The symmetries of the chromatic correction sections in the SLC Final Focus System allow a high-resolution determination of the pulse-to-pulse energy fluctuations by exploiting the information from beam position monitors (BPMs) in regions of large dispersion. By correlating this signal with other BPMs, one can infer the dispersion function as well as spatial components of transfer matrices anywhere in the arcs and the Final Focus System without interrupting normal machine operation. We present results from data recorded during either periods of stable operation or periods when the linac energy was intentionally varied. 6 refs., 7 figs

Burchat, P. R.

Emma, P.

Fieguth, T. H.

Lohse, T.

Panvini, R. S.

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3pfi<&<§) &oAJf- ^9or, n*:~-c?0J-SLAC-PUB-4907 Much 1989 (A) ONLINE MONITORING OF DISPERSION FUNCTIONS AND TRANSFER MATRICES AT THE SLC P. EMMA, T. H. FIEGUTH, T. LOHSE Stanford Linear Accelerator Center, Stanford University, Stanford, California S4SO9 P. R. BvitciiAT* VnivtTtity of California, Santa Cruz, California 95064 R. S. FANVWI** Venderitilt University, ffathviile, Tenntsttt S12SS SLAC-PUB—4907 DE89 013745 ABSTRACT The symmetries of the chromatic correction sections in the SLC Final Focus System allow thigh-resolution determination of the puke-to-palse energy fluctuations by exploiting the information from beam position monitors (BPMs) in regions of large disper­sion. By correlating this signal with other BPMs, one can infer the dispersion function as well at spatial components of transfer matrices anywhere in the arc* and the Final Focus System with­out interrupting normal machine operation. We present results from data recorded during either periods of stable operation or periods when the linac energy was intentionally varied, 1. INTRODUCTION The Final Focus System (FFS) ' in the Stanford Linear Collider (SLC) is a complex optical system for strong demagni-fication of beams at the interaction point. This requires not only a careful tninimiwtion of higher-order aberrations using a ded­icated chromatic correction section (CCS), sketched in Fig. 1, but also a precise matching of the dispersion function at the en­trance of the FFS. The input dispersion is measured by varying the energy in the linac and recording the correlated beam mo­tion at strip-line beam position monitors (BPMs) in the FFS. An online matching package fits the results and predicts the strengths of four corrector quadrupoles in the FFS. This is an efficient tool for dispersion correction but is not suited for dis­persion monitoring because it interrupts normal operation. In this paper we describe a complementary scheme which permits an online nondisruptive measurement of dispersion functions by-exploiting natural fluctuations of the beam energy. This allows, for the first time, monitoring of the sfesifiry of the dispersion match. The scheme is based on the information of CCS BPMs at positions where both dispersion and ft functions are large; i.e., BPMs with high sensitivity to energy and orbit fluctuations. ChrenlsSc Correction Section |-> ° l I 1-1 0l £ 0°°I 0°tt°IWi)ool OqplW B3 Sjrn A ' fe B2 B D B1 Fiy. /; Schematic of the CCS with positions ofBPMt — (A), (B), (C) and{D) — indicated. 2. GEOMETRIC AND CHROMATIC COMPONENTS We use TRANSPORT notation to represent propagation of a beam from point (A) to point {B), X<B> = RnXW + RuXW + RuS (1) where X is the transverse beam position, X' is the beam an­gle with respect to the design trajectory, and S (& Ap/p) is the fractional beam momentum deviation, which we identify with the fractional energy deviation since SLC beams are ultrarela-tivistic R is the transfer matrix from point (A) to point (£) , with X-Y coupling neglected. t Work supported by the Department of Energy, contract DE-AC03-76SF00515. * Work supported by the Department of Energy, contract PP-AMM— ** Work supported by the Nations! Science Foundation. The CCS is designed to correct lowest-order chro­matic aberrations using 4-dipole, 8-quadrupole, and 6-sextr pole magnets a* shown in Fig. I. These are arranged as tw identical —I telescopes such that local geometric aberrations du< to sexttipoles are cancelled. Given this symmetry, the two-by-two beam transfer matrix from BPM (A) in the first telescope to BPM (B) in the second (see Fig. 1) is the negative identity matrix. This holds for both transverse planes. From (1) and R.M:S) = —I, a simple relation for the beam energy deviation is found: XW) + *("> f = „ . (2) «is The Ait element from BPM (A) to BPM (B) is large and well known (460 nun), since it is almost completely determined by the two CCS dipolea B2 in Fig. 1. The position at BPM (A) or (fi) can be decomposed into a pure betatron component (independent of I), Xt, and a pure dispersive component, *M> = X, + !,<'»*- . X<fl> = -X, + »<«>« (3) where we again use R<**> = - I Now we define AX as the difference between the BPM readings: AX m i (*<<•>-*»») = *> + A, i , w where A»f = (l/2)(i)^' - ij' s') represents the component of the dispersion at BPM (A) due to an upstream mismatch. In order to separate Xa from 6 in Eq. (4), we assume An is not time de­pendent over one set of measurements and calculate it from the correlation of i with AX. X, (5) The measurement of trajectory angles at BPMs (A) and (0) require the information of another pair of BPMs in the CCS, indicated by the labels (C) and (£>) in Fig. 1. They are sepa­rated from BPMs (A) and (B) by simple drifts of known length At a 2.4 m. X,(A) As and *'<*> = As (6) This allows a derivation of AJf', Xf and An' in analogy to Eqs. (4) and (5). A careful study of uncertainties in the CCS optics showed that systematic errors in these measurements are small and that the resolutions are sufficient for online monitoring. 3. BPM DATA ACQUISITION An offline FORTRAN data acquisition program has been written to gather data from BPMs throughout the SLC and Presented at the IEEE Particle Accelerator Conference, Chicago, Illinois, March 20-BS, 1989. , , , iuU l l W ^ O r It-lib L / ^ u m W.S'IW .111 IS U^LIMITfcD write it to disk. The X position, Y position, and beam inten­sity is sampled for 850 BPMs {including the CCS BPMs (A), (B), (C) and (D)\ once every few seconds. The sample rate is one sample every ss 5 seconds. Presently, data is collected inter­actively over short periods, with 100 samples saved to disk for subsequent analysis. In the future, monitoring will run contin­uously, with data stored in a circular buffer. We will also store dynamically updating moments of BFM data for fast online tit­ling of lattice parameters, as described in the next chapter. 4. A MONITORING APPLICATION The correlation of measured betatron fluctuations Xg and energy fluctuations i with position measurements of BPMs is any region of interest can be exploited for a fast measurement of the dispersion function and elements of the transfer matrix. Let A'1'1 be the beam position measured at any BPM {labelled "())"]. Using Eq. (1) and the definition of Xf and X'y we can interpret this quantity in two ways: *<•> = R^X <-»> + flSf'X'W + fl'^'c (7a) or X«> = K<? : i ) X, + * , f ' * J +4*1 • (7») Both equations allow measurement of the transfer-matrix ele-oW:«l , p(A.l ments JtJ,' and Rl2 '. The energy correlations, however, de­termine the lattice dispersion Rit between BPMs (A) and («) in (7a), but the dispersion function ij'') [i.e., the total disper­sion between the source of energy jitter and BPM (i)] in {lb). Therefore, (76) is most useful for judgement of the total disper­sion mismatch at the entrance of the FFS, while (7a) allows in­vestigation of local lattice dispersion near the CCS and sources of mismatches within the FFS. In Fig. 2, we present a simulation of this procedure. We generated 100 trajectories with energy fluctuations of 0.4% and relatively large betatron motions of four times the betatron size of the beam. All BPM readings were smeared according to a resolution of 20 /im, The results from properly error weighted fits to (7a) and (76) are in good agreement with the input lattice for all BPMs inside the FFS. • Reconstructed — Generated IP at 4460 m - r 100-Fig. S; Rtconsiractti FFS lattice parameter* from simulated BPM data for 100 orbits with varying energies and trajectories. Reducing the amplitude of the betatron fluctuation, how­ever, quickly leads to resolution limitations for many of the FFS BPMs. It is therefore useful to reduce the number of fitted parameters in (7a) and (76). One possibility is to average the measurements over the angular information at BPM (A): <*W>I*<'U = <* ( , ,)|jr-„« = 16 + d s «H xw 6 (8a) Xs + tf'H (86) It is thus possible to measure n<"' and linear combinations of Jjft!<> and rtSf°, or fffi* and fl<f> with (8o) and (86), respectively. The correlation parameters in these linear combi­nations can is principle be extracted from the data if they are stable during a single monitoring period. Figure 3 shows the correlation terms in (8a) reconstructed from data taken during normal operation. The measurements are in good agreement with a linear combination of x\, '' and R[f'\ or R\l'} and R\j'">, which were obtained from fits of the nominal lattice parameters to the data and are superimposed in the figure. IP at 4480 m 0.8 ", 0.4 -l—I—I—I—r • Mnsurad (Mm)*! Fit —(H,,-0.14Snr* R 1 2 T 4 M«asursd - (Modal Fit , — ( B , , - ? . 6 7 5 i t O ' J R 1 j i -0.4 -0.8 400 200 4320 4360 4400 4440 :>"« Longitudinal Position (m) Fig. S: Linear combinations of FFS lattice parameters fnm tue-paramtcr fits to data taken during normal operation. Solid Una an bat fits to data using design parameters. Finally, averaging (8a) and (86) over all betatron fluctua­tions yields a direct relation for the dispersion function: (Jf'>"))|, = »«<5 (9) This simple one-parameter relation allows very stable fits. Fig. 4 shows the measurement of the dispersion function in the FFS Z DISCLAIMER 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 use­fulness of any information, apparatus, product, or process discloiied, or represents that its use would not infringe privately owned rights. Reference herein to any spe­cific commercial product, process, or service by trade name, trademark, manufac­turer, or otherwise does not necessarily constitute or imply its endorsement, recom­mendation, 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. taken when the beam energy was intentionally varied by ±0.3%. This precision measurement reveals a dispersion mismatch at the entrance of the FFS. This is confirmed in Fig. 5, which shows the correlation of &X with f, which according to Eq. (4) •§• 300 E - i — I r— _ — Nominal * Measured IP at 4460 m T T -100 4320 4360 4400 4440 iSu., Longitudinal Position (m) Fig. 4' Dispersion function in the FFS obtained from data urith large energy fluctuations intentionally introduced. 200 x < - 2 0 0 " -400 Fig. 5: Fit of the dispersion mismatch at BPM (A) for the data used in Fig. 4-is the dispersion mismatch at BPM (A). The dispersion function in the arc was derived for the same data set and i* displayed in Fig. 6. An example of a measurement of the FFS dispersion function taken during normal operation is presented in Fig. 7. The resolution of the measurement is satisfactory, although the dispersion function is derived solely from natural fluctuations in the beam energy. 5. PRESENT HARDWARE LIMITATIONS At present, the range of applications for this scheme is lim­ited, since most of the BPMs in the arcs and the FFS are read out in a multiplexed mod.. Only a fraction of the available BPMs are read on the same beam pulses as BPM* (A) and (B), which define the energy fluctuation via (2). This influences the dispersion measurements in a systematic way if the natural en­ergy fluctuations follow a fixed pattern in time. Similar limita­tions exist for the measurements of betatron orbit fluctuations. (Ill 60 III) 60 c 40 o «? ?0 o a. .S3 n a H -?o — I 1 1 1 1 1 — North Arc Dispersion —Nomina) A • Measured^ Front Arc „Jfam Back Arc \ Reverse Bend J _ _l_ Fig. 6: -40 -60 3000 3400 3B00 4200 Longitudinal Position (m) ., 4s Fig. 4, for the north are. 300 T — i — i — r — Nominal * Measured - IP at 4480 m o x T B"D 4320 4360 4400 4440 Wit, Longitudinal Position (m) ' Fig. 7: As Fig. 4, for data taken during normal operation. We plan to modify software and hardware such that infor­mation for BPMs (A), (B), (C) and (D) is available on all pulses of a multiplexer scan. This will further increase applicability of the new monitoring scheme. ACKNOWLEDGMENTS We would like to thank R. Grey, N. Phinney and B. Trailer for their help in setting up hardware and software. We are indebted to A. Hutton and W. Kozanecki for their enthusiastic support and many helpful discussions. One of us (T. L.) was supported by a grant from the Max Kade Foundation. REFERENCES 1. SIC Design Handbook, SLAC (December 1984). 2. J. J. Murray, K. L. Brown and T. Fieguth, "The Com­pleted Design of the SLC Final Focus System,' Pmc. Particle Accelerator Conference, Washington D.C., Vol. 3, (1987} p. 1331; SLAC-PUB-4219 (February 1987). 3. K. L. Brown, A Conceptual Design of Final Focus Systems for Linear Colliders, SLAC-PUB-4159 (June 1987). i. C. M. Hawke* and P. S. Bambade, "First Order Optical Matching in the Final Focus Section of the SLAC Linear Collider," Nuel. Inst, and Meth. A2T4 (1989) 27. 9. K. L. Browj, F. Rothacker, D. C. Carey, and Ch. Ise-b'n, TRANSPORT, A Computer Program for Design­ing Charged Particle Beam Transport Systems, SL-AC-9], Rev. 2 (May 1977); Fermilab Report No. 91, CERN 80-04. 6. T. Lohse, P. Emma, Linear Fitting of BPM Orbits and Lattice Parameters, SLAC CN-371 (February 1989). 3 

Online monitoring of dispersion functions and transfer matrices at the SLC

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Online monitoring of dispersion functions and transfer matrices at the SLC

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