To obtain specific beam charactctistic3

Transcription

1 SS-73/254 NSERTONS FOR COLLDNG-BEAM STORAGE RNGS W. W. Lee and L. C. Tf'ng National Accelera.tor Laboratory T';O high-energy colliding'-bearn 5 to:r.agc :r.\ ngs "'Jere r: tuuj cd. Both rings can store beams of 1000 GeV cit d bonding field of kg obtained with supcrcondlcting magnet5. Eacl-j \~ill have ~ight interaction straight sections with lengths of ~lcoo m Dipoles are placed in the drift spaces 0 to form the curved ~~ection. The simplest structure for the strili~lht sectioll is a continuation of the normal cells bur without. the )",nding dipoles. Thus, the lenqt-1 of a straight ~c(;li{)j),!'lame a~~ that of a curved section, should be an integral multiple of half-cell length. The beams in the t\"o rings collide in the straight Gection!, for particle-physics experiments. n the colli5.i.on region the be~m characteristics are modified to meet the requirements of individual experiments. To obtain specific beam charactctistic3 a number of contiguous half-cells are remov()d ;).nd replaced by special-function insertions. The lengths of all insertions should, therefore, also be integral multiples of half-cell length. The following specia1 function insertions arc us<lfu1. 1. Crossing insertion - the curved sections of the two ring~ arc stacked one above the other with a separ.ation of the order m between beams. n this insertion the t_wo beams are brought v<:'rtica11y together. 2. Low-S insertion - in which the beams are made narrow in the collision region, thereby giving hicjh luminosity (,fff'" beam transverse width). eilch for the larger rings and "'250 m each toy. the smaller rings. For both ring::> the curved sectiolls c6nsigt o[ sr:.paralf,(j hmctiolj FODG cells with a phase advance of 90 0 per Goll. ThiA r~oicc of phase advance i!) advantageous for locating beam deflectinq elements. -203

2 3. High-~ insertion - wider beams are more parallel, hence desirable for some experiments. 4. Low-dispersion (or zero-dispersion) insertion - in which the position (D) and angle (D') dispersion~ are made Bffiilll (or zero) in the collision region. 5. High-dispersion insertion - High dispersion can provide a better definition for energy of an interaction. 6. Tune-adjusting insertion - The phd50 advunce acro~s the in5ertion can be adjusted over a wide range of values to set the tune v of the ring at good operating values. For the prescnt purpose it is adequate to give examples of il few more essential types of insertions. All parameters are computed using the thin-lens and thin-bend approximation \~hich i~, fairly good for these insertion~. The optics and dispersion n1dtenings are obtained using the pro<]rarn J \J\GC (Ma~Jne t ngcrtion Code) 1 in f/hi ch all elements <lre assumed Lo be "thin" ilild mil tch i ng equiltions together with constrain t conditions arc solved by the Variable Metric Minim.i~ation ~kthod. 2 tva illwl1ne a normal cell length af ilnd that ei1(;\1 one of: eight curved sections conti\ill~ 16!, cells,!wnrc h;'~3 il lon'llh of 990 m. The bending angle per cell is, therefore, 47.6 m~ad. With a phase advance of 900 per cell and using thin-lcny-andbend approximation one gets for normal cell orbit paramet:cj:r-l a F (1 +h) x ~ 2 60 n = 102 n (F +" ( ) = +" 2.41 (1 -.! ) x = 17.6 m 6 D -fl. D ~ (12-1) _. ~ Yl (2 + F.! ) x (47.6 mrad) x (60 m) ,1 T! "4 {2 1 (2 +!. ) x (47.6 mrad) '" Yp :!:. 2tt/2 J2 (2 -!.) x (47.6 mrad) x (60 10) 11 = m 0 " n (2 ) x (47.6 mrdd) D +" -Ji 2fi. -204

3 t is important that the dipoles and qlji'.ldrupoles should be physically resonable with superconducting magnet.s. n the thinlens and thin-bend approximation, the dipole strength (bend-angle) is e '" (field) J{ and the quadrupole strength is n a normal half-cell, one gets (length) - (Dp of particle) k ~ (field gradient) x (length) (Bp of parhcle) 23.S mrad k 2 12/60 n O.04?l/m A. CroBsing insertion An insertion which brings the two beams vertically together without altering the optics of the beams is ohown i.n Figure 1 together t~ith the i)-functiong, ''hir.; insertion with a total length of >:9.. '" 90 n will replace l~ norl\\al cells. 'rhe optical functions Cl and B at either end match those of il normal cell. As shon'n in Figure 1 the beams collide immediately to the right of the fourth belld. One can, of courr;c, tri.m the bend-angles to keep the beam slightly sopar'lted at that point and use additiunal small vertical dipoles to form collision rcgionn wi th d~sired geometry at desired locati.ons fart_he:!: to the right. The vertical bends in the insertion introduce a f.imal1 amount of vertical dispersion. t is possible to construct a crossing insertion in which the vertical bends ~re achromatic. rouch an insertion will h~ve to be longer and more complicated. n or nc;n- the collision region.it if; unavoidable t-bat some quadrupolcs will be used in cornmon by both bgams, \-.'ill produce opposite fucusing actions (" VeH;\S Dj Th(,,,r, quadrupolch on the two b8~ns going in opposite directions. Hence, it i5 expected ~hat all pairs of corresponding quadrupoles between the two rings -205

4 ~.ill have the same field-gradient polaritie", J1~nce Dppw.;ito focusing actions on the t~~o beams, as cxhibi ted in Figur.e 1. An insertion which replaces an even number of half-cells will have to match from F to F' and from D to D. The focusing actions of such a symmetric insert_ion have reflcctiol) symmetry i)bout the midpoint. An in»ertion ~hi.ch replaces an odd l1umber of half-cell::; will match from F to D and from D to F. For Dueh iln ilntisymmetric insertion the focusing acb OilS of :he horizont_al and the vertic,al pl<'ines are midpoint reflections of cclch other, hence the phase advances in the two plilnes an, :i. denti ea1. Antisymmetric insertions are, therefore, pref~rred. B. LO'J- (i insertion An example of a 2~ - cell (150 m),mtisywl41etric ]JJw- e insertion is shown i.n Figure 2 toge.t.her with 1;h~ (3 -functions. The low- (i values in both the horizontal and t.he vertieal p1anc~i at the midpoint where the beams collide are 1. m. The total fr.ee drift length on either s~de of the midpoint'. when the J(,n~lthfl of physical quadrupoles are taken into account is about 18 m. 'rhi~l length is limited by the very high maximum f! values elsewhere in the insertion when the midpoint a, or a, hi15 the ext:reme low vi'l1\l0 of 1 m. With higher a this central free drift space can be made longer. Presumably several similar insertions with various low a* values and central free drift lengths ~an be made availab.ln to SAtisfy specific experimental needs. C. Zero-dispersion insertion For such an insertion, one has to satisfy not only the zerodispersion conditions of n = 0 and ~. = 0, but also the. geometric conditions that the beam should end up along the Bame straight line. An example is, given in Figure 3 where ~tarting from an F-quad zero-dispersion is accomplished in two cell9 (120 m) with four bends. n order to keep dipole strengths phy~ically reasonable the insertion starting from a D-quad must be 3~ cells (210 m) long, as shown in Figure

5 O. Tune-adjusting insertion t is QC'sirable to be able to adjust. the 1.une of the dng over a range of OV '" 0.5. With one ~uch insertion in the ring the range of the phi.i.~c advance adjustment ~;hould then be 6 tj> :; 21T6v -~ 180. Figure 5 shm"s a l~ cell (')(1 ll) antir;ymln",tl:ic insertion (equal horizontal and vertical pha~e advances) with four quadrupoles. The proper quadrupole strengths ale plotteq against the desired phase-advance ~ in Figure S. The corr~5 ponding i...,functions for certain lj' 5 are also plotted. The phase advance in this case ranges from to With computer control of the quadrupole strengths it should be possible to vary lj by one single kno~. f for some reason it is desirable to have a larger adjustable tune range one can use hu"j or more of these insertions. n the case when the end quac]s are not allowed to change six quadrupoles are needed for the insertion n,,; shown in Figure 6. 'l'he phase advance 1/1 is now adjustable from l:wo to 300. n all the example insertions given ahovethe thin-lens and bend parameters are chosen to be physically obtainable with super. conducting magnets. The exact thick lens and bend parameters can be computed using the program TRANSPORT with the approximate parameters as initial trial values. Now we can construct an example for the structure of a complete straight section. We assume a straight section 16 cells or 960 m in length. Since the dispersion function n has a periodicity of four cells (for a lattice with a 90 0 phase advan~e per cell) the choice of a l6-c~11 straight section automatically matches ~-function at both ends. Furthermore, by making curved sections an odd number of half-cells in length and straight sections an even number of half-cells as in our c~se, the focusing,'sequence in the two rings is therefore identical. The example is shown in Figure 7. n this example there are two law-a, ~ero-dispersion collision regions available for two -207

6 experiments. (A small amount of vertical dispersion is introduced by the vertical bends in the crossing insertiona.) A tune-adjusting insertion can be installed in the straight section for the beam with F - F sequence. The tune-adjusting insertion for the second beam can be installed in some other straight section where the polarity of the focusing sequence is reversed. Described here is a design concept and procedure for straight sections with maximum flexibility for experiments. The thin-lens and bend parameters serve to illustrate the practicability of this concept and procedure. For realistic engineering designs further detailed studies must be made. Also omitted here, are considerations of two injection insertions (one in each ring) for beam injection into the rings and t~o dump insertions (one in each ring) for fast extraction and dump of the beums. 1. M. Lee, W.W. Lee and L.C. Teng, Magnet nsertion Code, NAL Report TM-447 (Ocl. 1973) 2. W. C. Dallidon, Variable Hetric Method for. l1inimization ANL-5990 (Rell. 2) (Feb, 1966). Also program Variable Metric Minimization, ANL-ZOl3S (1967) -208

7 ~_.. 8,! k 3 k, =O.0369/m i, =6m 14=12rn k 2 =O.0303/m 12=29m l5= 1m k 3 =O.0595/m 1 3 =7m 8, =5.62 mrad nserton REGON (90m)---.., k 3 CROSSNG NSERTON FG. -209

8 p(m) fjx"=p;= 1m k l =O.lO8/m =8.5m =25m 0 k 2 =-O.l037/m 0 12=23.lm,, "~ 0 ""max 1Jmax 1000 "'x ="'y =365.6 k 3 =0.0588/m ~ P max \ fjmin =3.14m :, 800, ~ \,: \ \ \ l3=22.9m = m k4=-o.l329/m:~ 14=8m \ NSERTON REGON: '.! \ (150m) : 600 / : o~ : 1Jy,, ~ o, 400 / :, \ '\, \ ' \, '\ 200 ' \. Q 'M_ Q _ ' \ \ 1J -"" - m \ / fjmin \... x ~y \. fjmin... / "..J " -'...J '.L 1 ~JJ ~ffi~ t~t- ---tllt f14~~ ~ l~ ~.J -k 4 -k 3 -k 2 -k l k l k 2 k 3." k 4 L.~ Z LOW-fJ NSERTON Z FG.2.1

9 ",', / ~ z 4-.'-NSERTON REGON (120m)--r~ ~ k 0.l, 8, 8 t Q: t5 ~ 8 -k l 2 l l 3 l -k k ~ G l C) ~ t) g Z CJ) LLJ "" m..j..~ Z 8, =-18.85mrad 9 k=o =18.55mrad l = 15 m 8 3 =19.45 mrad L=O.515m 8 4 =-19.15mrad ZERO-DSPERSON NSERTON FG.3-211

10 Ol----~ :""r---.., ;;;;;=--., , Z a 4j NSERTON REGON (210 m) ' <3 -k w 0:: o -+-t+----t-- Z W m 8 1 =-21.4mrod 8 5 =-21.4mrod 8 2 =21.4 mrod 8 6 =-79 mrad 8 3 =2.0mrod 8 7 = 59 mrad 8 4 = 21.4mrod k=0.047 l::15m L=O.642m ZERO-DSPERSON NSERTON FG.4 -l12.

11 E... -.x TUNE-ADJUSTNG NSERTON 400 _ 300 E -)( en NSERTON REGON (gom) --~ -2.13

12 O.15r--"'-----~---~ O.15,L ' l/!<deg.) l-----nserton REGON (90m)-----t _ E )( -~ 200 TUNE-ADJUST,NG NSERTON FG.6

13 ZERO- TUNE ZERO DSPERSON ADJUSTNG DSPERSON FlO F \ CROSSNG CROSSNG o F / F 2 Y 2 / \. A Y2 2 CELLS CELLS "\... CELLS CELLS F LOW-{J 0 0 LOW-fj F ~ 2~ t 2~ ~ o CELLS F F CELLs 0 ~ 3'k CELLS.~ CELL / 3Y2 CELLS! tj1 F CROSSNG CROSSNG o F \ 0 ZERO ZERO DSPERSON DSPERSON NSERTONS FOR A 16-CELL LONG STRAGHT SECTON FG.7