During the course of last RHIC runs the beta-functions at the collision points ({beta}*) have been reduced gradually to 0.7m. In order to maximize the collision luminosity and ensure the agreement of the actual machine optics with the design one, more precise measurements and control of {beta}* value and {beta}-waist location became necessary. The paper presents the results of the implementation of the technique applied in last two RHIC runs. The technique is based on well-known relation between the tune shift and the beta function and involves precise betatron tune measurements using BBQ system as well as specially developed knobs for {beta}-waist location control

Della Penna, A.

Litvinenko, V. N.

Malitsky, N.

Ptitsyn, V.

Satogata, T.

UNT Digital Library

...•.::.;;.:;.:;.:;.;;.::::::@:BROOKHAlIENN L~T I ~)'>J,A.'··L LA B 0 RLL\.T ORYBNlr81850~2009-CPBeta* and beta-waist measurement and controlatRHICv. Ptitsyn, A. Della Penna, V8NoLltvlnenko, No Malitsky ~T. SatogataPresented at the Particle Accelerator Conference (PAC09)Vancouver, B.C ., CanadaMay 4-8, 2009Collider-Acceterator DepartmentBrookhaven National LaboratoryP.O " Box 5000Upton, NY 11973-5000wNw.bnl.govNotice : Tnis manuscript has been authored by employees of Brookhaven Science Associates, LLC underContract No. DE- AC02-98CH 10886 with the U.S. Department of Energy. The publisher by accepting themanuscript for publication acknowledges that the United States Government retains a non-exclusive, paid-up,irrevocable, world-wide license to publish or reprod uce the published form of this manuscript, or allow othersto do so, for United States Government purposes.This preprint is intended for publication in a journal or proceedings. Since changes may be made beforepublication. it may not be cited or reproduced without the author's perm ission.DISCLAIMERThis report was prepared as an account of work sponsored by an agency of theUnited States Government. Neither the United States Government nor anyagency thereof nor any of their employees, nor any of their contractors,subcontractors, or their employees, makes any warranty, express or implied, orassumes any legal liability or responsibility for the accuracy, completeness, or anythird party' s use or the results of such use of any information, apparatus, product,or process disclosed, or represents that its use 'would not infringe privately ownedrights, Reference herein to any specific commercial product, process, or serviceby trade name, trademark, manufacturer, or otherwise, does not necessarilyconstitute or imply its endorsement, recommendation, or favoring by the UnitedStates Government or any agency thereof or its contractors or subcontractors.The views and opinions of authors expressed herein do not necessarily state orreflect those of the United States Govern..ment or any agency thereofBETA*' AND BETA~'VAIST MEASlJREMEN'"{ AND CO~'TROL AT RHICV. Ptitsyn, A. Della Penna, V. N. Litvinenko, N. Malitsky, T Satogata, BNL, NY 11980, USATo get the information on the value of beta-f..motion atan interaction point. the of a quadrupole, closestto the interaction point, should be changed. LVi RIDe thisis Q1 quadrupole; a part of lR focusing triplet . Th edistance L from the common point to the entrance of theQ1 quadrupole is 25.4m. There is Q1 quadrupole on eachside of a given interaction point, but the gradients of thosequadrupoles are of oppo site signs. The linear opticsfunctio ns (!3o.(J.{hl Q) at the entrance of the Q1 quadrupoleare related with the functions at the location (8*) offi-w-aist by simple relations of transformation through adrift:AbstractDuring the course of 13St RIDe runs tile beta-functionsat the coll ision points (~'!') have been reduced gradually toO.7m. 1."1 order to maximize the collision luminositv andensure the agreement of the actual machine optic; withthe design. one, more precise measurem ents and control of~* value and ~waist location became necessary. Thepaper presents the results of the implementation of thetechnique applied in last two R..IUC runs,The technique isbased on well-known relation between the tune shift andthe beta function and involves precise betatron tunemeasurements using BBQ system as wen as speciallydeveloped knobs tor ~-waist locat ion control. 1Yo = P" (2)where the index 0 refers to the entrance of Ql and the starsymbol de-notes the values taken at s*.The average value of ~-function at the Q1 can berelated with the optical functions at the quad entrance,using the elements (m{j) of the quadrupole transformationmatrix:(5)"s = L(P1.{J_ - jJ.a+)+2(fJ+b_-- P_b.r )"i(Pr{J_+ItaJ ---p' =-}(a,L'+2b,L- 2a,Ls')where fJ+and Ii are the average ~-flli"1ction taken at leftand righ t Q1 quadrupoles, and a and b are used to denote(13) =(m{l )Po - 2(mll 1n12)ao+(~22 )Yo (3)The matrix elements m ij are taken from the thick-lenstransformation matrix of the Q1 quadrupole.On the next step, subst ituting the relations (2) into theequation (3) , one gets the expression, which relates theaverage j3-function in the Q1 with i3* and s* . 'With twoQ1 quadrupoles, on each side of the IF, we have then thesystem of two equations, which should be resolved toextract P* and f3-waist values. Although those twoequations are non-linear in ~* and S*9 somesimplifications can bemade. The terms, presented in theseequations, have the following hierarchy of the order ofmagnitude : 13 Ljjt2 ' pe ; 1 (4)Since L=25.4m and expected ~* is less than lm, theterms of the order of 1 can be neg lected withoutnoticeable loss of the accuracy. After that the system ofthe equations becomes linear in ~* and s* and can beeasily resolved, leading to the following expressions :INTRODUCTIONOne of the year-to-year improvements, which haveprovided the substantial increase of the RHIC luminosity,was the reduction of p* at two collision points (lP6 andIP8). Over years the f)* in those interaction point s hasbeen reduced from 3m to O.7m.Further plans consider theattempt of the reduction to O.5m in near future . As ~* isreduced the need for its accurate measurement becomesmore and more important. The measurement shouldconfirm that the actual optics of the accelerator agreeswith the design one and, thus. the machine luminosity isclose to what is intended by 'the design . Besides that atsmaller p* values, the control of the longitudinal positionof Jj*, or ~~wais4 has to be tightened to avoid thereduction of the luminosity.flQ ::: (P)A(Kl) (1)4trwhere A(Kl) is the change of integrated normalized ouadgradient and <13>is the beta-function value averaged overthe length of a given quadrupole..I!< Work supported by Brookhaven Science Assoeiates , LLC underContract No . DE-AC02-98CHJ 0886 ·with the U.S. Depertmeat ofEnergy.MEASURE.\-IENT TECHNIQUESIn previous RIDC run s several methods have beendeveloped for the ver ification of the linear lattice of themachine [l ,2]. In Run-B, we have decided to develop anadditional method, aimed only at the measurement of theP* and ~-waist at the interaction points, 1."1 the hope to getmore reliable values of those parameters. The methoduses die well-known formula fur the change of thebetatron tune due to B small change of quadrupolegradient:the values corning from the averaging of the matrixelements of left and right Q1 quadrupoles; For the beta tron tune measurements, the BBQ tunemeasurement sy-stem has been used. It yovides verygood tune resolution at the level of 10 . In order toeliminate possible effects of the betatron coupling on themeasured tune shifts, the R..1JC rings were decoupled toAQmin-10-3and the betatron tunc separation was increasedabove0.01.An example of the tune measurements done by theBBQ system duri ng the Q1 gradient changes is shown inFigure 1. Tune shifts exceeded 0.005 for a gradientchange of an individual Ql by 10-4 mol. In the case ofsimultaneous changes of the gradients of two Q1s withopposite signs the tune shift was at the level of 0 .001 forAK1+=-L\KL= 10-4 m". The integrated normalized gradientofQ'l quad is about 0.08 mol.MEASUREMENT RES1JLTSFigure 1: BBQ betatron tune data during the variation ofthe Ql gradients. The dashed lines show the measuredtunes at A(Kl) = O.The maximum value of the gradient variation waslimited by the shift of s*, caused by this variation. Forinstance, for aKl = 2'10 -4 m" the calculated shift of s* isabout Scm. Therefore , to keep the s* measurement erroras low as few ern.. the variation of the gradient should notexceed 10-4 m '·! . ' That gave a preference to the techniquewhich uses individual gradient changes, since lessergradient variation can be used dur ing the betatron tunemeasurements.Table 1 summarizes the results of first round of themeasurements in both RIUC rings (Blue and Yellowrings), in both interaction region s (IR6 and IRS) withsmall P* and both tran sverse .plan es. The data wereobtained using the technique with the individual gradientchanges. i\ ..ccordin g to the des ign optics one shou ld havefj* in [O.7..0 .75]m range in both interaction points. InYellow, the measurements showed large deviations of themeasured i3* from the design values. In additi on, f3-waistpositi ons (s") were found sh ifted by noticeable amounts.The measurement precision, based on the 10-4accuracy ofthe BBQ tun e measurements, was evaluated to be at thelevel of +- Scm for s* an d 1.5% for ~* values . However(6)A(KlL =-A(KIL =!l.(Kl)(9)A(KI)~ =i1(Kl) _ = A(Kl )After the flr 3...7ld/i are extracted the vah..ies of ~* and s*can be calculated, usin g the formulas (5).In another technique , the grad ients of both Q1qua drupoles are changed simultaneously, If one looks atthe diffe rence and the sum of the averaged ~-functions inQ1 quads, the following expressions can be found (on thebasis of formulas f(2}-(3) or (5»)):There two techniques, based on the same set offormulas (I )~(3),(5), that have been tried . In onetechn ique, thep+and f1 are directly found by making thetune measurements due to independent gradient variationsof left and right Qls and using the formul a (1). Thus, forinstance: 4n jj,Q (7){J,. == A.(ii.~·~'r,Using the formulas (8) and (1), with calculated a and bparameters, one gets following dependences of the tuneshifts on ~* and s* for the RHIe case :(• \ A(KJ)h.Q = 4.32-8.08s 17 ;108.26.(Kl)110=----·- p. ,Here, the first line describes the tune shift when thegradient in left and right Qls are changed 'With ~eopposite sign, while the second line corresponds to tnesame sign of the gradient adjustment. On the basis ofthese two expressions both 13* and s* values can beobtained.The values (a,b) of the averaged products of the matrixelements are calculated aSS'..nning the design gradient andlength of the Q1 quadrupole. The fact that some design,but not measured, values have to be used in calculationslimits the accuracy ofboth techniques.Let 's note that in the case of a symmetric optics, whenthe parameters a; and a. , as wen as b+ and b. would beequal, the difference of P+ and Ii the expression (8)would be then proportional to s* . In th is case, the tuneshift due to the gradient change of opposite sign win bealso proportional to s" . Unfortunately, this is n ot the casefor the present mea surement scheme, since left and rightQ1s have opposite gra dient. But, as descri bed later in thispaper ("Future plans"), the scheme can be modified in thefutu re to allow for simpler measurement of s* in thesymmetric schem e.as mentioned before, larger errors possibly come from theimperfection of the design optics (Q1 transport matrix).Table 1: The results of the measurements of !3* and s*, bythe technique using individual gradient changes,r YeHow---r Blue~~ IR6 fR6 IR8 IRS IR6 fR6 IR8 IRSI Ii V H "'It' H V H Vb*,m 0.80 0.88 0.85 0.89 0.81 0.73 0.71 0.75~~~~~.~~~~s*,cm -34 ··33 2 30 -5 -3 20 sMEASUREMENTS W1m BET~t\· WAISTKNOBSSince the ~waist location for Yellow ring was foundconsiderably shifted, next step, tested during RHIC Run-S, was an attempt to reali ze a correction of that location.Specific knobs have been developed, which adju st thegradients of the interacti on region and matching sectionquadrupoles in such way that ~-waist shift is produced,while ~* changes are minimized and the ~-wavedistortion does not propagate outside of a giveninteraction region . Those knobs were tested duringanother series of the measurements done in two weeksafter the first one. This ~-waist correction was attemptedonly in the Yellow ring of RHIC . The results aresummarized in Table 2. The knobbing worked mostly asexpected. except the horizontal plane in the IR6 region.The quality of the knobs, calculated on the basis of thedesign optics, was limited by the deviation of the realmachine optics from the design . Several iterations of theknobbing correction may be required in such situation .FUTURE PLA.-l\1SThe measurements have demonstrated the feasibilityand efficiency of tested techniques. But the operationalusability of the measurement method and the accuracy ofthe measurements can be improved with smallmodifications. The modifications include the installationof additional small quadrupole magnets, close to the Qlmagnets. Those small warm magnets can be used asdedicated hardware for the ~* and s* measurements. Thegradient of the small magnets win be varied during themeasurements (in stead of Ql gradient). L, this case, dueto the symmetry. we 'will have: ai>a; bv-b.; providingthe simplifications of the formulas (5) and (8). In additionthe matrix elements, m~i, in this case , come from thematrix of the drift, instead of the quadrupole, and will beknown with greater precision. Also, one will have moreprecise knowledge of the magnet transfer function, and,therefore, better accuracy of the gradien t variations duringthe measurements.As already was noted earlier in the paper, thissymmetric system can simplify signi ficantl y themeasurement and control of s* . When changing thegrad ients of two magnets with opposite signs, but by thesame absolute value, the betatron tune shift will beproportional to s~ .Table 2: The measurement of ~* and s* in Yellow ringdone before and after the applications of fS-waist knobsI.\~IR8! IR6 IRS !; ! H V ~ H V I: •B*,m I Ibefore 0.80 : 0.91 0.90 0.94knobbingB*,mafter 0.76 0.96 0.86 0.88knobbings* .cmbefore -29 -53 -8 15knobbing ! I,ts*,cm!after 13 -29 -9 -5knobbing I !expected 24 I 27 0 -28lAs"'. emmeasured 42 I 24 -1 I -20lAs*,cmREFERENCES(1] M. Bai~ S. Peggs, T. Roser, T. Satogata, D. 'Irbojevic,PAC'03, Portland, WPAB072, p.2204 (2003).[2] R. Calaga, M. Bai, S. Peggs, T. Roser, T. Satogata,EPAC'04~ Lucerne, TUPLT 177. p.1541 (2004).

Beta* and beta-waist measurement and control at RHIC

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Beta* and beta-waist measurement and control at RHIC

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