M. Lee's program RESOLVE has recently been in extensive use at CEBAF to help identify and correct optics problems in recirculation arcs and in linac beamlines encountered during the commissioning of the 4-GeV accelerator. The authors describe the integration of the program with their machine applications software package. A significant vertical focusing error in one of the recirculation arcs, which is attributed to edge focusing of dipole magnets, was found from the analysis of difference orbit measurement data. A corrective measure has been successfully implemented. Optics checks in the spreader and recombiner regions are discussed along with linac optics and 60Hz jitter. 7 refs., 4 figs

Li, R.

Simrock, S.

Yunn, B. C.

UNT Digital Library

RESOLVE AT CEBAF* Byung C. Yunn, Rui Li, and Stefan Simrock Continuous Electron Beam Accelerator Facility 12000 Jefferson Avenue, Newport News, VA 23606, USA Abstract M. Lee's program RESOLVE[l] has recently been in ex- tensive use at CEBAF to help identify and correct optics problems in recirculation arcs and in linac beamlines en- countered during the commissioning of the 4GeV acceler- ator. We describe the integration of the program with our machine applications software package. A significant verti- cal focusing error in one of the recirculation arcs, which is attributed to edge focusing of dipole magnets, was found from the analysis of difference orbit measurement data. A corrective measure has been successfully implemented. O p  tics checks in the spreader and recombiner regions are dis- cussed along with linac optics and 60Hz jitter. energy changes from 500 keV to 5 MeV. A quite elaborate cavity handling routine[3] has been incorporated into the DIMAD being used at CEBAF in order to model transverse cavity focusing also into a cavity element. Consequently, the North Linac model in RESOLVE is likely to predict a slightly different trajectory in the beginning section for the first pass beam compared to DIMAD. However, the mod- eling difference should be negligible in the North Linac at higher passes and in the South Linac at  all passes. Our RE- SOLVE decks start from the 45 MeV beamline known as the Injector Chicane to minimize effects of cavity modeling presently available 'in the code. 111. DATA TAKING AND READING RESOLVE runs on a VAX system while machine control I. INTRODUCTION RESOLVE is a generic beam simulation code (up to sec- ond order in the transfer matrix) which can be used to find the possible causes of trajectory errors with multi-track data fittiDg capabilities. Usually, alignment errors and/or focusing errors of t e a  line magnets cause particle tra- jectories to deviate from the nominal path. Errors also show up when the beam energy is different from the design value. Finding and correcting sources of such errors quickly in the commissioning stage of a machine (CEBAF is cur- rently commissioning a 4 GeV CW electron accelerator) is extremely helpful. 11. PREPARATION OF RESOLVE DECKS Most CEBAF accelerator beamlines are designed with the optics code DIMAD[2] and a layout of any beamline must agree exactly with a corresponding DIMAD deck. The accelerator is divided naturally into 18 beamline units (45 MeV injector, two linacs - North and South, nine arcs - Arc 1 to 9, five beam switch yard lines, three experimen- tal hall lines - Hall A, B, and C). A conversion program from a DIMAD deck to a RESOLVE deck has been writ- ten to help preparing RESOLVE de& for these beamlines. For all beamline elements except a cavity, a straight for- ward translation of conventions and formats adopted in DI- MAD to those of RESOLVE is required for the conversion. Currently, a cavity element in RESOLVE is supposed to simulate a traveling wave linear accelerator as in TRANS- PORT with an energy gain proportional to the length of the element. However, we find that CEBAF cavity pro- vides significant transverse focusing in both directions, to low energy electron beam. This is especially true in the first two cavities of the 45 MeV injector where the beam is by UNIX based computers at CEBAF. We have devel- oped a fully interactive and easy to use RESOLVE data handling process integrated into CEBAF machine control system.. The program is written in Tcl scripts since most high level optics control software such as orbit brrection and energy and orbit lo& programs are presently also written in Tc1[4] which is a very pcwerful scripting lan- guage based on 2 library of C procedures for developing GUI applications. From an operator console we can pull up an optics menu and initiate a data taking procedure. Fig. 1 shows the main window for a data taking. A click on SelectBeamliine brings a menu of beamlies made of the 18 basic beamline units described in the previous .section. One then assembles a beamline of interest concatenating several units selected from the menu. Usually a corrector is chosen to provide a kick to the *This work was rupportedby the U.S. Department of Energy, under Figure. 1. A me contract No. DEAC-05~4ER40150. D!s!'f!lfNl'ION 6f m!g bOCUMEM IS UNLIMITED, 'R DISCLATMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or use- fulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any spe- cific commercial product, process, or service by trade name, trademark, manufac- turer, or otherwise does not necessarily constitute or imply its endorsement, mom- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. , beam by a specified amount and then all beam position monitor(BPM) readings are recorded along with magnet settings and cavity gradients for future reference. After collecting all necessary data one can close a data file and quit or continue to prepare BPM input files required for the RESOLVE program with a click on either the GetDif- ference or GetAbsolute button. Data files taken previously are converted into .bpm files with a data read procedure written also in Tcl. Data analysis is performed with R E  SOLVE. after transporting .bpm files to a VAX. IV. OPTICS CHECK WITH RESOLVE During the machine commissioning, we have systemat- ically checked optics of beamline components with R E  SOLVE to ensure proper transport of the beam through the accelerator. A. X-Y Coupling in Linacs Data shown h Fig. 2 agree well with the linac model in the second(South) Lux, where the 1st pass beam with an initial energy of 445 MeV gains 400 MeV in energy. As ex- pected, BPM data for the 1st pass beam in the first(North) Linac cannot be fitted with the model as a whole as a re- sult of iavity focusing in the front end of the North Linac. An interesting feature seen in Fig. 2 is the existence of x-y coupling due to a skew quadrupole component of the fundamental accelerating mode of CEBAF superconduct- ing cavity. A numerical calculation[5] predicts a total inte- grated gradient of the skew quad component, which is well localized ai the location of higher order mode couplers, to be approximately 4 gauss when a single 5-cell cavity is powered at 5 MV/m gradient. Furthermore, it is shown that the skew quad component from each cavity of linaca (we have 180 cavities in each linac) adds when cavities are phased for acceleration. BPM data in Fig. 2 are for the beam motion initiated by kicking the beam horizontally I 460.00 S20.00 110.00 6dO.00 7 1 0 . 0 O l  Figure. 2. Fit of BPM data with model in S. Linac for the 1st pass beam. Phase advance per cell is set to 60 deg for this run. (top figure) at the entrance of the South Linac. The x-y coupling in cavities induces the motion in the vertical plane (bottom figure). The strength of skew quadrupoles used for the fit agrees with the numerically estimated value. We should also mention that an experiment to measure the skew quad component of a CEBAF cavity has been per- formed[6] a t  the first cryomodule of the North Linac and results qualitatively confirmed the theoretical estimate. B. An: Optics Each arc is an isochronous 2nd order achromat, consist- ing of 3 distinct optical units called spreader, recombiner and arc proper. The nine arcs allow for 5 passes through the linacs. In higher energy arcs starting from Arc 5 we find that difference orbit data at spreader/recombiner modules gen- erally fit well with the models, while BPM data clearly deviate from the models at spreader/recombinet modules in the Arc 1 and 3. However, the agreement between the model and data is excellent in the spreader region of AX 2 as shown in Fig. 3. Figare. 3. A difference orbit in 845 MeV Arc 2 spreader region. BPM data in the Arc 1 shown in Fig. 4 clearly indi- cate that the verticaI phase advance across the arc proper is more than the design value. RESOLVE finds that with a 2.7 % reduction in the strength of all 16 vertically fo- cusing quadrupoles a t  the arc proper, the data agree well with our Arc 1 model as shown in the bottom figure of Fig. 4. Initially, we implemented this solution into the machine to correct arc optics and proceeded to the next Arc 2 expecting a simiIar optics problem. However, differ- ence orbit data in Arc 2 proper agreed well with the Arc 2 model in both horizontal and vertical planes. This was a puzzle because Arc 2 appears optically almost identical to Arc I. However, arc dipoles are not shimmed in general except in Arc 1. (All spreader and recombiier dipoles are shimmed.) In the 445 MeV Arc 1 beamline, an arc dipole is a l-m long parallel faced magnet with a bending radius p = 5.10m and with a bending angle 0 = 11.25O. With the nominal shimming, the angle of inclination = 5.625' of the entrance face and the angle of inclination = 5.625' of the exit face, the dipole is vertically focusing with an edge focal length f,, = 51.89m. As a result of shimming the beam following the reference trajectory now traverses the arc dipole with 81 = 61 = 7.165O. An added edge fo- cusing changes f,, to 40.65 m. One must compensate an est ra phase advance introduced by reducing the strength d?/. 0 I lu.1-4. 90.00 1bO.00 130.00 300.00 370.00 1 8 Figure. 4. BPM data in Arc l(top). The data fit nicely after vertical focusing correction(bottom). of a vertically focusing quadrupole (with a nominal focal length fg = 6.72m) located next to the dipole. Conse- quently, we expect a change in fq to 6.93 m which amounts to a 3.2% change, qualitatively explaining the discrepancy seen between the model and data. The vertically focusing quadrupole family now has a strength in complete agree- ment with the value found with RESOLVE after DIMAD refitting Arc 1 optics with the shimmed dipoles. C. 60Ht Pe1-tur6ations When a pulsed beam was line synchronized, RPM data were collected through each section as a function of time delay from the AC zero crossing in order to identify distributed 60Hz perturbations[7]. To describe an algorithm employed to analyze data, we start by introducing the initial beam vector incoming to beam- line & = (zo,z~,y0,~,60), the BPM reading X = (z('), d2), , d")) (We use only x readings for the sim- plicity of illustration.), and ' where d*) is the horizontal position at the ith monitor, M$) is the tranafer matrix fiom the start of the beamline to the ith monitor. These are related as X = &M. A good fit requires terms upto the 3rd harmonic in the Fourier decomposition of 60Hz perturbed quantities. For example, n=3 z(t) = ~(0) +C[S~ sin(2~nfot) + Cn C O S ( ~ ~ ~ ~ O ~ ) I ,  n=l  where fo = 6OHz. Each element in the vectors X and Iz, can be Fourier expanded yielding the vector coefficients Srn and Czn for the expansion of X, and Son and Con for the expansion of &. Assuming the transfer matrices are static, and using the orthorgonality of sinusoidal functions, we get Srn = SonM, Czn = C0n:M (n=1,3). This suggests that the propagation of the Fourier coefficients can also be treated by RESOLVE as difference orbits with respect to the time independent orbit (or the orbit averaging over time). Therefore, for each Srn and C r n  (n=1,3) a RE- SOLVE difference orbit can be obtained,.and the incoming beam vector can be constructed by fitting Son and Con. A localized kick generated by a 60Hz field perturbation can be simulated as an additional 6R = (0,6z', 0,66,0) at its location. One can decompose 6R with coefficient vectors S6n and Can. For a given n, the coefficients and Can behave just like kickers in the RESOLVE difference orbits for the corresponding Szn and C=n. As a consequence, we can quantify the distributed 60Hz kicks 'by resolving the difference orbits obtained from the coefficients of the frequency components of all the position monitors in the beamline. -_ - As fully described in [7], a 60Hz kick of approximately 5 microradian in the path length adjusting "dogleg" region for the first pass was identified using RESOLVE. This is consistent with a measurement which shows that a mal- function in the dogleg magnet supplies generates ripple of approximately the same magnitude. V. ACKNOWLEDGEMENTS We thank Martin Lee for graciously providing his pro- gram RESOLVE and Joe Eisognanc, Andrew Iiutton, and Hamici Shoaee for many helpfu! suggestions. [71 References M. Lee, "RESOLVE User's Guide". R. Servranckx et al., "Users Guide to the Program DI- MAD," SLAC report 285 (1985). D. Douglas, private communication. J. K. Ousterhout, Tcl and the Tk Toolkit, Addison Wes- ley Professional Computing Series (1994). 2. Li, UBeam Dynamics in the CEBAF Superconduct- ing Cavities," Ph.D. thesis, The College of William and Mary, 1995. M. G. Tiefenback, 2. Li, and B. C. Yunn, "Emittance Measurement and Transverse Cavity Transfer Matrix in the CEBAF Nuclear Physics Accelerator," unpub- lished, 1993. M. G. Tiefenback and R. Li, "Survey and Analysis of Line-Frequency Interference in the CEBAF Accelera- tor," this conference. 

Resolve at CEBAF

M. Lee`s program RESOLVE has recently been in extensive use at CEBAF to help identify and correct optics problems in recirculation arcs and in linac beamlines encountered during the commissioning of the 4- GeV accelerator. We describe the integration of the program with our machine applications software package. A significant vertical focusing error in one of the recirculation arcs, which is attributed to edge focusing of dipole magnets, was found from the analysis of difference orbit measurement data. A corrective measure has been successfully implemented. Optics checks in the spreader and recombiner regions are discussed along with linac optics and 60Hz jitter. 7 refs., 4 figs

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Resolve at CEBAF

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