MAGIC--A THIN LENS AND BENDS MATCHING PROGRAM M. J. Lee SLAC and W. W. Lee Natioo.al Accelerator Laboratory

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1 S5-73/258 MAGC--A THN LENS AND BENDS MATCHNG PROGRAM M. J. Lee SLAC and W. W. Lee Natioo.al Accelerator Laboratory The design of the intersection region for the NAL main ring and proton storage ring (30-70 GeV) has been carried out with the aid of a computer code "MAGC" specially written for magnet lattice insertion using thin-lena magnets, This COlYlputer code enables the user to fit the values of the 13, a, 7), 7) and -functions t at both ends of an insertion and the values of the transport l matrix elements. The fitting is done by using VMM a least aquare fitting code from ANL. Since MAGC is a special purpose code and since it uses thin lens magnets, the computation time and the rate of convergence are faster than those of a general puspose code such aa TRANSPORT. 3 The method of computation and its application in designing the insertions for the intersection region are presented in this report, Method of Computation Consider an insertion composed of a number of quadrupole magnets, bending magnets and drift lengths. The transport matrix for either horizontal or vertical motion for the insertion fs given by (t) where M is the transport matrix for the th element in the insertion and n is the total number of elements. For a focusing quadrupole magnet M -x 0 (2) o ( ), where x 1/focallength; for a bending magnet M 0 (3) o ( : ) where x = bend angle; for a drift space where x = drift length. ( ) x 0 M (4), -2t 7

2 The values of the 13. 0', '. T/', and 4J -function at the exit of the insertion are given by: T 2 2 U -2T 1?12 T 12 -T H T l1 1+ 2T 1ZT Z1 -TU T 12 (5) 2. 2 T 21-2T T 2Z 21 Tn Til rj' 2. r/ i (6) o o -i where &jjz ' tan (7) (8) and the values of these functions at the entrance (with subscript 1) equal to the values desired. h -. Let f be the value of the 1 function and f be the corresponding deslred value with i i i= 1,3,..., Z1refertol'z' 0'2' '12' '12' "'2' Tit' Tn' Tn' T 21, T 2Z ' T Z3 for the x-motion. and i = 2, 4,.,., ZZ refer to these functions for the y-motion. Consider the function (9) with summation over the indexes of those functions whose values are to be fitted, The fitting is done via a least square minimization of F, n particular a Bolution is obtained if the minimum value of F is zero, i, e., f = i for all the desired functions, f the minimum value of F is not i 1 zero we fail to find 8. solution. parameter For this minimization procedure we need to compute the derivatives of F with respect to each (fo) -218

3 From the differentiation of Eqs. (5) to (7) we can express of/llx in terms of T and (DT}jj' ij where (tt) DM is the derivative of the M matrix with respect to x t may be noted that the DM matrix. has only one nonzero element. n addition, we need a guess solution (xo's). Constraints may be imposed upon the values of system parameters by the conditions (t2) where c's are constants whose values may be specified by the user. For example, c : b ( - p) eeps x : x : c : t for all drift spaces and c = 0 for the other elements eeps the length of p po the insertion fixed. nsertions for the ntersection Region The low-13 insertion for the main ring utilizing the available free space of 50 m in the longstraight section is shown in Fig, t, The insertion, which is anti-symmetric in its focusing actions with respect to the midpoint of the insertion region, gives the midpoint 13. or 13*, a value of 7 m, The corresponding tune shift tl.v, which is the same for both planes in the case of an anti-symmetric lnse Mion, is The insertion quadrupoles, whose focusing strengths are defined as :: (field gradient) x (length) (l3p of particle) are physically resonable with conventional magnets. The resulting momentum dispersion function in the region is also shown in Fig. 1. The midpoint 1), or T *. is now 0.6 t m. Since it is desirable to match the beam sizes at the interaction point, the value of the 13* for the proton storage ring is to be determined by the beam energies involved. Figure 2 shows an insertion for 13* = t m corresponding to an interaction of, say, 30 GeV X 2tO GeV. The insertion, which is also antis ymmetric, has a length of 56 m (3-1/2 cells) and quadrupoles used are phys ically resonable with superconducting magnets. The vertical crossing insertion is accomplished using a pair of septum magnets together with a series of superconducting dipoles. The insertion has a crossing angle of 6.67 mrad and a clear space of 15 m for the experimental apparatus, The detailed arrangements for the interaction region are shown in Fig. 3 and the relevant parameters are given in Table 1. The total insertion length in this case for the proton storage ring is 88 Tl (5-t/2 cells). Additional space is needed if low (or zero) dispersion at the interaction point is desired, Since any colliding beam experiment using the main ring will be run parasitically, the insertions described here fulfill the basic requirement that they constitute a minimum interference with the normal main ring operations. -219

4 Table 1. Parameters for the nsertion Magnets Main Ring conventional Ouadrupoles: B' 140 G/m at 210 GeV Vertical Dimension = 22 em Length lm) Distance from nteraction Point (m) OM Storage Ring Superconductinq Ouadrupoles: B' = 354 G/m at 30 GeV Vertical Dimension = 30 em Length (m) Distance from nteraction Point lm) Os and 44 (normal quad) Septurn Magnet: B = 4.94 G at 30 GeV Vertical Dimension = 22 em Length lm) V Distance from nteraction Point (m) Superconducting Dipoles: B = G at 30 GeV Vertical Dimension = 30 em Length. lm) Distance from nteraction Point lm) H 2 22 V V V

5 References ie. D. Courant and H. S. Synder, Ann. of Phys., 1 (1958). Zw. C. Davidon, Variable Metric Method for Minimization, ANL-5990 (Revised 1966) ANL Z0135, Variable Metric Minimization (1967). 3K. L. Brown and S. K. Howry, Transport/360, SLAC Report No. 91 (i970). 4C. Bovet et a., A Selection of Formulae and Data Useful for the Design of A, G. Synchrotrons, CERN Report MPS-S/lnt. DL/63-3 (t968) nserton REGON (SOm) _l, 1'7=0.6/m 1.0 )( li=o.o1 &l*r lll=26m p 213m 2=4.354m FROM l [ =5.396m = = =2.25m X Y t. 1..!)W-8 NSERTON FOR THE MAN RNG FG

6 NSERTON REGON (56m) ',8(m), \ \ 400 \ \ lq / l3max ' d f3 Y / * tp=tm... f!jmln 10=0 l+-ll-----._.j ,= /m ll= 34m {smox=872.6m = 02886/m l2= 2.17m pmin=os7m at 1.63m { =-o.43731m L3 = 8B3m FROM END QUADS 'J..= 'J!. = x y LCNJ-S NSERTON FOR THE PROTON STORAGE RNG FG

7 o V3 Q3V2(8H) 25CL H F...nQ2D o 210m SCALE, N, C Z w C) cl 0::: r. MAN RNG fl :"-l*:15 F D F'-- QMQM2QM3 h r--l 92 MAN.' n_ o,30m2qm t- CJ) o F 0 rj) 9 1 =6.67 MRAD 9z=28.4MRAD 9 3 =62.5 MRAD Q Q2 84 =35.0MRAD F 0 H (9H)VlQ3V3 F ELEVATON VEW OF THE CROSSNG NSERTON C) z llj a:: FG.3 '