Very-high-luminosity insertions for the CERN intersecting storage rings

NUCLEAR

INSTRUMENTS

AND

METHODS

I20

(I974) 9-I6;

© NORTH-HOLLAND

PUBLISHING

CO.

VERY-HIGH-LUMINOSITY INSERTIONS

FOR THE CERN I N T E R S E C T I N G STORAGE RINGS B. W. M O N T A G U E and B. W. ZOTTER

CERN, Geneva, Switzerland Received 22 April 1974 The luminosity of the CERN 1SR could be brought into the range of 0.5 to 2 x 10as cm-2 s-1 by modifications in the vicinity of one interaction region. The high luminosity is obtained by a combination of near-zero crossing angle, low-beta and vanishing momentum compaction at the intersection point. The attainable performance will depend on whether or not super-

conducting magnetic elements are used, the maximum tolerable level of the electromagnetic beam-beam interaction and the available stacked proton current. Provision is made in the design for adjusting the crossing angle to achieve the optimal conditions.

1. Introduction

for detectors in the modified interaction region, which would then be dedicated to the large-angle experiments which require the highest luminosities. Nevertheless, solid angles in excess of 0.7 x 4 n should be accessible to the detectors. Two examples of this insertion have been studied3), the one using only conventional bending magnets and quadrupoles, the other incorporating some superconducting elements. The superconducting version yields a higher luminosity and leaves more free space for detectors. The design aim is to bring the luminosity up to the level corresponding to the beam-beam limit with proton currents already achieved in the ISR. Since the beam-beam limit is still only imperfectly known, provision is made for adjusting the crossing angle around zero to achieve the highest luminosity with the available stacked current.

The C E R N Intersection Storage Rings have reached a luminosity of over 6.7 × 1030 c m - 2 s - 1 , comfortably above the design aim of 4 x 103°. Continued improvements in various directions, together with regular use of the PS Booster, are expected to bring the ISR to a luminosity of around l03~ c m - 2 S - 1 without modification of the beam optics in the interaction regions. Further increases in luminosity can be achieved by the introduction of additional focusing elements to reduce the beam cross-section in the interaction volume. One such scheme, using conventional quadrupoles a) is scheduled for installation this year, and will increase the luminosity by a factor of about 2. A more ambitious scheme, using superconducting quadrupoles2), is under detailed study and should yield a further factor up to 5 in luminosity. Such methods, which reduce essentially only the beam height, are not expected to bring the ISR to its ultimate performance limit if this is determined by the beam-beam non-linear electromagnetic interaction. To reach even higher luminosities it is necessary to reduce both the beam cross-section and the crossing angle, which involve changes not only in the focusing properties but also in the geometry of the central orbits in the interaction region. [n this paper we describe modifications to an ISR interaction region which would result in luminosities approaching, or even exceeding, 1033 c m - 2 S-2. This is obtained by reductions in crossing angle and dispersion to approximately zero together with low values of the betatron amplitude functions at the crossing point. To achieve such luminosities without undue disturbance to the present ISR structure, it is necessary to accept a rather limited length of free space

2. General considerations

A major constraint we have imposed on the design is the need to carry out the modifications with the minimum disturbance to the ISR experimental programme. Consequently we are discussing here modifications to only one of the eight interaction regions, although two or more modified regions would be preferable for reasons of machine symmetry. With unit superperiodicity it is particularly important that the insertion be fully matched to the adjacent lattice in the betatron functions /~v, /~h, momentum compaction %, and their derivatives, at least in linear approximation. A further design constraint requires that the insertion should not limit the useful aperture of the ISR as a whole, so as not to reduce the performance at the other interaction regions.

10

B. W. M O N T A G U E A N D B. W. Z O T T E R

To achieve zero crossing angle in the limited space available, two bending magnets, of opposite polarity, are located immediately adjacent to the interaction region. These separating magnets are common to both beams and serve not only to separate the beams but also to reduce the long-range contribution to the beambeam interaction 4) and to provide local dispersion for reducing the % function to zero. In order to keep the size of these magnets within reasonable limits, some existing ISR magnets in the adjacent inner and outer arcs are rearranged in position so as to reduce the extra overall bending strength required. The modified geometry is such that the major part of the preparatory work on magnet supports, pipework and cabling could be undertaken during normal ISR shut-downs without disturbing the existing magnet geometry. The final rearrangement should then be possible in a shut-down period of only a few months. The design of the insertion is based on the assumption that the ultimate luminosity will be limited by the nonlinear incoherent beam-beam interaction, though other effects may impose a lower limit, at least temporarily. Since the beam-beam limit for protons is only imperfectly known, provision is made for steering magnets to adjust the crossing angle over a few milliradians near to zero, in order to achieve optimal conditions. The same steering magnets also permit operation at unequal energies in the two rings. The luminosity 50 of an interaction region can be expressed in the form

5O = fcnyAQ___b,

vourably small. This is illustrated by the asymptotic behaviour of £,qoin Keil's calculationsS). Secondly, low values of/30 at the intersection result in large values of /3 in the neighbouring quadrupoles, requiring stringent tolerances and large corrections for chromaticity of the machine. These constraints lead to the very general conclusion that the highest luminosities can only be achieved by a sacrifice in the field-free length available for detectors around the interaction region. Fortunately, high luminosities are of particular interest for those experiments studying large transverse-momenta events of small cross-section, and we therefore believe that an insertion of this type, despite the limited free space available, would offer a considerable extension to the range of feasible ISR physics at large transverse momenta. With these considerations in mind the maximum value of the betatron amplitude function in the adjacent quadrupoles has been limited to about 250 m in order not to make the machine unduly sensitive to tolerances with the unit superperiodicity present. The luminosity attainable with this type of insertion is expected to lie in the range of 0.5 to 2 x 1033 c m - ~ s - ~ depending on the beam-beam limit, the assumed stacked current and whether or not superconducting elements are used. The upper end of this range is in close agreement with the limiting luminosity estimates of KeilS). Calculated values of 5O for various conditions are given in table I and in fig. 5, and the distribution of 5O and 5 ° ' ( = dso/ds) along the interaction region in fig. 4.

(1)

l'o fi o

where AQb = linear tune shift corresponding to the beambeam limit, fl0 = beta function at the crossing point, r0 = classical proton radius, n = proton line density, 7 -- proton energy factor, f = form factor, of order unity. Implicit in this formula is the assumption that some hidden parameter, typically the crossing angle, has been adjusted to bring the linear beam-beam detuning to the limiting value d Qb. The luminosity cannot arbitrarily be increased by reduction of fl0 for two reasons, Firstly, the length of field-free region around the intersection must not greatly exceed fi0, otherwise the long-range contribution to the beam-beam interaction grows faster than the luminosity, and the form factor f becomes unfa-

3. Geometrical constraints In order to achieve a zero crossing angle in the limited space available it is necessary to transfer some bending from the outer arcs to the inner arcs in the neighbourhood of the intersection and to move the bending centre of the inner arcs nearer to the interaction region. This not only reduces the bending angle required of the separating magnets but also makes more free space available for the interaction region and for satisfying the matching requirements. Suitable changes in the geometry can be achieved making use of most of the present ISR magnets, suitably displaced, with a few additional bending magnets of higher field strength. The result of these rearrangements is a small outward displacement of the intersection by about one metre and a lengthening of the machine circumference by 30-40 cm. An embodiment using both conventional iron and superconducting magnets is shown in fig. 1, where also the existing ISR is shown in thin lines. In total, twelve ISR magnets have to be moved per ring,

V E R Y - H I G H = L U M I N O S I T Y INSERTIONS

ISR

1]

LATTICE

----4

~

oO

\

~ ' , ,

c=~tC..'.~

,

_

~

F

INNER

o

D

F

~

'-""'- /

--~L~_

'7

.........

-_.L_

--

'\/

v

-

o3

J

- -'Y

........

/

A

//

_~,..~'

01/

/ Fig. 1. Lay-out of half of the insertion using some superconducting elements. The present ISR arrangement is shown in thin lines. The dashed line is the position of a pit in the tunnel

and a total of six new bending magnets is used. Clearly, modifications to the vacuum chambers will be necessary to fit the new geometry. The reason for not using quadrupoles common to both rings, directly next to the intersection, is twofold: on the one hand unequal energy operation in the two rings would be extremely limited, and on the other hand, the contribution to the beam-beam Q-shift does not become negligible before the two beams are physically separated by a bending field. The concomitant disadvantage is that the beta functions grow to quite large values ( ~ 2 5 0 m), before they can be focussed back in both planes by a pair of quadrupoles. The distance to the quadrupoles now includes not only the actual free space around the intersection, but also the length of the separating magnets, and the space required for sufficient transverse separation of the beams to accommodate the quadrupoles. This can be somewhat alleviated by using slim quadrupoles and by staggering the quadrupoles in the two rings as shown in fig. 1. The space near the quadrupoles can be used for steering magnets which are required for unequal energy operation, and for optimizing the crossing angle to the still unknown beam-beam limit. The total extent of the insertion is from the first or second long magnet in the outer arc (about 15 or 20 m from the intersection), to the centre of the inner arc (about 56 m). However, the inner arc still contains 20--25 m of displaced, and slightly compressed, ISR lattice. Subtracting also the free space around the intersection and the lengths of the separating magnet, less than 50 m is available for quadrupoles and other lenses required for proper matching and for achieving a small beam size at the intersection.

4. Insertion matching At each end of the insertion, we have to make the beta-functions in both planes, the momentum compaction function, and their derivatives match the values of the existing ISR. In addition both beta-functions should have minima at the intersection, and the momentum compaction should vanish there. Because of the large momentum spread which should fit into the vacuum chamber (some 5% from the injection orbit to the outer edge of the stack) the momentum compaction is the most important factor in determining the beam size. We therefore must ensure that it remains small enough everywhere not to increase aperture requirements unduly. Solutions have been found which keep all magnets and quadrupoles within the limitations of either normal or superconducting magnet technology. The criteria used for normal elements are B~< 1.8 T for bending magnets, and B'w<~l.1 T for quadrupoles (~< 1.2 T for longer ones), where w is the beam halfwidth calculated for a momentum spread of __+2.5%, and allowing 5 mm for closed-orbit distortions. For superconducting elements we permit maximum field levels of 4.5 T for both bending magnets and quadrupoles. In keeping with the original ISR design, a maximum proton momentum of 28 GeV/c has been assumed, although operation of the ISR has been extended to 31.4 GeV/c. Assuming that there will be the same safety margins in the design of the new elements as in the original ones, operation at this energy might still be possible. A fundamental restriction in the design of matching sections is the Courant-Snyder invariant W, which can be calculated from the horizontal beta-function flh, the momentum compaction function %, and their derivatives

12

B.W. W

MONTAGUE

2 t t2 7h~p+2Cth~pC~ p'~-flh~p ,

=

AND

B, W .

ZOTTER

TABLE l

(2)

where

Main characteristics of ISR modifications.

l+~

7h = - - ,

1 ,

and

Ph

% = -~flh" Parameter

W remains invariant in field-free regions a n d q u a d r u poles, b u t is changed in b e n d i n g magnets. A t the intersection, where C~p= O,/~ is small, a n d c~ is small or zero, W is also small or zero. It w o u l d therefore be a d v a n tageous to start the insertion at a p o i n t o f the I S R lattice where W is small. In the near p a r t o f the outer arc there is little choice; W varies only between 0.225 m in the centre o f the first long (D) m a g n e t a n d 0.205 m in the next long (F) magnet. I n the inner arc there is m o r e dispersion and this restriction is less critical. I f we calculate the change o f the invariant f r o m the intersection t h r o u g h the separating magnet, we can solve for the derivative o f the m o m e n t u m c o m p a c t i o n function at the intersection --

-o + I = -

('+'. o"?- r

- LP.o k ~

2/ / '

Normal

Superconducting insertion

21.54 --0,20 13.86 0.12 2.24 0.00

2,66 0.15 1.55 0.004 - 0.015 -0.18

0.51 -0.015 0.49 0.002 0,004 -0.015

41.2 51.4 2.29

42.7 125.6 - 3.41

56.40 249.40 2.39

8.79 8.70 8.97 942.637

9.84 8.86 9.22 9 4 3 . l 11

10.09 8.94 9.12 942.963

Intersection

~h (m) :oh ¢~ (m) c~ ~v (m) ~

Maxima

~h (m) /% (m) ~'v (m) Ring

Qh

(3)

Present ISR

vtQ~ c (m)

P e r f o r m a n c e f o r I = 15 A , eh = ev = 1 ~ × 10 6 r a d m AQb 4x 10-4 0.01

:o't

¢ (mrad) (cm-2 s-1)

.6 .4 .2 zero Ot~H=.076 I

1.0

-.2

2.0

3.0 J3H (m)

-.6

-.8 rain = - . 9 2 5 a t _P H ; . 1 5 -1.0

129 6 x 1030

0.0l 1.24 1.93 x 1038

where 0 is the b e n d i n g angle o f the separating m a g n e t o f length lB, l is the (total) free space a r o u n d the intersection and flho is the m i n i m u m o f the h o r i z o n t a l betafunction at the intersection, where we have assumed %0 = 0. F o r the n o r m a l m a g n e t solution, W = 0 . 2 2 5 , 0 = 65 m r a d , 1B= 3 m, a n d l = 15 m, yields the required values o f @o as function o f the desired fib0 (see fig. 2). Since/?hO ~ 10 cm is not feasible because o f q u a d r u p o l e limitations, we have to m a k e flho o f the o r d e r o f a few meters in o r d e r to reduce c¢;o to acceptably low values. N o such restriction limits the vertical beta-function, which we can therefore choose s o m e w h a t smaller. A slightly different a p p r o a c h has been used for the s u p e r c o n d u c t i n g solution. There we can o b t a i n m o r e b e n d i n g and stronger focusing within a r e a s o n a b l e space, a n d hence achieve %0 = ~'po = 0 at the intersection. Behind the separating magnet, the invariant then becomes for 0 = 97 mrad, 1B = 2 m, l = 2.68 m, and/~h = 0.5 m. W = [3ho 0 z

Fig, 2. Slope of the momentum compaction (~'po)as a function of /3ho for thenormal-magnet solution, with C~po= 0 and W = 0.225.

0.95 9 x 1032

1 + \2-~ho/_]

0.108.

(4)

This value o f W can be o b t a i n e d by an intermediate

VERY-HIGH-LUMINOSITY

13

INSERTIONS

TABLE 2 Additional elements for S.C. insertion. A. Bending magnets n No. (total)

/ (m)

0 (mrad)

fly (max) (m)

flh (max) (m)

[~Pl (max) (rn)

B(T) a

2 2

97 98.9

23 47

23 3

0.10 0.54

4.52 "1 4.61

2 3.4 3.24

97 68 64

23 68 44

23 3 8

0.10 0.57 0.94

4.52 •.87 ~/normal 1.84 J

O u t e r arc

Bl B2

1

2

B1 B2 B3

2 2

)

S.C.

I n n e r arc

1

B. Quadrupoles No.

1 (m)

K (m -2)

fly (max) (m)

flh (max) (m)

]Ctpl (max) (m)

B(T)

0.8 0.8 1.4 0.9 1.5

-0.95 0.91 -0.65 0.38 -0.20

125 245 29 58 34

57 27 4 7 24

0.29 0.24 0.28 1.18 2.22

3.40 4.47 j s . c . 1.22 1.15 ] 1.10 ~ normal

0.9 0.9 0.5 0.5 0.9 0.5

-0.62 0.62 -0.37 -0.11 0.10 -0.06

100 210 88 15 20 15

48 28 21 23 13 19

0.27 0.26 0.49 2.08 1.78 2.29

2.02 2.83 ) S.C. 1.13 | 0.71 0.54 normal 0.39

O u t e r arc

2 2 2 2 2

Q Q Q Q Q

1 2 3 4 5

I n n e r arc

2 2 2 2 2 2

Q Q Q Q Q Q

I 2 3 4 5 6

)

p = 28 GeV/c, A p / p = ~ 2 . 5 % , Eh = Ev = 10~ m m mrad, C.O. = 3 ram.

bending magnet between the lattice and the separating magnet. The change of W is greatest at a cross-over of the ap trajectory, where it is given approximately by AW

0z

20

W

O~lp2

~p!

(5)

We need to reduce W from 0.205 at the lattice to W = 0 . 1 8 8 behind the separating magnet and find therefore, %t =

0

1 +(1 + A W / W ) ~

--- 0.044,

(6)

for an intermediate magnet of the same strength as the separating magnet (97 mrad). A cross-over of the ctp

trajectory with the above value of the derivative is just feasible by two lenses in the space available between the lattice and the intermediate magnet. Another three lenses are required in the outer arc to match the three trajectory functions and their derivatives to the desired values at the intersection. In the inner arc, the problem is somewhat simpler. We first use three lenses to match the intersection to the residual section of ISR lattice, but we accept a certain mismatch there as long as the momentum compaction function does not become too large for the available apertures. Then we match from the other end of the residual lattice to the actual ISR lattice with another three lenses. There it was found useful to seek analytic solutions with three short lenses, a problem which can be brought into the form of a single quadratic6). The

14

B. W.

MONTAGUE

AND

B. W.

ZOTTER

n)

2.5-

!50

2.0-

!00

"\.\

I /

"N. \.

~-,\

// \'\.X j / . I

I

\.

.

\

Ii

I

J i

I I

\

I

/.~,\ 1.5-

50.

/ /

\

-\

•\

"~../

./

I

\.

•

I I I I I

\. 0~ \. P \ \ \ \ \

i

00'

\.

.5-

50,

/~ I /

.

10

.

20

.

I I !

\.

\

\X

/

/

/

.

30

\

/ //

.

I J

I

/ \

J I

/

"\""

40

~

50

60

\'\

--

,

70

\

/IJ

~ 1 , i

\

80

V-.

~

S (m)

!

Fig. 3. Trajectory functions fin,/3v and ~p along the superconducting version of the insertion, starting at the centre of the inner arc. approach can even be generalized to long lenses, where it leads to higher order algebraic equations, which can be solved rather efficiently on a computer. For the complete match, the existing computer program AGS was extended to permit insertion tracking and matching, and solutions were found using powerful minimization routines for functions of many variables. The results of these studies are summarized in tables 1 and 2; the values of the beta- and momentum-compaction functions along the insertion are shown in fig. 3 for the superconducting version. 5. Effects on the ISR Although the insertions are fully matched at both ends, some influence on the rest of the machine is unavoidable. The first effect is purely geometrical - the total circumference of the machine is slightly increased by about 40 cm for the normal, and 32 cm for the superconducting version. This leads to a dilution in phase space density of a few percent, which is quite negligible. Due to the additional phase shift of the low-beta sections, the Q-values of the machine are increased. Although they can be readjusted in the ISR within limits by correction quadrupoles and poleface windings, Qh will be approximately one integer above Qv. If operation with split Q-values should turn out to be

difficult, the match could rather easily be redesigned using D F D triplets rather than F D F next to the separating magnets. This would reduce Qh and increase Qv, and bring them close enough to work without a Q-split. A direct consequence of the increase in Q-values is a small increase in transition energy, which is of little importance. A more serious problem will be the non-

4.0-

\.

3.0-

2.O-

\

\ \ \

,,t'

1

o

0:2

o.'6

Fig. 4. Distribution of total luminosity ~ ( I 0 3s cm -') s- I ) and specific luminosity ~ " ( I0 ~I crn -~ s- I ) about the centre of the interaction region (superconducting version), For / = ] 5 A and a crossing angle 2¢ = 2.4 mrad.

V E R Y - H I G H - L U M I N O S I T Y INSERTIONS

15

ISR is encouraging, the non-linear perturbations produced by a high-luminosity insertion will be substantially stronger and will require careful attention. A possible problem is the accurate steering of the two small cross-section beams to obtain the full luminosity and to minimize beam-beam resonance excitation. Closed-orbit correction may be more critical than at present in order to keep the beams within the rather tight aperture limitations of the insertion elements. In general, operation of the ISR would become more complex, as is to be expected for an increase of luminosity of several hundred times.

,,~ (1033 en~ z s -1 )

6. Conclusions i

;

0.02.

2

9( mrud ) 3

'2

~(mrad) 3

&Qv

A

0.01,

,

I

P--

Fig. 5. L u m i n o s i t y ~q and linear b e a m - b e a m Q-shift L1Qv as a function o f h a l f the crossing angle ~b for two values o f stacked current. (Superconducting version, flh =/3v = 0.5 m, emittances Eh = Ev = 10-~ :r rad m, fly = 30.)

linear effects. This has been explored superficially only for the normal magnet solution, where, mainly due to the large values of fl. . . . an absolute chromaticity Q' (= pd Q/dp) of about - 2 to - 3 is found. Correcting sextupoles will have to be added to the already crowded insertion in order to make the chromaticity positive and large enough to avoid transverse instability. In this connection, the location of the separating magnets next to the interaction region brings an extra advantage, in that the dispersion is appreciable where the beta functions are large, so that much of the chromaticity can be corrected close to where it arises, rather than distributing the correction around the rest of the ring. The destruction of the superperiodicity of the existing machine may lead to the excitation of non-linear resonances that have so far been considered harmless. Ahhough experience with the split-field magnet in the

Luminosities around 1033 cm -2 s-a could be achieved in the ISR with stacked currents in the present range, by modifications in one octant bringing the crossing angle to zero and reducing the betatron and dispersion functions at the crossing point. The length of the field-free space in the interaction region would be restricted to around 1.5-2.5 m, with an accessible solid angle for detectors in excess of 70% of 4 n; the insertion would thus be dedicated to large-angle experiments. Horizontal steering magnets permit varying the crossing angle over a few milliradians, to take account of the uncertainty in the beam-beam limit, and also to permit the use of unequal momenta in the two rings (in a ratio up to at least 1.7). The modifications to the ISR require the displacement of some 20 existing magnets and the addition of about 8 bending magnets and 22 quadrupoles in total. In the preferred version of this insertion 6 bending magnets and 8 quadrupoles would be superconducting, yielding a higher luminosity and more experimental space than the version using only normal magnetic elements. The two examples studied are sufficiently similar that one could be converted into the other with relatively modest changes in lay-out. The insertion would not significantly change the present conditions in the other seven intersections. It could be installed with relatively little disturbance to the normal ISR experimental physics programme by carrying out a substantial fraction of the preparatory work during the regular shutdowns. Some further studies will be necessary to work out in detail the non-linear corrections required and to make a final optimisation of parameters. However, there appear to be no insurmountable difficulties in the realisation of this ambitious development, which would bring one intersection of the ISR close to the theoretical upper limit of luminosity at these energies.

16

B.w.

MONTAGUE AND B. W. ZOTTER

W e wish to t h a n k all those who have in some way c o n t r i b u t e d to this work, in p a r t i c u l a r E. Keil, M m e Y. M a r t i a n d A. S u d b o for their help in the a d a p t a t i o n o f the c o m p u t e r p r o g r a m A G S to our needs.

References 1) E. Keil, Report CERN/ISR-TH/73-39 (1973).

2) B. Autin, Report CERN/'ISR-MA/72-45 (1972). z) B. W. Montague and B. Zotter, Reports CERN/ISR-TH/73-23 (1973) and CERN/ISR-TH/73-47 (1973). 4) E. Keil, C. Pellegrini and A. M. Sessler, to be published in Nucl. Instr. and Meth. ; B. W. Montague, Report CERN/ISRDI/72-44 (1972). 5) E. Keil, Nucl. Instr. and Metb. 113 (1973) 333; and Report CERN/ISR-TH/73-48 (1973). ~) B. Zotter, Report CERN/ISR-TH/73-43 (1973).