DEUTSCHES ELEKTRONEN-SYNCHROTRON

b.ESY 81/031June 1981

DESY

M I N I - B E T A I I

by

H. Newman

Eigentum derProperty of

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Leihfrist:e r s : •» TogoLoon pertod: / d o s

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D E S Y 81/031June 1931

MINI-BETA II

BY H, NEWMAN

DESY

MINI-BETA II:

IMFROVED PETRA MINI-BETA INSERTIONS FÜR HIGHE_R_B_EAM ENERGY AND LUMINOSITY

An improvcd mini-beta System has been found which uses readily available

conventional quadrupoles, and its properties and limitations have been investig-

ated. A f our-f öl d Symmetrie arrangement matched t o MI8 optics i s assumed. The new

quadrupole arrangement is flexible and adaptible to PETRA Operation at beam

energies up to 23 GeV; minor adjustments of the System can be made to reduce

the chromaticity (or increase the luminosity) over a broad ränge. The relation-

ship between the linear chromaticity £ and the luminosity gain relative to

the present mini-beta set up is roughly linear, and it is not sensitive to the

absolute k-values of the quadrupoles. The luminosity gain may be äs high äs

a factor of two, bu t it depends critically on the niaximuni tolerable chromaticity

and the assumed machine acceptance.

INTRODUCTION

1 2 3 * *The mini-beta insertions nnw installed at PETRA ' '"" (ß = 1.2 m, ß =

x z0.08 m at the interaction point) have resulted in an increase in the peak

3l -2 -1luminosi ty from 0.5 t o 1.7 x l 0~ cm sec and in the maximum integrated

luminosity accumulated by a PETRA experiment in a 24 hour day from approximately

135 to 650 nb . The mini-beta design is based on an original idea by3 4

K. Steffen , and on a series of earlier reports and discussions . The optics2

has been implemented by J„ Rossbach . The succcss of the present scheme has

naturally stimulated continued discussions and reports " on the best means

to achievc the highest luminosities during future PETRA Operation.

This note examines the possibility of using readily available conventional

quadrupoles for an improved set of mini-beta insertions at PETRA, which could beQ

ready in 1982 for running at beam energies upwards of 20 GeV. Another

- 2 -

approach which uses small diameter superconductlng quadrupoles has been

considered elsewhere . It is presumed that Implementation of the more

sophisticated superconductlng solution will take considerably Ionger5 and

that it could follow Installation of the improved conventional set up which

is discussed in this report.

The study consists of results found on the analog-digital hybrid

Computer HRS 860 , which were checked using the PETRA Simulation PETROS .

PETROS also provided the linear chromaticities £ and £ corresponding to eachX Z

solution. The PETROS output files have been kept at the ÜESY IBM Computer

center for further studies involving beam tracking, Variation of optical

Parameters, etc, which are not covered by the present work„

THE SET-UP

The improved mini-beta arrangement, shown schematically in Fig. l,

consists of a Variation of a design by Steffen which uses a QAI followed by

three QD's on either side of each interaction point (I.P.). The QD' s are assumed

to be taken frotn the second DORIS ring and to be modified äs for DORIS II,

The free space for experimental apparatus is chosen äs + 2.86 rn, according5 9

to preliminary Information provided by the experimental collaborations " ' .

A four-fold Symmetrie solution has been assumed, and problems of asymmetric

machine Operation are not considered.

CON5TRAINTS; DEFINITION OF THE PROBLEM

(I) The QAI and QD geometrical aperture limitations are:

for QA, QAI : E , E < 60 mm, /E E < 46 mm (=RT),X Z X Z I

for a modified QD

where E and E are the beam envelopes in the horizontal and verticalx z

planes, and R refers to the radius of the inscribed circle tangent to

the pole tips.

- 3 -

Änother significant vertical aperture limitation is given by the

good field region of the weak focussing (17%) bending magnets M4K:

E < 54 mm, E < 27 mm.x z

The horizontal aperture is limited at the entrance to the Q1K quadrupoles

to E < 73 mm.x

(2) The maximum focussing strengths of the quadrupoles are limited by~r)

Saturation of the pole pieces. Expressed in terms of k(m ), the12

limitations which are given by 3-4% Saturation at 20 GeV are:

QA, QAI : |k| < 0.2225

QD: |k| < 0.2665,

, , -2, , dB Tesla, , ,_ ,, , . 13where k (m ) =0.3 -r— /m / p(GeV/c) . The above maximum

QX V -^J

value for QA and QAI quadrupoles shows that the present mini-beta System

with ß* = 8 cm is limited in this sense to 20.0 GeV. The Saturationz

limitation is not absolute, of course, but PETRA Operation with larger

degrees of magnet Saturation requires additional experience . Additional

hardware and Computer Software for non-linear time dependence of the magnet14

currents during ramping may also be needed . Higher levels of Saturation

have been previously encountered at DORIS.

(3) The dispersion at the interaction point D* has been kept small. The hybridX

Computer does not constrain 9D*/3x to be zero at the I.P. äs does PETROS

in its solution for the closed orbit. It was found empirically , however ,

that by restricting the hybrid Computer to Solutions such that D l cm,X

the corresponding PETROS solution also gave D*< l cm.X

(4) Solutions involving high linear chromaticities are less desirable for

several reasons:

(a) Experience and beam-tracking simulations have shown that correction of

chromaticities with strong sextupole field s leads to enhanced non-

linear effects, resulting in a highly non-linear momentum dependence

of the tune shifts. This Icads in turn to a reduction in the machine2 l 5

acceptance . The non-linear components of the chromaticity £

corresponding to the quadrupole and sextupole settings currently in

use at PETRA are indeed limiting the momentum acceptance to — ~ 0.7%A

at 17 GeV. The machine momentum spread — *- is proportional to the beamP

- 4 -

momentum p so that the machine acceptance for a given £ is reduced äs p

increases. The E, limit may therefore be the dominant factor which

determines the maximum 3 usable in the raini-beta quadrupoles at energies

above 17 GeV. As a consequence, the minimum ß* at the I.P. and the

maximum luminosity obtainable could also be limitcd by the £ limit

(b) As discussed in Ref. 2, a reduction of the sextupole field strengths

by use of large values of the dispersion function D in the arcs leadsA

to larger emittances £ and a larger momentum compaction factor ct. This

results in a reduced maximum PETRA energy for a given amount of R.F.power,

In an initial response to this problem only Solutions withl 8

l £, l < 110 were considered (for comparison: the original MI8 has

£ = -76.5; MI6 has £ = -95). It was soon realized, however, thatz zthe background rates seen by experiments resulting from particles lost

from the beam could be significantly reduced by using a modified MI8

optics with £ --65 instead of -76.5. The approach to the problem of

future mini-beta Solutions was therefore made more general. A ränge

of Solutions was found so that the relation between £ and the luminosity

gain /L could be seen over a broad ränge of chromaticity values. The

achievable luminosity gain is thus given äs a function of the maximum

tolerable £ , which depends in turn on the state-of-the-art of handling

non-linear effects in PETRA.

RESULTS

GASE l

Figure l shows the results obtained for a series of solut ions based on the

f ollowing conservative assumptions :

MAX MAXU) £ : 30 mm rar ad , e = 8 mm mrad , corresponding to thex z

geometrical aperture of the machine, and

(2)

-2The magnet settings k(m ) of all elements which are changed from the present

MI8 optics are shown. Q4K is off in all Solutions and MAK and M5K (the 17% and

- 5 -

83% bending magnets) are unchanged. The beam envelopes E and E are siven at the_ _ x z

entry and exit of each magnet and the value of /E E is shown where it is largest.x z

Underlined numbers approach the nominal magnet aperture limits,and numbers in a

box slightly exceed the limit. The "luminosity gain factor" is a multiplicative

factor relative to the present MI8. "Chromaticites" indicated are those given

by PETROS äs the vertical "linear chromaticity MODE II". For each case the beam

envelopes E* and E* and the beta function values ß* ß* at the I.P. are alsox z x z

given.

Gases l(a)-l(e) represent a ränge of chromaticities and luminosity gain

factors which has been obCained principally by varying Q5K. This has the effect

of changing the E (and ß ) values with only small changes in the x envelope2 £*

because 3E /3x is small in Q5K (äs is E ).This means that only minor adjustmentsA A

in the QA1 or the QD's which focus in Z are needed to recover a periodic

solution after each change in Q5K. The system is therefore very flexible and allows

variations in 3 and Ej over a wide ränge. The intermediate beam waist in Q5K isz z

achieved by strongly exciting QO and Ql (which are of the "QA1" PETRA type).

Ql is seen to be at a similar level of Saturation as QA1 in the figure. Exciting

QO and Ql less strongly leads to slightly higher luminosities for a given £

(e.g. a gain factor of ~ 1.6 for E, = -110) but such Solutions are less flexible.2

It was found difficult to keep D* small at the I.P. while varying £ and respect-x z

ing the raagnet apertures with smaller k values in QO and Ql

Vertical aperture lirnits for Solutions like case l .a) - le) are only

reached at ^ ~ - 1 1 7 in the mini-beta quadrupoles. The vertical aperture

limit at the exit of M4K is reached at nearly the same F (see Appendix A).

GASE 2

Fig. 2 shows how the principle used in case l can be readily adapted when

A hi , chromaticity and a lower chromaticity solution are shown.BEAM

Once again, larger (more negative) k values in Q5K give lower chromaticities.

Since Q5K is actually of the "QA" PETRA quadrupole type, very low chromaticities

4 (and corresponding lower luminosities) can be obtained without significant£*

Q5K Saturation.

CASE 3

The luminosity gain factor obtainable for a given £ is also dependent on

the machine acceptance assumed. Fig. 3 shows a series of Solutions for highMAX ^

luminosity gains and high t, . We assume c =20 mm mrad and f 5 min mrad

- 6 -

l 9for this case, corresponding to a slightly optimistic estimate of the

machine acceptance äs measured during machine shifts. It should be noted,

however, that the effects of the extreme tails of the beam (many o off the

equilibrium orbit) are of no consequence in the machine acceptance measurements,

but are crucial to the background conditions seen by the experiments. It is

therefore possible that the beam envelope E = /ß c cannot be äs fullyX X X

expanded in Q1K äs is shown in Fig. 3, and it is reasonable to consider

case 3 äs an "optimistic" - and case l äs a "pessirnistic" - estimate of the

gain factor achievable with acceptable background conditions for experiments,

provided £ is also chosen to be "sufficiently small" äs previously discussed.

The Solutions in case 3 hav.e a significantly lower ^ for a given luminosity

gain than those in case 1. This is obtained by increasing the beam envelope

to make use of the füll vertical aperture at the M4K exit. This leads to larger

3 values in the magnets which defocus in z, partially offsetting the

contribution to £, of the mini-beta quadrupoles closest to the interaction point.

CASE 4

Fig. 4 shows how lower chromaticity solu tions are obtainable at EMAX MAXBEAM23 GeV. following the metbods introduced for case l for £ and c äs inx z

case 3,

DISCUSSION

The relation between /L (~- l - luminosity gain factor)and £ is shown

in Fig. 5 for cases l and 2 corresponding to e = 30 mm mrad and c = 8 nrn

mrad, and in Fig. 6 for cases 3 and 4 corresponding to c =20 mm mrad andMAX

= 5 mm mrad. The arrows in Fig. 5 refer to the f, values for MI8, MI6z z

and the "reference" limit discussed earlier, for the present mini-beta system.

The straight lines in the figures are fits by eye to the E = 23 GeV points.A -r O Ljri-1. I

It is apparent that the £ vs /L relationship is quite linear and that the

slope d£ /d (— ) depends little on E over the ränge from 21.2 to 23 GeV,LJalthough it is sensitive to the machine acceptance assumed .

- 7 -

CONCLUSION AND FUTURE OUTLOOK

The improved mini-beta System proposed which has been discussed in terms

of a case study, can be used for PETRA Operation up to the maximum feasible

beam energy of 23 GeV. It is quite likely that a net luminosity gain could be

realized, relative to what would be obtained if the present mini-beta insertion

could operate at coraparable energies (which indeed it cannot at the present 3* ),

The. size of the luminosity gain will depend critically on the maximum tolerable

chromaticity £ , which will no doubt increase with time äs non-linear effectsz

from lattice imperfections and correcting sextupoles are better understood.

The flexibility of the proposed system allows one to maximize the luminosity

by working near the £ limit, or to decrease C in order to reduce backgrounds£• 2

for the experiments. It will also clearly be useful during future studies of

the chromaticity during machine shifts.

The principal advantage of this conventional scheme over the superconducting

set-up is in its cost and in the relative ease and speed of Implementation.

The luminosity gain factor ultimately achieved with the Solutions discussed here

could at best be a factor of two. The long term advantages of the superconducting

systern i.e. higher luminosites which result from much sraaller ß äs well äs20

3* , and lower chromaticities, are clear. This proposal is therefore viewed äs az

forerunner, rather than a substitute, for the System proposed by K. Steffen

and G.-A. Voss.

ACKNOWLEDGEMENTS

This work would not have been possible without the help and cooperation

of many people in the PETRA niachine and physics groups. It is a pleasure to

acknowledge discussions with Prof. G.-A. Voss and Drs. K. Steffen, D, Degele,

R. Kose, J. Rossbach and F. Willeke on matters relating to the machine and the

methods of optics Solutions, and with Prof. E. Lohrmann, Drs. J.D. Burger,

M.M. White, W. Bartel and U. Kotz on matters pertaining to the experiments.

Dr. I. Borchart and Mr. U. Naujokat provided indispensible help with tbe

Operation of the hybrid Computer. I would also like to thank Dr. White and Mr.

Jiang Da-Zhen for technical assistance, and particularly Dr. D.P. Barber for

bis collaboration in the early stages of this project.

ACKNOWLEDGEMENTS (cont.)

I am also grateful to Prof. S.G.G. Ting and the raembers of the MARK-J

collaboration for their aid and encouragement.

REFERENCES

The original mini-beta idea is presented in:K.W. Robinson and G.-A.Voss, Cambridge Electron Accelerator ReportCEAL-1029 (1966).K.W. Robinson and G.-A.Voss, International Symposium on Storage Rings,Vol. _8, Paris, 1966.

2J.Rossbach, PETRA Mini-Beta Optics, DESY Internal Report M-81/01,January, l 981.

K. Steffen, Internal Note of March 6, 1980;PETRA Proposal of March 10, 1980.

4See references 2-7 in J. Rossbach s report (Ref. 2 above).

K. Steffen, PETRA Kurzmitteilung of April l , 1981.

K. Steffen, DESY Internal Report HERA-80/03, September 1980.

K. Steffen and G.-A. Voss,DESY Internal Report M-81/17, April 1981.o

Problems of finance and work scheduling relative to other DESY projectsare beyond the scope of this report.

9MARK-J, CELLO, JADE and TASSO Collaborations, private communication.

I. Borchart, DESY Internal Report Rl-76/02, Jauary 1976.

J-Kewisch: Berechnung der Linearen, Gekoppelten Optik und der Strahl-parameter , Diplomarbeit, DESY, 1978.

l 2D. Degele, R. Kose and K. Steffen, private communication.

Also see K. Steffen, DESY Internal Report M-79/23, May 1979.14

D. Degele, private communication.

R. Kose, G. Ripken, and A, Wrulich, DESY-Internal Report M-80/12;S. Kheifets and E. Messerschmid, DESY PET 77/18;J. Kewish and G. Ripken, DESY PET 79/09.

R. Kose and D. Degele, private communication.

This effect is considerably reduced in the superconducting solutionpresented in Ref. 7

l 8Based on the advice and the machine studies of R. Kose et al.

19R. Kose, private communication.

20As pointed out in Ref. 7, beam-beam interaction sitnulations by Piwinskyindicate that ß* reductions below 3 times the bunch length are relativelyineffective in increasing the luminosity.

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APPENDIX A

The proposed System was selected from a series of geometries and optics

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1-4 are given here for completeness. Each line of the solution refers to the

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