and vertical direction. The shapeof the merit function is a paraboloid and by finding itsminimum one can determine the optimal position of thebeam inside the quadrupole. Figure 1. Sketch of COSY [10] with labeled quadrupoles and BPMs along the ring. The black elements represent the quadrupolesand the yellow elements the BPMs. The quadrupoles in the straight sections are called ”QT”, whereas the quadrupoles in thearcs are called ”QU”, which is used to distinguish them due to a different width of the magnets. The dipoles are shown in redand horizontal and vertical steerers in gray and purple, respectively.
III. MEASUREMENTS AT COSYA. Hardware upgrades at COSY
In order to perform the measurement each quadrupolestrength has to be modified individually. In the power-ing scheme of COSY though, four quadrupoles are pow-ered by one main power supply. Some quadrupoles areequipped with back-leg windings, which allows for anindividual control. A first beam-based alignment mea-surement has been performed with those 12 quadrupolesalready [9].As not all quadrupoles could be equipped with back-legwindings, a new solution was found. A smaller floatingpower supply was added in parallel to one quadrupolemagnet in order to add or bypass some of the current.The devices chosen are source-sink power supplies andare ideally suited for the beam-based alignment. For costreasons, it was not possible to acquire 56 of these powersupplies. Instead it was decided to purchase only four ofthem and connect them as needed during the beam time.For that, connectors were mounted on each quadrupole,where the mobile power supplies can be plugged in.The communication with the power supplies was re-alized with serial communication over Ethernet in orderto dynamically control them during the measurement. H¨ocherl & Hackl GmbH
As an additional safety aspect the power supplies weredisconnected during the acceleration of the beam not tointerfere with the ramping of the quadrupoles and werelater connected with a relay after the acceleration.With this hardware upgrade and the existing system of31 BPMs the measurements described in the next sectioncould be performed.
B. Measurement procedure
As a first step a rough calibration of the BPMs wasperformed where only the quadrupoles, which have aBPM next to them, were measured for the calibrationof the BPMs. This first calibration was applied and thenthe measurement for all the quadrupoles was performedas a second step. This first calibration was done in or-der to know the approximate optimal position inside thequadrupoles and use a scan with a better resolution andsmaller range afterwards.The measurement procedure scans multiple differentbeam positions inside the quadrupole to find the opti-mal position, where a strength change does not steer thebeam. For the measurement the beam was prepared andthen the additional power supplies were connected withthe help of a relay. Then during the cycle the beam wasmoved to a position inside the quadrupoles with the helpof nearby steerers using a local orbit bump. This or-bit bump was kept while manipulating the quadrupolestrength and then removed in the end to have a compar- +∆ k − ∆ k nominal nominal nominal Q u a d r up o l e s t r e n g t h Timebeamprep. 10 sOrbit bump applied
Figure 2. Pattern of strength change of the quadrupole duringthe measurement. In the beginning of the cycle the beam isprepared, i.e. accelerated, bunched and positioned as desiredwith the use of an orbit bump. Then the quadrupole strengthis left at the nominal strength to have a reference point tocheck if something changes during the measurement time dueto outside effects. Next the quadrupole strength is increasedby +∆ k and afterwards again set to nominal strength. Thenthe quadrupole strength is set to nominal strength − ∆ k andafterwards set to nominal strength again. This is a completepattern leading to one data point for the merit function. ison of the orbit in order to check for long-term driftsduring the cycle. In between the variation steps ofthe quadrupole, the quadrupole was also set to nomi-nal strength in order to check for beam movement dueto other effects, which has to be corrected for. Thequadrupole strength variations were done all in a singlecycle, as different injection points with a shift of a fewtens of µ m have been observed at COSY. This was doneto avoid additional systematic errors. The pattern of thequadrupole strength variation can be seen in Fig. 2. C. Optimal position inside the quadrupole
Each measurement for one quadrupole is character-ized by 50 points (i.e. 50 cycles), where the effect ofthe strength change was measured for different positionsin the quadrupole (i.e. steerer settings). The choice of50 points was done to have sufficient information for thedetermination of the optimal position of the beam in-side the quadrupole magnet and to be able to finish themeasurement in the given time frame (50 cycles takingapproximately 1.5 hours). For each of the 50 points themeasurement procedure described beforehand is used andthen the merit function (see Eq. (2)) is calculated. Someof the 50 measured points had to be discarded due tobeam loss, low beam current at corner points and otherissues. The resolution of the BPM reading (20 µ m) isused to compute the error for the merit value of eachpoint. Note, that the absolute transverse position of theBPM with respect to a fixed reference frame is not neededhere. Then a paraboloid is fitted to the data points, withwhich one can extract the minimum, i.e. optimal posi-tion inside the quadrupole. The error on the minimumfor all the fits is of the order of 10 µ m. Since there isno BPM inside the quadrupole, the two BPMs on eitherside of the quadrupole were used to extrapolate into the quadrupole to determine the beam position inside. Thisextrapolation also took the steerers and their beam de-flections into account.An example of such a fit is given in Fig. 3, where onecan see the shape of the paraboloid as expected from themerit function. In addition one can see the optimal posi-tion inside that quadrupole as the green point, where thelines at the bottom of the plot are to guide the eye. Thequadrupole change ∆ k was kept constant during such ascan. ) / m m H o r i z o n t a l x ( s - - - - - ) / mm V e r t i c a l y ( s - - - - M e r i t V a l ue f / mm Figure 3. An example of a fit for the determination of theoptimal position inside a quadrupole is shown. This exampleshows a measurement of QU17, which is located in the arcs.The white points are the data points, where on the x- andy-axis the horizontal and vertical displacements of the beaminside the quadrupole are shown, and on the z-axis the calcu-lated merit function f ( x ( s ) , y ( s )) is depicted. The displace-ment of the beam inside the quadrupole is obtained by extrap-olation from BPMs up- and downstream of the quadrupole.The z-axis has been drawn upside down to make the minimum(highest point in the plot) easier to identify. The data pointshave a small error ( ≈ .
008 mm ), which is not displayed here.The fit to the data is the colored paraboloid, where the greendot marks the minimum of the fit. In order to guide the eyewhere the minimum is two lines at the bottom of the plothave been added. The two to four measurements that were taken for eachquadrupole were combined to get a value for the opti-mal position in each of the quadrupoles. In some casesthe variation of the optimal positions between the in-dividual measurements is around 150 µ m, which is largerthan the uncertainty on the minimum of the fit ( ≈ µ m).In other cases the variation between individual measure-ments is nearly zero. Thus the error on the combined op-timal position from the repeated measurements has beenestimated by looking at the distribution of the differ-ent spreads of all the quadrupoles to get an estimate onhow much repeated measurements differ from each other.From this an error of 40 µ m has been calculated and ap-plied to all optimal positions. An example of the spreadof the repeated measurements can be seen in Fig. 4, where Figure 4. Spread of measured optimal positions insidequadrupole QT04. The data points are the results from theindividual fits with the errors obtained by the fitting proce-dure. On the x-axis the date and time of the measurementare shown. In addition the weighted average values of theindividual measurements are shown as the horizontal yellowlines. The yellow shaded band around those has a size of ± µ m, which is the error assigned to all average positions,as explained in the text. one can see the individual measurements and their errorsfrom the fit. In addition a weighted average of the in-dividual measurements with an error band of 40 µ m isshown.The resulting optimal position in terms of the uncali-brated BPMs in all the quadrupoles are shown in Fig. 5with the light blue bars. There one can easily see thatoptimizing the beam to the zero position of the uncal-ibrated BPMs will lead to a beam not passing throughthe center of the quadrupoles. In addition one can alsosee that the quadrupoles in the straight sections whichare close together (see Fig. 1) are usually on one axis(compare Tab. III), which is expected as all quadrupoleswere aligned mechanically with a precision of 0 . D. BPM calibration
With the now known optimal positions inside thequadrupoles one can calibrate the BPMs such that thenew zero in the BPMs corresponds to the quadrupolesalso being at the zero of the coordinate system (see blackdashed line in Fig. 6). The BPM calibration is quitestraight forward with all the optimal quadrupole posi-tions known. This will move the optimal position insidethe quadrupoles close to the zero orbit in the BPMs, asthere are more quadrupoles than BPMs. In addition onecan use the sets of four quadrupoles in the straight sec-tions for the calibration as nearly all of them have a BPMinside them and are aligned mechanically. Thus not onlythe two closest quadrupoles but the whole set is used forthe calibration. An example for the calibration of a BPMcan be seen in Fig. 7, where the calibration was computedwith the help of nearby quadrupoles.Some observations also resulted from the calculationof the calibration, which is that some of the quadrupolesare actually not aligned correctly within the set of fourquadrupoles. This will be discussed in more detail later.In addition a part of the positions inside the quadrupolescould not be moved close to the zero line with the cali-bration of the BPMs, which is also due to a lack of BPMsthat can be calibrated in that section, as there are morequadrupoles than BPMs, see Fig. 5.
IV. DISCUSSION OF RESULTSA. Optimal position inside the quadrupoles
For each quadrupole the optimal position has beenextracted from the measured data as described above.These positions then have been used to calibrate theBPMs properly in order to have the zero orbit (see blackdashed line in Fig. 6) in the center of the quadrupoles.With the new calibration of the BPMs one can recalculatethe optimal positions in the quadrupoles in that coordi-nate system and see the improvement, that the centersof the quadrupoles are now at or close to the zero line ofthe coordinate system. This can be seen in Fig. 5, whereone can compare the light blue bars, which are the cal-culated optimal positions inside the quadrupoles beforecalibration and the dark blue bars, which are after thecalibration.
B. Alignment of the quadrupoles
As mentioned before the procedure requires that allquadrupoles are mechanically aligned. According to thesurveying this is the case within a tolerance of 0 . F i g u r e . T h e o p t i m a l b e a m p o s i t i o n i n a ll q u a d r up o l e s . T h e t o pp a r t o f t h e p l o t s h o w s t h e h o r i z o n t a l d i r e c t i o n a nd t h e b o tt o m p a r t s h o w s t h e v e r t i c a l d i r e c t i o n . T h e o p t i m a l p o s i t i o n i n s i d e t h e q u a d r up o l e b e f o r e t h e B P M c a li b r a t i o n c a nb e s ee n i n t h e li g h t b l u e c o l o r a nd a f t e r t h e B P M c a li b r a t i o n i t i ss h o w n i n t h e d a r k b l u e c o l o r . T h ee rr o r o n t h e o p t i m a l p o s i t i o n s i s µ m a s i nd i c a t e db y t h e r e d e rr o r - b a r s . T h e o p t i m a l p o s i t i o n s b e f o r e t h e c a li b r a t i o n a r e n o t c l o s e t o z e r o , w h i c h i s c o rr e c t e d a f t e r t h e c a li b r a t i o n , a s t h e o p t i m a l p o s i t i o n s h a v e b ee npu ll e d c l o s e r t o z e r o . I n t h e s t r a i g h t s e c t i o n s t h e q u a d r up o l e s l a b e ll e d Q T a r e c l o s e t og e t h e r i n s e t s o ff o u r a nd a r ee x p e c t e d t o b e o n t h e s a m e a x i s , a s t h e y r e f e r t o t h e s a m e B P M s . T hu s o n e c a nfi t a s t r a i g h t li n e t h r o u g h t h e m t o c a li b r a t e t h e B P M s t h e r e . F o r t h e a r c s , w h e r e t h e q u a d r up o l e s a r e l a b e l e d w i t h Q U , t h i s i s n o tt h e c a s e , a s t h e y a r e d i s t r i bu t e d m o r ee q u a ll y a l o n g t h e a r c . A f t e r t h e c a li b r a t i o n o n e c a n s t ill s ee s o m e p a tt e r n s t h a t d e v i a t e f r o m z e r o , w h i c h c o rr e s p o nd i nd i v i du a l q u a d r up o l e s t h a t a r e o ff b y up t o1 . mm . I n t h e s t r a i g h t s e c t i o n s o n e c a n c o m p a r e t h a tt o t h e o t h e r t h r ee q u a d r up o l e s i n t h e s e t a nd s ee a m i s a li g n m e n t o f t h e q u a d r up o l e . I n t h e a r c s t h e t h r ee d e v i a t i n g q u a d r up o l e s w i t h o u t a B P M c l o s e b y a nd t hu s o n e c a nn o t pu ll t h e m t o t h e z e r o li n e . T h e r e i t i s n o t c l e a r w h i c h q u a d r up o l e c o u l db e m i s a li g n e d a s a c o m p a r i s o n i s n o t p o ss i b l e a nd o n e h a s t o t r u s t i n t h e m e c h a n i c a l a li g n m e n tt o b e c o rr e c t . Figure 6. Model sketch of the optimization of the beampath in the accelerator. This model contains only threequadrupoles and has a total ring length of 4 . µ m.With respect to the quadrupole centers the beam can bealigned to a precision of 40 µ m. of quadrupoles close together, one can check if individ-ual quadrupoles are not correctly aligned, which is thecase for some of them. This can be seen for examplefor quadrupole QT01, which is not on the same axis asthe rest of the set (see Fig. 5, where the first four op-timal positions inside the quadrupoles do not fit on oneline for the horizontal direction). This observation hasbeen further investigated with a local re-measurement ofthe mechanical alignment of the quadrupoles. The me-chanical shift of the magnetic center has been verifiedby observing a small rotation of the quadrupole, whichleads to a shift of the magnetic center off of the beamaxis like observed with the beam-based alignment. Forthe arc sections of the accelerator this comparison is notpossible, as there are multiple elements in between theindividual quadrupoles. The outliers in the arcs are thequadrupoles, which do not have a BPM close by andthus could not be perfectly accounted for. Here one hasto trust the mechanical alignment and assume that allthe quadrupoles in the arcs are correctly positioned.A further observation in Fig. 5 is that there is a patternin one part of the straight section (QT04-QT12, verti-cally), where the optimal position inside the quadrupolesrises and then falls. This effect could also not be cor-rected for with the calibration of the BPMs due to tech-nical reasons. C. BPM calibration
The calibration of the BPMs has been calculated asexplained above and is depicted in Fig. 8. There one can
Figure 7. In order to calibrate a BPM in the straight sectionsall four quadrupoles were used to calculate the BPM offset.The bars are the optimal positions in the quadrupoles, whereone can fit a straight line (top plot). With that line one canthen calculate the offset at the position of the BPM, which isthe new BPM calibration. The optimal quadrupole positionafter the BPM calibration can be seen in the lower plot, wherethe optimal quadrupole positions are all close to zero. Theshaded region around the fit is used to indicate the alignmentprecision that the company Stollenwerk achieved. For thisspecific set of quadrupoles it was better than 0 . see the calibration that has to be applied to the BPMsin total. Not included in the bars are mechanical shiftsof BPMs, which have been introduced on purpose, e.g.BPM No. 25, which is a BPM close to the extraction.The overall pattern in the offsets is that for the verticaldirection the offset tends to be positive. This can beexplained by the fact that the BPMs are mounted on thebeam pipe, which itself is mounted on some fixed points,but otherwise laying in the iron yokes of the magnets.Without further support this causes a shift downwards,thus a positive offset has to be applied. For the horizontaldirection also a trend towards positive values can be seenas well, but here no easy explanation is obvious. Alloffsets were applied to the BPMs for future experimentsat COSY. Figure 8. The new BPM calibration. The horizontal offsets are shown in red and the vertical ones in yellow. On the x-axis theBPM name is displayed and on the y-axis the corresponding offsets. Before the beam-based alignment was done most of theoffsets were zero and the BPMs were not properly calibrated. One sees that the BPMs are off by several mm with respect tothe optimal beam axis given by the magnets.
D. Improvement of the orbit
Now the orbit in the accelerator will improve, but somesteering power is still needed, as the mechanical align-ment of the quadrupoles is only 200 µ m, whereas we coulddetermine the optimal positions inside them with a pre-cision of 40 µ m. Thus the design beam axis of the ac-celerator (blue horizontal line in Fig. 6) will not exactlymatch the optimized orbit in the machine. The optimizedorbit, going through the zero reading of the calibratedBPMs (red line in Fig. 6), will be significantly closer tothe center of the quadrupoles than the design orbit, asthe quadrupoles are slightly off the design axis due totheir alignment precision. The fact that the beam doesnot pass exactly through the centers of the quadrupolesis due to the optimization algorithm, which makes surethat the beam passes through the zeros of the BPMs. Thecloser a BPM and quadrupole are together the closer thebeam passes through the quadrupole center.In order to judge by how much the orbit improveddue to the correct calibration of the BPM offsets twomeasurements were performed. One with the BPM cal-ibration before applying the offsets and the other oneafterwards.For both measurements one tried to correct the orbitas good as possible with the orbit correction software [11] used at COSY. It tries to move the orbit as close as pos-sible to the predefined golden orbit, which correspondsto zero readings in the BPMs. This is done by using thesteerers in the accelerator.For the first measurement before applying the offsets ofthe BPMs the resulting steerer current RMS can be seenin Tab. II. The RMS values for the second measurementwith the applied offsets from the beam-based alignmentprocedure can also be seen in Tab. II. In order to seethe improvement one has to achieve similar orbit RMSvalues, which was the case for these measurements, asthe orbit correction software ran until the best solutionwas found. Then a comparison of the steerer currenttells by how much the new calibration is an improvement.For the horizontal direction one needs 20% less steerercurrent and for the vertical direction 80% less steerercurrent, while keeping similar orbit RMS values for bothdirections. This improvement shows that one does nothave to correct against the beam being offset inside thequadrupoles anymore and thus the beam is not deflectedby the quadrupoles anymore.This result shows that the beam-based alignment hasbeen successfully applied at COSY and it helps improvethe orbit in the accelerator. This then also enables acomparison of the measurement with the simulations, asthe BPMs are now calibrated, and also to compare sim-ulations to previous measurements. Table II. Change of Steerer current RMS depending on thecalibration of the BPMs with similar corrected orbits RMS.Before the calibration with the obtained results only knownand deliberate shifts of BPMs were included, which was thecase for 3 out of 31 BPMs. After the calibration all of theBPMs were calibrated to show zero when the beam is cen-tered in the nearby quadrupoles. The Orbit was corrected tominimal orbit RMS, where the goal was to reach a zero orbit,and the values for the corresponding steerer currents, whichare given in a percentage of the maximal current and their cor-responding kick in mrad, were recorded. Due to constraintsduring this test the performance of the horizontal directionwas not as good as it could have been.Horizontal Steerer RMS x Before calibration 5 .
03 % / 0 .
63 mradAfter calibration 3 .
90 % / 0 .
49 mradVertical Steerer RMS y Before calibration 4 .
39 % / 0 .
25 mradAfter calibration 0 .
79 % / 0 .
05 mrad
V. CONCLUSION
With the beam-based alignment procedure we suc-ceeded in aligning the beam with respect to the centerof the quadrupoles to 40 µ m. This is an important in-gredient for spin tracking based on a further improvedCOSY model, to finally be able to understand system-atic errors of the EDM measurement at COSY [12]. Thebeam position monitors (BPMs) were calibrated suchthat the quadrupoles are located at (or close to) thezero line of the coordinate system defined by the BPMs. The quadrupoles themselves are aligned to a precision of200 µ m with respect to the design beam axis, see Fig. 6.In principle the method could be further improved.The limit of 40 µ m originates from fluctuations betweenmeasurements with some time gap in between (see Fig. 4)where mechanical drifts of this order, due to e.g. tem-perature changes, are expected. A single measurementreaches an accuracy of about ≈ µ m (Fig. 4). Thus,running a feedback system and continuously monitoringthe quadrupoles one could reach the precision of a singlemeasurement.As a result of this BPM calibration, the orbit cor-rection now leads to an orbit passing close to the cen-ter of the quadrupoles. This could be confirmed by thefact that after the beam-based alignment procedure lesssteerer correction power is needed to reach the optimalorbit, as one does not have to act against the steering ofoff-center quadrupoles.Apart from a better orbit in the machine, alsomisalignments of quadrupoles were observed and con-firmed with a mechanical measurement. Those observedquadrupole misalignments will be corrected in the futureimprove the quality of the accelerator further. ACKNOWLEDGMENTS
The authors would like to thank the staff of COSYand especially the power supply group of COSY for pro-viding excellent working conditions and for their sup-port concerning the technical aspects of the experi-ment. This work has been financially supported by anERC Advanced-Grant (srEDM [1] A. Sakharov, Sov. Phys. Usp. , 392 (1991).[2] C. Abel et al. (nEDM), Phys. Rev. Lett. , 081803(2020), arXiv:2001.11966 [hep-ex].[3] F. Abusaif et al. , Storage Ring to Search for ElectricDipole Moments of Charged Particles – Feasibility Study(2019), arXiv:1912.07881 [hep-ex].[4] M. S. Rosenthal, Experimental Benchmarking of SpinTracking Algorithms for Electric Dipole Moment Searchesat the Cooler Synchrotron COSY , Ph.D. thesis, RWTHAachen U. (2016).[5] P. Lenisa (JEDI), AIP Conf. Proc. , 020009 (2020).[6] G. Portmann, D. Robin, and L. Schachinger, Conf. Proc.C , 2693 (1996).[7] J. Niedziela, C. Montag, and T. Satogata, Conf. Proc. C , 3493 (2005).[8] T. Wagner, Hyperfine Interact. , 61 (2018).[9] T. Wagner and J. Pretz (JEDI), in (2019) p. THPGW024. [10] R. Maier et al. , Nuclear Physics A , 395 (1997), pro-ceedings of the Third International Conference on Nu-clear Physics at Storage Rings.[11] J. Ritman et al. , Berichte des Forschungszentrums J¨ulich(2016).[12] V. Poncza and A. Lehrach, in (2019) p. MOPTS028. Appendix: Mechanical alignment of the quadrupoles
The appendix contains two tables listing the values forthe mechanical alignment of the quadrupoles.
Table III. Mechanical alignment of COSY quadrupoles in thestraight sections relative to design specifications. ∆z is alongbeam direction and ∆x and ∆y are horizontally and verti-cally, respectively. The mean error on those measurementsis 0 .
06 mm. The additional separation in the table indicatesthe sets of quadrupoles which are located close together. Thealignment and measurement of the data has been performedby Vermessungsb¨uro Stollenwerk & Burghof.Element Translation [mm]∆z ∆x ∆yQT01 -1.21 0.02 -0.37QT02 0.42 0.01 -0.11QT03 -0.46 0.02 -0.18QT04 3.43 0.07 -0.34QT05 0.39 -0.04 -0.06QT06 -0.73 -0.06 -0.07QT07 -0.14 -0.07 -0.03QT08 -0.62 -0.08 0.98QT09 -0.33 0.03 0.06QT10 -0.13 -0.19 0.15QT11 -0.43 -0.07 -0.10QT12 -0.45 -0.03 0.09QT13 -0.34 0.08 0.21QT14 -0.07 -0.18 0.18QT15 -0.25 -0.22 0.16QT16 -0.33 -0.09 0.01QT17 0.11 -0.13 0.56QT18 0.08 -0.26 -0.28QT19 0.13 -0.12 0.34QT20 -0.92 -0.23 0.24QT21 2.72 -0.31 0.35QT22 0.76 -0.39 0.10QT23 0.60 -0.21 0.02QT24 0.75 -0.27 0.12QT25 0.45 -0.28 0.04QT26 0.51 -0.30 0.86QT27 0.59 -0.30 -0.11QT28 0.70 -0.19 -0.04QT29 1.78 -0.16 -0.12QT30 0.32 0.15 0.13QT31 0.50 0.05 0.23QT32 0.43 -0.24 0.16 Table IV. Mechanical alignment of COSY quadrupoles in thearcs relative to design specifications. ∆z is along beam direc-tion and ∆x and ∆y are horizontally and vertically, respec-tively. The mean error on those measurements is 0 ..