PEP has been operated successfully under computer control. It is necessary for colliding beam operation that the errors in closed orbits, dispersion and beta functions be corrected. The schemes in the PEP control program for on-line correction of these errors are described in this paper. The orbit control tasks in the PEP control system perform the functions of data gathering, data presentation (color display, printing), calculation and setting of corrector magnets. The tasks are generally small and modular, taking information from the database, processing it, then returning the results to the database. The PEP operator communicates with the tasks through touch panels monitored by the Director program. The display task, which displays orbit and corrector information on a TV color display, provides the main information required by the operator

Blocker, C.

Chao, A. W.

Donald, M. H. R.

Hollebeek, R. J.

Lee, M. J.

Linstadt, J. E.

Siegrist, J. L.

Spencer, N.

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SOME SCHEMES FOR ON-LINE CORRECTION OF THE CLOSED ORBIT. DISPERSION AND BETA FUNCTIONS IN PEP M. H. R. Donald*, C- Blocker**, A. W. Chao, R. J . Hol lebeek, M. J . Lee, J . E. L i t i s t a d t , J . L. S i e g r i s t , N. Spencer Stanford Linear Acce le ra to r Center S tanford U n i v e r s i t y , S t an fo rd , CA 94305 SLAC-PUB-2666 PEP-NOTE-352 February 1981 (A) ,_>* y/tj/1/-Introduction PEP has been operated successfully under coaputcr control. It is necessary for colliding beam operation that the errors In closed orbits, dispersion and beta functions be corrected. The schemes In the PEP control program for on-line correction of these errors are des­cribed in this paper. The orbit control tasks in the PEP control system perform the functions of data gathering, date presenta­tion (color display, printing), calculation and setting of corrector magnets. The casks are generally snail and nodular, taking information from the database, pro­cessing it, then returning the results to the database. The PEP operator communicates with the tasks through touch panels nonltored by the Director program. The display task, which displays orbit and corrector infor­mation on a TV ;olor display, provides the main infor­mation required by the operator. The Orbit Calculator The orbit calculator task enables the operator to manipulate orbit data stored in the many orbit regis­ters. Manipulations are: fetching, storing, comparing and function calculation. Orbit information is stored in the database in various registers. Each register normally holds information for both c + and e~ beans, and for both horizontal and vertical planes. Each re­gister holds: a) the displacement at all beam position Eonltsrs (BPMs), b) the strength of all correctors, c) calculated displacement and slope at the interaction regions, values of maxima's and nns deviations through the regions, d) the time of the orbit scan (or calcula­tion). The many orbit registers are necessary to pro­vide flexibility. Registers are provided for: display, last scanned oroit, last calculated dispersion and beta functions, global and local corrections, RF orbits (se­paration of the e T and e~ ovbits due to the RF accelera­tion, both calculated and scanned). An orbit stack (depth of four) is used for calculations; and a memory register is provided for the operator's convenience. Local/Global Orbit Correction Local orbit correction is done by changing the displacement and/or slope *t the interaction regions. Local symmetric, anti-syroetric or combination bumps are made by changing the strength of two correctors on either side of the interaction regions. The corrections cay be keyed in using the orbit correction touch panel, or b, ci-r.necting the bumps to knobs by software. In the latter case the correction is monitored by reading the current in the corrector magnets as the knobs are turn­ed. Four knobs may be connected at any one cine allow­ing correction of x, x 1, y and y*. Clobal orbit correction is done by minimizing the rms orbit deviation at the BPMs. Calculations are done for one particle type (e+'e~> and one orientation (hori­zontal/vertical) at a lime. In this scheme the sensiti­vity matrix is calculated first. This matrix of partial derivatives relating the displacement at the Brits to Work supported by the Department of Energy, under con­tract number DE-AC03-76SF00515. Work supported by the Department of Energy, contract r+W-74Q5-ENG-A8 (Lawrence Berkeley Laboratory). Work supported by the Department of Energy, contract DE-ACO2-76ERO3064 (Harvard University). changes in corrector strength is derived from the ex­pression1 ^- 2 5 I r i T . y " j "i •"BT 8 . COSV(TI -1», - • jD. to Two methods of selecting the correctors are now avail­able: 1. One corrector is chosen as the most effective and the results are stored- Another corrector is then chosen that is the most effective partner to the first one, then a third corrector that is most ef­fective with tSe first two, etc. The matrix manipu­lation subroutines come from the program MIKADO.2 2. Orthogonal sets of correctors arc chosen by reducing the non-square sensitivity matTfx to its single value form. These sets are thc.i chosen in a manner similar to that of aethod 1, the singular values giv.> the effectiveness of each particular set. If all correctors are chosen then the two methods give identical results. Corrections may be applied on top of an existing set of corrections or by starting from scratch. In the latter case the orbit caused by the existing correctors Is removed from the scanned or­bit, and corrections are done on this orbit. Figures 1 and 2 show the result of a global correction to com-c E e e ••16-1 5 T | | i i' 1 1 1! [ Fig. 1. Typical vertical orbit for an operating PEP configuration. SC£\ 2'C 'C:0? Mi. . 3 A-&& 10FES6' 10:09:3? Fig. 2. Vertical orbit after global correction using Method 2. pletely change the corrector pattarn using tn« second orbit correction method with 10 sets of correctors. The predicted maximum and raw values were 4.24 and 1*60 mm; animnmTfisiMBsaiis Contributed to th« 1911 F««lclt AcctUrator Conf.r.nc, Vuhlniton, D . c , M»rch 11-13, INI. those achieved were 4.27 and 1.58 mm. One iteration using 20 sets of correctors further reduced the maximum and nns values to 3.5 and 1.37 mm. When correcting in the horizontal plane allowance is made for deviations of the machine energy from the ideal energy. The BPH da-.a together with a knowledge of the dispersion function and corrector strengths al­low us to find the energy deviation and the equilibrium orbit corresponding to this energy. The correction Is calculated using displacements about this equilibrium orbit. At Che end of the calculation the equilibrium orbit is added back in, taking account of changes In corrector strengths. In a similar manner we may sub­tract out the RF orbit of the positrons or electrons since this orbit is another Form of equilibrium orbit. Here we may choose between scanned or calculated values. Vertical Dispersion Function Correction The dispersion function is measured by scanning two orbits with the RF accelerating system running at different frequencies. The change of momentum of par­ticles on the synchronous orbit is given by of/f • -a(Ap/p) where a is the momentum compaction fac­tor. Using the relation ox<s) - n(s)*&p/p we calculate n(s) at all the EPMs. Examples of dispersion function <n> before and after correction are shown In Figs. 3 antf 4. Two schemes are available for correction of the '̂YipViy-- —-Fig. 3. Typical vertical dlaperaion function before correction. j l 1 ' l l l l | M | | | | l t l pu I'll' n»s •- c . i j BfiC MSV10R5 | f*T£BiC'CN REG'O'. C*E»6i 5 : 4 i : COfl^ECTO" ST*ENSTn using Eq. (1) twice. A change in one corrector causes a change In orbit at each quadrupole and sextupole. This change in orbit is a driving term for a change in dispersion function at every place in the ring. An efficient algorithm is used that does not require the integration over all quadrupoles and sextupoles for every corrector and BPH. 2) Correction by antisymmetric bumps. The correction of vertical dispersion function by changing corrector strengths as above results in chan­ges of orbit that may be undesirable. By using loc.;< antisymmetric bumps we may change the global dispersion function by Introducing only local changes in orbit. Correction may be achieveJ empirically by putting local bumps onto the knobs and tweaking for minimum beam height. A task is being tested that makes corrections in all r-Lx interaction regions simultaneously using method (2) of the orbit correction scheme. Local bumps may also be undesirable and steering in the interaction regions may be determined solely by the requirements f tie experimenters. Beta Function Correction Two methods are used for measurement of rhe beta functions: 1. Small changes are made to the currents flowing In the trim windings of the insertion quadrupoles and the change in machine tune caused by these varia­tions is recorded. Using the first order pertur­bation forauli' fiu • ££flK/(4») relating the tune change Av to the change in focussing parameter AK we may estimate B at the insertion quadrupoles. 2. Small changes are made to a corrector magnet be­tween the insertion qudrupoles and close to a BPM-Using Eq. (1) and assuaing that the nearest monitor is close enough to the corrector that the beta function perturbation &B/B is the same at both, we calculate fl». Ue then calculate Bj at the posi­tions of the other BFMa. Because the phase term will be unfavorable at many monitors we change cor­rectors at several interaction regions, summing the raaults with weight functions appropriate to the phase term. Using the sensitivity function i oKj coa2v<« - 1*1 - fjl> we use method (2) of the orbit correction scheme to ap­ply corrections oX to the trim windings. This task is at present used off-line from the control system. Figure 5 shows an uncorrected asymmetry in the beta 716.8 r SCAN • ir 37 JUJ Fig. 4. Vertical diapcraion function after correction. diapcraion function: 1) Correction by individual correctors. The global corraction of the vertical dispersion func­tion Is done by the same taak that globally correcta tha orbits. In this case the sensitivity matrix la the sensitivity of change in vertical dispersion function to change in corrector strength. This is calculated by Fig. S. Measurement of 0 function asysaretry (the atrangth of the orbit correctors used in the measure­ment is also shown). function Chat was later corrected. For this calcula­tion of the beta function, correctors in regions 2, A, 6, and 8 were changed in sequence. Performance of the Measurement and Correction Systeir At present the reproducibility of position mea­surement at 9b monitors is about O.03 am allowing us to measure the dispersion function to an accuracy of 1.3 cm. The absolute accuracy of the position measurement is difficult to determine. Using a measured orbit the correction programs will not predict a corrected orbit with peal, displacement values less than 3 mm; but using a simulated orbit this peak displacement can be reduced cany times further. (The simulated orbit is generated by random misalignment of magnets in a mathe­matical model)- Soaie of the discrepancy could be due to position errors, the rest to deviations of the renl nachir.e from the computer model. Orbit correction Is used on a daily basis and both horizontal and vertical orbits may be reduced to 3 mm peak <!.3 mm ras) at the monitors. The accuracy of correction is enhanced by changing the model of the machine as represented by a configuration having the measured tune values. Local correction by symmetric and antisymmetric bumps is very successful, the orbit changes outside of the bunps being very snail. More time needs to be devoted to investigate the performance of dispersion function correction. Cor­rection by local antisymmetric buxps performs much as predicted but is limited by the orbit requirements at the interaction points. Experiments have been started to simultaneously correct both the vertical orbit and dispersion functions. Beta functions can be measured at the insertion quadrupoles to an accuracy of 102 by the focusing per­turbation method, but not enough work has yet been done to determine the accuracy of the orbit change nethod. Using changes lar^e enough to give reproducibility comparable to the other method may cause changes to the linearity of the machine due to orbit deviations through the sextupoles. The correction of beta func­tion asymmetries also works well but a bad asymmetry requires iteration because Eq. (1) is only accurate to first order in A6. To reduce time consuming measure­ment we shall later do the iteration on a mathematical model. Acknowledgements The authors wish to acknowledge the help given by members of the PEP Machine Physics• Operations and I & C Groups. References 1. E. D. Courant and H. S. Snyder, "Theory of the Alternating Gradient Synchrotron", Ann. Phys. 2» 68 (1958). 2. B. Ai*tin and Y. Hartl, CERN/ISR-MA/73-17 (1973), (unpublished). -3-

Some schemes for on-line correction of the closed orbit, dispersion and beta functions in PEP

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Some schemes for on-line correction of the closed orbit, dispersion and beta functions in PEP

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