Calculation of antiproton yields for the fermilab antiproton source

Nuclear Instruments and Methods 2116 (1983) 67-83 North-Holland Publishing Company

67

CALCULATION OF ANTIPROTON YIELDS FOR THE FERMILAB ANTIPROTON SOURCE Carlos HOJVAT and A. VAN GINNEKEN FermiNational Accelerator Laboratory Batavia, Illinois 60510, U.S.A. Received 27 July 1982 The available experimental data for antiproton production are described by an analytical formula, including target nucleus dependence . This formula, in conjunction with a Monte Carlo program that includes the effect of hadraraic showers, is used to optimim the design of the Fermilab Antiproton Source. Comparison is made with measurements of yields at the CERN Antipmrtm Accumulator.

1 . Introduction Due to developments in beam cooling techniques it is now possible to accumulate antiprotons (P) in sufficient numbers within phase space'areascompatible with utilization in accelerators. The possibility of increasing thephase space' density of antiprotons is a direct result of the development of electron cooling techniques by Budker [1] and! the invention of stochastic cooling, by Van der Meer 12] . Intense bunches of p can be made to collide with proton bunches in colliding beam machines with large gains in center-of-mass energy over collisions with stationary targets. Several laboratories have proposed such facilities [3] . At the CERN SPS accelerator experiments which study 270 GeV pp collisions have recently started [4]. This red.rt summarizes a set of calculations on antiproton production in complex targets for aiding in the design of the Fermilab Tevatron I Antiproton Source. The emphasis is on the optimization of the accumulation rate of antiprotons to maximize the expected peak and average luminosity of the pp collisions in the Tevatron accelerator. A;though several other calculations [51 exist a comparison is presently not attempted. The calculations rely on the Monte Carlo (MC) program CASIM [6] . This program generates three dimensional nuclear cascades . Antiproton production by all members of the cascade is incSuded, along with the subsequent transport of the P through the target and collection devices . An empirical fit to available data of P production is introduced into the program expressly for this study. This fit is describec below, along with a brief sketch of its implementation into CASIM. The CERN Antiproton Accumulator has now been in operation for some time. It provides the opportunity of comparingexpected p yields from the present calculations with actual measurements for that specific geometry. Such comparisons are ra, de below. ` 0167-5087/83/0000-0000/$03.00 0 1983 North-Holland

This report is divided in six sections. Section 2 contains themodel for P production, Section 3 discusses its adaptation to the MC code CASIM. The results for the Fermilab parameters are given in section 4 and the comparison with CERN data in section S. Section 6'contrasts the differences between Fermilab and CERN designs. 2. Antiproton production cross section The calculation of P yields relies on the production cross section not only for beam protons (primaries) but also for particles participating in the shower development (secondaries) . In the present calculation the seeondaries considered are p, n, r*, m- , and P: Production of ii which may subsequently transform to P via charge exchange (including inelastic charge exchaugc, i.e., transformation of a leading particle) is` not considered explicitly. To first order this process and its (likewise neglected) inverse are expected to compensate each other. For nucleons and pions incident on protons as well`' as on nucleartargets the available data are described by an empirical formula which factors into three parts: 1) a fit to data [71 in the (high energy) scaling region . 2) a factor describing the approach to scaling at lower incident energies, and 3) nuclear mass dependence . The scaling variables chosen are the transverse momentum, p,, and the radial scaling variable, xR( the Penergy in the center of mass expressed as a fraction'of its largest kinematically allowed value) . It has been shown18) that se ahasbetter scaling properties, especially at lower incident energies, than the more conventional Feynman x. The empirical formula for theinvariant Pproduction cross section (divided by the target absorption cuss

E/E_

C My-, A. Van Gin-k. / A»riprarne yiefds

section) with the three factors separately bracketed is given by: (E/oam)(d'o/dp 3) = [k (I - xa )m exp(- 3p,2 )1 x [1 +24s -2 exp(8xa)] [ aexp(bp,) p(-- .)] , ( 1) where ant . is the absorption cross section of the target nucleus. Theprojectile dependent constants k andm are given in table 1 . The target dependent constants and a, b andcare given in table 2 forfive elements. For other materials the constants are obtained by interpolation. The cross section is assumed to vanish abruptly at the kinematical limit for p production on a proton target. Some subthreshold production in nuclear targets aided by Fermi motion is thereby ignored . From eq . (1) it can be seen that the fit in the scaling region follows a fantiliar form. Theapproach-to-scaling factor is based on very few data and therefore not well established. It is not significant in the Fermilab case (cg., for 120 GeV/c protons producing p near x=0, the factor is 1.0(4), although it is somewhat more important fortheCERN case (at 25 GeV/c, thecomparable factor is 1 .13 al 15 GeV/c it is 1.96). Note from these examples and from eq . (1) that scaling is approached "from above" in accordance with ref. 8. The factor describing the nuclear effects also contains some uncertainties. This is especially true for backward production in the center of mass where the crosssection might be enhanced as is observed for total hadrot production (9) . The expression in eq. (1) is

Table 1 Dependence of the parameters of tire invariant cross section formula on incident particle type.

p.n o. s-

0.063 0.057 0,053

8 .0 3 .2 2.7

Table 2 Dependence of the parameters of the invariant cross section formula on target spades. Tar8t

a

b

c

H

1 .00 0.90 1,22 1 .50 1.69 1.73

0 .00 0.95 1 .15

0.00 0.61 0.87 1 .56 1.79 1.83

3e

Al Cu W Pb

1 .43

1 .38 1.37

exclusively based on forward p production in the c.m. Some of the uncertainty about backward production is removed by computing the p yield following two different prescriptions. The first assumes symmetric c.m. p production for all nuclear targets . The second prescription starts from a simple formula of Brodsky et al. [10) which predicts the ratio of total hadron production off nuclei to that off protons as a function of the rapidity variable. This formula is used here only to predict forward-to-backward ratios of p production on nuclear targets, with forward production taken from eq. (1). It can be argued on kinematical grounds that this second procedure overestimates any nuclear enhancements. These computations show that even with such an enhancement, backward produced p arenotlikely to be of great interest in this study. In addition, recent results [11) not included in the data basis of eq. (1) show no significant enhancements to be present at 70 GeV, even for heavy nuclei . For these reasons, all results quoted below assume p production to be symmetric in the center of mass. Both approach-to-scaling and nuclear mass dependence are based on proton projectile data only . For incident pions they are assumed to be equal to the proton case. For backward p production by incident pions theconstants k and m in table I are taken to be those for proton projectiles. This leads to unphysical discontinuities in the cross section and in its slope at x=0which are tolerated for simplicity . Production c f p by inelastic collisions of p is assumed to follow the leading proton distribution of the Hegedom-Ranft model [12] for p-nucleus collisions. This is for convenience since this model is already coded into CASIM. A thorough statistical evaluation of the quality of fhe fit of eq. (1)to the data is not attempted. The presentation is limited to three projections of the fit, with special attention to the low p low x region of interest here . The data are projected onto the graphs by applying a correction to thecross section using eq. (1). Information from the fit outside the plane of the graph is thereby introduced. The comparison is obviously more significant if such corrections are reasonably small and uniform. For this reason as well as for clarity of thegraphs, the sample of data included is somewhat restricted. Comparisonsareshown forproton projectiles on hydrogen and lead targets. Fig. 1 shows the dependence on incident proton momentum with p, =0 and x =0 held constant. The steep rise in the cross section is primarily the result of thedecrease in xa with s at constant x =0: (xa)x-o -2 mf/(s- 8m2),

(2)

where mis theproton mass. At low incident momentum there is also a significant contribution to the rise from the approach-to-scaling factor. Fig. 2 presents a fit of

69

C. llojvnt, A . Van Cinneken / Antiproton pieldv

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10,0 = 0 ail

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a set of data from different experiments in an unbiased way. Some peculiar consequences of this might he seen in fig . 3 where the fit underestimates the hydrogen data of Allab, et al. but overestimates the data for lead of the same experiment. A somewhat similar inversion exists with respect to the data of Dekkers eu al., though not in as uniform a fashion. Acritical evaluation of the data might suggest a set of weights to he applied in constructing the fit. This is not attempted here . It must bt: emphasized that eq. (1) is expected to he

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4 6 7 0 1 2 3 4 5 6 7 0 1 2 3 5 x xN q Fig. 2. Invariant differential 0 production cross section vs . .r R with p, =0 held constant and v --"x. Thesolid line represents eq. (1).

C Hojuar, A. Van Ginneken / Antiproton yields

70 IOo

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1 I I s.o +.5 10.0 MOMENTUM GW/c

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C Hojtwt, A . Van Ginneken / Antiproton yields

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0 MOMENTUM GeV/c Fig. 6. Total laboratory P production on tungsten below 60 mrad from eq. (1) (per interacting proton). more -rate for small pt(<_ 1 GeV/c) and small to moderate x R( < 0.75), which is the region of interest for the present application. The p yield for a given target and collection device, depends on many, variables in addition to those of eq . (1). It is the purpose of we MC program to include these variables in' the analysis. However; as an intermediate step it appears useful to present' graphs of cross sections based on eq. (1) and simple integrals thereof. Fig . 4 presents the differential cross section in the laboratory, dNldpdl2, evaluated in the forward direction versus P laboratory momentum for a number of incident proton momenta on a tungsten target . Figs . 5 and 6 show total P production p(a interacting proton on tungsten below 30 mrad and 60 mrad respectively as a function of P laboratory momentum forthe same set of incident' energies. Figs. 7 and IS present the total P production per interacting proton on tungsten below p, of 0.3 GeV/c and 0.6 ' GeV/c, respectively, again for the same range of p momenta and the same set of incident '; momenta . In all these graphs the results at very low p momenta (<_2 GeV/c)-am suspect because the procedure of symmetrizing the cross section about x = 0 on a

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nucleus does not take account of the influence of Fermi notion of the target nucleons. 3. Monte Cart calculation The purpose of this calculation is to obtain the expected P yield for specific geometries of production and collection . It incorporates the fit to the p cross sections described in the previous section as well as all relevant details of a particular collection geometry. The physical model of the calculation is essentially that used in the MC code CASIM (6) . Particle prolixtion in CASIM is based on the Hagedorn-, Ranh'(121 model . Though somewhat outdated, its predictions agree well with experiment in the regime of interest here. In CASIM a hadron shower is composed of only nucleons and pions. Effects of other hadrons which can participate in the cascade are not outright neglected since energy conservation is enforced (in the mean) among the nucleon and pion members. For the present study this model must obviously be supplemented by some information on P production and transport.

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R

production cat p is represented in the program by eq . (1). The (stepwise) transport of p is like that of protons in CASIM and includes multiple 17oulomb scattering, ionization loss andcoherent as well as incoherent nuclear elastic scattering. Above SO GeV the p absorption cross section is assumed constant and equal to that of protons, below SO GeV the pp cross section is known to grow with decreasing energy. Far hydrogen this energy dependence is taken from experiment 1131, For nuclear targets it is derived from pp data plus a simple geometrical model of the nucleus 1141. The enhanced cross sections at lower energy are due to p annihilation . It is assumed that the ratio of annihilation to total cross section is independent of nuclear species. As in CASIM a shower is initiated by an incident particle selected from a prescribed beam distribution, This particle is forced to interact in the target and collection system anda representative shower particle is then traced through the target and focusing elements. The representative members of this shower are called propagating particles and are themselves not subject to analysis. Frown each vertex of this shower one or more particles are generated and then traced through the target system. Upon emergence they are analyzed for

their contribution to various distributions, These tire caliotit recandhtg particles and in thepresent problem all lire p, In addition to p generation by 11111:100H and pion tnenubers of theshower tine extra 1notie of production is explored, i .e ., leading particle p resulting from p inelastic collisions, For this reason p are included among the propagatingparticles . To obtain it statistically meaningful stunple of such event chains, selection of p is en. handy) by several orders of magnitude its compared with the actual production probability . The low weight thereby incurred is offset by the increased probability to produce a (leading) p, Annihilation of p is included on an averaged basis, Lc by reducing the outgoing p weight by the annihilation probability of the incident p, The recording particles (exclusively p) tire selected with amomentum chosen uniformly within the accepted mange plus the expected ionization loss. The number of such p generatedat each vertex depends on the incident particle type. It varies from one to five and is empirically determined such its to roughly minimize thestafis" tical error in total p yield. The angle of the p with respect to the proiectile is chosen from a Caussian distribution with standard deviation dependent upon depth in the target system, The p so generated tree traced through the target and collection devices to the downstream endof the system, They are then projected onto a conveniently located aperture plane where they are either analyzed on-line or listed on a file for later use, e.g., in a beam transport code, The recording p undergoes elastic processes in stochastic fashion during transport but absorption is taken into account on the average, i,c  by reducing the weight at each step, The typical stop size selected for transport of both propagating and recording particles is 11,2 cm . Sensitivity to the focusing process in the collection dcvt:es precludes substantially larger steps, Typically, the p yield is calculated to within a few percent (statistical errors only), Most MC runs for this problem use correlated sampling of the random number sequences to help reduce relative errors between runs which differ only slightly in beam size or dispersion, geometry, target composition, magnetic field, etc. The MC program lists the p yield as a function of acceptance for each of aset of values of the aspect ratio of the acceptance cut ellipses. The yield is further separated according to whether the p originates from primary interactions, secondary nucleons, pions, or p. In addition, a selected number of histograms andscatter plots are produced, The histograms include yield as a function of production angle and of phase space accep.ance as well as of the depth and radius of p origin within the target, Thescatter plots display thepyield as a function of x-y position at production and of transverse phase space(at theacceptance cutplane as well as projected back to the center of the target). Some histo-

r'.

ffrglvu, A. ISUr Girutekrn

grants and plots are presented separately for primary and secondary production and for it set of fixed values of lite areeptance'lus, 4. Ferndlab 4, 1, t "lwirr o% purumrfrr, As seen in figs, 4-8 the p yield increase, ovilh increasing primary 1lrotun energy, Both the 01,tinluol 1 , nl1aetnuun and tile optinuun yield increase ahnost pro, laortional to the incident proton energy, Once the Tevatron and the Colliding Ilvaln Favility are eon11nixsioned tire highest Main Ring energy is expected to he 21X) (ieV, The autxinuun energy which ran he extracted tit is medium straight section is Imo (ieV, Extraction at the Main Ring nlrdilun straight section F17 offers it convenient locution for both torso station and Antiproton Source within the Fernkluh complex, Therofore, while it higher p yield nuly he obtained with 200 fl0V protons, the convvilivilvV of 111V F17 locution plus the, txpecled lower operating cost, support the choice of 1211 GOV for tile incident protnll energy 1151. For the above primary proton energy, 911I f  f the optimum yield can he obtained for p inonlcnia hvtwcon 8,5 QeV/t, and 16,5 CIvV/o, The aevlt111ulatilm pr ca of p, requiring compression of their 6-thownsional phase space, or "cooling", favors a lower antiproton momenturn. Since the normal Main Ring igjevthon momentum of 8,89 GeVA is within the yield platc,ut, this semis to he an obvious choice for the p energy, Antiprotons can he inieçted back into the Main Ring after accounuhuin and coolinla without pre-acceloration (151, As presently envisaged Ow Antiproton Source can effectively accommodate fl total longitudinal p nlonlenturn spread of less than ; t,%, In calculating the yields, this variation in momentum is included . For small momentum spreads theyield of pcan be assumed no he directly proportional to the range of longitudinal mom;nta accepted . However, foe any finite acceptance the number of p actually transmitted will not increase in the same proportion due to chrommic effects. The present calculations include only chromatic effects of the p collection system. The collection of antiprotons assumes the utilization of a lithium Ions 1161 . The advantages of an element focusing simultaneously on both planes are self-evident . In addition the very short focal c.istances that can be obtained result in very small chromatic effects. The merits of a lithium lens to adapt the phase space of p emerging from the target to a beam transport system have been already discussed 1171, Based on the experience at the INP, Nmosibirsk, !USSR (181, thecollection lens is taken to be a lithium lens of I cal radius, a

Anripnnon rirLtr

magnetic field gradient of 1(Mk) 'lean 1 and a length of I S cm, For such a lens and for a p monlenta of 8.8N (ieV/r the distance hetveen focal plane and the leu, entrance surface (f*) ix 14.45 'nt . 'l'lle 'enter ".,f 'lie target is itssuntcd to he at the up,trecua foal plan' unless ullterwise inolicuteol, As (cart of the ptitnitation I,rucedure lenses of larger radius or larger gradients sue eon,iolereoh 'l'he advantages of v short local length'olleetor arc hesl exploited by Ilte use of high demily targets lo offset the depth"of" f,eus effect by collccniratins Cllr production of p in us short il length it, possible. l'he antiproton eulleeti,al system un11se1 a nlau " olunl angle within wlkeh antiproton, run he e011ovied 1'lle area in l,ltaw space over Much the antipr1 m arc produced is then delernkned I, y the apparent we at Ihs largo of the source of antipr,aon,, i .e ., the proton heata ,iec, Therefore, 111' detl,ily of p in phase pa,v dare :-, with decrrusing proton beam site until ilratilolr sitter ills land nc.andary prooduction essentially de"mple the apparent site of the sourer of 1, fr,nu the atrtual proon brawl site, A higher 1, density in phaw sofa', rroluiw, Its, c,xling and tvdura, Ihr 'w'umulatr ,gleltn" nccded to aclkvve a given filial 1, dea,ily . I he nulumonl 111,01011 spul saw Modell eatlt he utihted 1, lunlied 1, 1% the enerlsv rhn,ily deposited in Ihr target. 1lnetit% drn,mc, in excess of 21M1 ,l - s I are exported to rc,uh in target failure unddensity depletion rv,ultinlt faun shock e,ov,

1zo ' 6 v rI`ROTONS iam

w

1

TAR,itI

Fig. Y, xlaximum cnrrgy drnsily, ffn, d:posited by Cu (ic%' protons in a 5cm tangue. target vs rms brun liar. Nun,hrr of protons on larget, NI  for a maxinunn rnrrgy density of ZOO Jg .` vs rnu proton beam size.

C. Hojvat, A. Von Ginneken / Antiproton yields

74

Table 3 Standard Feindlab parameters proton energy 120 GeV 8 .0 GeV Antiproton energy Antiproton momentum 8 .89 GeV/c Proton b- size o eo,, (tins) 0.038 cm Protons per pulse 3.0X lO n2 Cycle tinte 2.0 s Target material W w W-Rh 5-7 cm Target length Target dia neter > 0.20 cm Li leas radius 1 cm Li leas gradient 1000 T/m 15 .. Li leas Ismgth Li lens distance to focal plane 14.45 cm (j") Acceptance 20a mm " .rad 0 OP p production o dQdp le9' (41 2.52x10-1 sr " GeV/r collision length 9 .86 cm (tungsten) Proton p absorption length 9.29 cm (tungsten)

propagating through the target [19] . Among high density materials tungsten (and its rhenium alloys) have good mechanical properties at elevated temperatures. A study of the energy density deposited by a 120 GeV proton beam in tungsten is performed with the program CASIM [5]. The maximum of the deposited energy density, E o , within a 5 cm long tungsten target is shown in fig. 9 as a function of o, the rms size of the proton beam (assumed equal for the x and y dimensions). It is assumed that the protons are incident on the target over a time interval short compared with thermal diffusion times. It is seen that Eo follows closely a Is' dependence. From the value of E D for a given a, the maximum number of protests, NP , that can be targeted so as not to exceed locally the amount of 200 Jg - t is also shown in fig . 9. For beam intensities of about 3 x 10 12 protons/pulse, o TARGET WRA

of about 0.04 cm are indicated . Schemes involving rapid sweeping of the proton beam and the p acceptance channel, have been proposed to eliminate this limitation [201. A summary of the parameters discussed above for the Fermilab geometry is given in table 3 . The geometry of the target region and collector lens is shown in fig. 10 . 4.2. Results Antiproton yields are calculated for a range of parameters in order to optimize their collection. Yields are typically quoted as number of antiprotons per GeV/c of longitudinal momentum acceptance and per incident proton. The incident proton beam is assumed to have a circular waist at the center of the target. The beam distribution are described with Gaussians in each of the four transverse dimensions. The normalized proton beam emittance (containing 95% of the beam) is assumed to be 2477 x 10-d m " tad [211. Beam sizes are quoted by their transverse a(rms) size . By choosing the aperture plane to be, the second focal plane of the lithium lens, particle distributions are essentially symmetric with respect to the transverse phase space coordinates. On this aperture plane, machine acceptances representing the aperture of the Antiproton Source assumed equal in both transverse phase spaces are imposed with upright ellipses. The aspect ratio of these ellipses is varied to obtain the maximum p yield for a given acceptance and always these optimum values are quoted. For the standard parameters of table 3 a subset of the distributions obtained from the MC program is presented. Fig. 11 shows the distribution of all p generated as a function of their production angle with respect to the (central) proton beam direction. The only cut is that imposed by the outer radius of the lithium lens. Also shown is the distribution of p accepted within 20ir LITHIUM LENS R " I OCm q " I g q6 T/m

"a6Nxud PIN)70 aiAY

N."SCm-

130 Cm -----.-- .+IF-

FOCAL PLANE 1"06£7

i"45 CM ----I FOCAL PLANE CUTS

0

3em

Fqg. 10. Standard Femrilab geometry for the target and 0 collection system .

C. Hojoat, A. Van Ginneken / Antiproton yields

73

only cut is that of the outer radius of thelithium lens . A clear band is seen for theproduction of p in the lithium lens region . The same distribution for an acceptance cut of 20a mm " mrad in both planes is shown in fig . 14 . The change in the x' (= dx/d¢) scale should be noted. The imposed elliptical cut is clearly seen and it is also obvious that the aspect ratio of the ellipse is not exactly at the optimum value. 4 .2 .1 . Target length

P ANGLE Irad)

Fig. 11 . Predicted p yield (unnormalized) vs . production angle with respect to the (central) proton beam direction for all p emerging from the back face of the lithiam lens and for those accepted within 20rr mm " mrad. mm - mrad. Fig. 12 shows theyield of p (primaries only) as a function of distance alongthe beam direction of the point of production . In addition to production within the target, p originating in the lithium lens and beryllium entrance window areobserved. The distribution of p accepted within 20ir mm - mrad shows the depth-offocus effect of thelens at thetarget andeliminates all p from the lens region. The center of the distribution is a few millimeters downstream from the center of the target, indicating a larger optimal distance to the lithium lens . The phase spacedistribution of all p at the downstream focal plane of the lens is shown in fig . 13. The

The expected yield of p is calculated a a function of target length, both for copper and tungsten targets. The results are presented in fig. 15 for two values of the transverse acceptance . Tungsten provides the higher yields and a choice of 5 to 6 cm forthe target length is indicated. Most of the accepted p originate from interactions by the primary proton beans. The fraction due to sccondaries vs target length is shown for both copper and tungsten in fig. 16. Close to 22 .0% of the p originate from secondaries at the optimum tungsten target length. This fraction is essentially the same for 20 or 40r mm - mrad acceptances. 4.2.2. Proton beam si:e

The effect of beam size on the p yield is shown in fig. 17, for tungsten targets of several lengths and for two values of the acceptance. The yield increases almost linearly as the beam size is reduced down to rms sizes (a r, = a,) of about 0.015 cm. For smaller beam sizes the yield starts to saturate. as multiple scattering begins to dominate the effective proton beam size.

200 ALL 150

0

w

100

50

20 n

mm. mrad

~L

x 2 .5

a

1.

7.5

t l 10 .0 DEPTH (cm)

1

Fig. 12 . Predicted yield of P dueto urimaries (unnormalized) a a function of distance along the beam direction for all p emerging from .he back face of the lithium lens avid for those accepted within 20rr mm-mrad.

C. Htyoat, A . Van Ginneken / Antipromn yields 15.0 .

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v X

x (cm)

Fig . 1!. Predicted distribution of pin phase space (unnormalized) at the second focal plane of the lithium lens andaccepted within ä1rmin-voted.

C. Hojuat, A . Van Ginnekm / Antiproton yields

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!

iDOC

2

1590

6

Fig. 15. Calculated yield of p, per incident proton, as a function of target length . As discussed in section 4.1, the maximum number of protons per pulse that can be targeted is inversely propo:ü-al to the square of thebeam size. Since the p yield only o-greases linearly with increasing beam size, this will favor larger proton beam sizes if higher proton intensities can therebv b^ achieved . For the standard Fermilab parameters this ~àfect is summarized in table 4. The number of protons of 3 x 10) 2 per pulse is just below the present record Boosterintensity . I

,.. I -T -T-,~ T

Fig. 17. Calculated yield of p, per incident proton, as afunction of proton beam rms beam size. The effect of increasing the lithium lens radius and magnetic field gradient are also shown. 4.2.3. Lithium lens parameters

The effect on p yield of increasing the gradient to 1500 T/mas a function of beam size appears also in fig. 17 for two values of the acceptance . For each gradient the distance between target and lens has been adjusted such that the center of the target is at the upstream focal plane of the lens . For an acceptance of 20r mm - mrad the increase in gradient produces an increase of 10% in the yield for very small beam sizes. For 40r mm - mrad the p yield is clearly limited by a lens of 1000 T/m and I cm radius.

0.4

o.a

Table 4 Dependence of the number of antiprotons per pulse into mm -mrad acceptance on proton beam size.

ô Û

TUNGSTEN x COPPER

01

0

0

4

6 a 10 TARGET LENGTH (cm)

12

-

la

Fig. 16. Calculated fraction of p originating from secondary interactions.

Proton beam rms size o., =o,, (cm)

Maximum protons per pulse

p yield ;` (418 .1p/l

p per pulse

0.022 0.031 0.038

I .0x10" 2 .0 .10" "Ox 10 t=

6.8x10- s 5.7x10-s 4.9 .10- '

«68x10' 1 .14 .10' 1 .46xt0'

20%

78

C. Hojuat, A . Van Ginnekan / Antip- yields

Fig. 17 also shows that the effect of increasing the lets radius to 2 cm is identieal to increasing the lens gradient . It follows that the proposed lithium lens collector is veil matched for the standard Fermilab parameters . If the acceptance of p is to be increased beyond 20s, matt " mrad, either the gradient or the radius of the lens is to be increased to optimize their collection. 4.2.4. Lens distance to target Fig. 18 shows the p yield as a function of distance between the center of the target and the entrance to the leans for two values of the acceptance. The optimum occurs at a distance of 15 cm with at most a few percent increase in yield over'the geometry with the center of the target at the upstream focal plane (14.45 cm). 42.5. Acceptance In fig. 19 the p yield as a ftutction of acceptance is shown. The yield is expressed as p per incident proton for a total longitudinal acceptance of dp/p=0.04. The increase in yield. when reducing the proton beam rms size from 0.038 to 0.022 cm, is clearly seen below 20ar mm " mrad. For larger emittantes the present parameters of the collecting leas limit the yield for the smaller beast size.

ACCEPTANCE Ax-A,[-

Fig. 19. Calculated p yield dplp e 0.04 .

le.]

vs. acceptance,

within a longitudinal

The yield increases as the square of the acceptance up to l0ir mot -mrad. The choice of Ap/p of 0.04 and the acceptance of 20ar mm " mrad is a compromise between number of p per pulse accepted, requirements of the cooling systems and the required aperture o` the magnets in the first ring (Ihbuncher) of the Antiproton source. S. CERN S. I. CERN parameters

DISTANCE (Ctrl) Fig. 18. Calculated variation of the p yield, per incident proton. a function of distance between target center and entrance platy of the lithium leas .

The p yields obtained for comparison with the measurements performed at the CERN Antiproton Accumulator are based on the geometry that includes a linear horn for collection. The horn geometry in CASIM is based on a numerical representation [221 of the inner surface and the assumption that the horn is of uniform thickness (0 .07 cm) in a direction perpendicular to that surface. Multiple scattering within the material of the horn is included. Acceptance cuts, assumed" equal in both transverse planes, are performed-with' upright ellipses at the exit plane of the hem . The quoted yields are for, the optimum aspect ratio of these ellipses for a given acceptance.

7-

C. Nojoat, A . Van Ginneken / Antiproton yields

TARGET I~-- --

LINEAR HORN (146 KA)

Ilcm

-

a.scm

40cm --

PROTON_ BEAM

GRAPHITE

`Rh or Cu R-0 .15cm

0

5

ACCEPTANCE PLANE

1-

Fig. 20. Standard CERN Antiproton Accumulator geometry for the target and linear horn collection system. LITHIUM LENS R=1ocm q=1000 T/m

TARGET WRh R=0.1scm

0.075 rad

J____

PROTON BEAM

FOCAL PLANE TARGET

-

B.4 cm ----

0 Fi.' .

- IOOCm __

.

B4Cm

.j FOCAL PLANE CUTS

5
21 " A possible lithium lens collector geometry for the CERN Antiproton Accumulator.

Table5 Standard CERN parameters. Proton energy Antiproton energy Antiproton momentum Proton beam size = aF (rms) Protons per pulse Cycle time Target material Target length Target diameter Horn current Acceptance do 0° p production ~ leq. (1)) a dßdp Proton collision length p absorption length

o

26 GeV 2.758 GeV 3.575 GeV/c 0.075 cm '1 .0 .101, 2.4 s Rh or Cu 11 .0 cm C.3 cm 146 kA (nominal) 100v mm " mrad P 1 .30x 10-2 sr " GeV/c 9.86 cm (tungsten) 8.74 cm (tungsten)

The geometry for theCERN calculations is shown in fig. 20, with the relevant parameters listed in table 5. For comparison with the horn geometry, yields for the target and lithium lens collection geometry of fig . 21 are included. 5.2 . Results Comparison of the predicted yields is performed with data obtained by the CERN Antiproton Accumulator staff during early operation. The yield measure_ ments require p identification among all negative particles emerging from the target and that thelongitudinal and transverse acceptances are known. This is achieved by storing the p into the accumulatorring until all pious have decayed. The longitudinal and transverse acceptance are thus determined within the ring. Hence, the yields areobtained through a procedure sensitive to the operationof the ring. For the CERN geometry of table 5 with a tungsten

so

C. Hojtwr, A. Van Ginneken j Antiproton yields r . ._._t . .

300

I

r_ . . 1

1.

1

250 ALL

L

.

..

Lf

100 rrmX .2mrod 0.02

0.03

n~t-t . 0.04

P

1. ._ 0.05

1. tl 0.06

l4

l -1

V

0 .07

0.08

ANGLE (rod)

Fig. 22. Predicted pyield (unnormalized) vs. production angle with respect to the (central) proton beam direction for all ptransmitted through the hom and for those accepted within 100v mm " mrad.

target, the calculated distribution of all p versus the angleat production is shown in fig. 22. Theonly cut is that of the outerradius of thehorn. The distribution of these pwithin a 100m mm " mrad cut is also shown. The p yield as a function of distance along the beam direction of the pointof production is shown in fig. 23 along with theyield within a 100ir mm- mrad cut. In addition to thoseoriginating from the target there are p treated in the graphite windows. The phase space distribution of all p at the exit of the horn shown in fig . 24, has a "butterfly" shape more pronounced than in the Fermilab case. The p distribution is not upright but locks slightly convergent. Thedistribution of accepted p within the 100a mm - mrad cutis presented in fig . 25 .

Fig. 23. Predicted yield of p dueto primaries (unnormalized) as a-ftmction of distanec alongthe be.. direction for nll p transmitted through the hom and for those accepted wn'thin 100e rtutt" rarad.

5.2.1 . Target length

The effect of target length on p yield is presented in fig. 26 both for copper and tungsten targets andfor two values of the acceptance. A length of I1 cm optimizes the yield for tungsten at the 100îr mm - mrad acceptance, while for smaller acceptance there is only minimal dependence on target length. For very long targets the yield of a copper target is predicted to exceed that of tungsten. It has been reported (231 that for targets of 1I cm in length copper yields are consistently larger by about 20% than those from heavier targets like lead . A possible resolution of this peule may reside in eq . (1). Fig. 3 indicates that (if the data of Fermilab and of Dekkers et al. are ignored) the fit to the p product: m data may overestimate the cross section for lead by approximately 20% with respect to thedata of Allaby et al . and Eichten et al. A similar comparison with copper gives a more accurate representation of these last two sets of data. If it is assumed that the tungsten cross section is indeed overestimated by 20%, then it is predicted that the yield from copper equals that from tungsten for target lengths of about 9cm. For 13 cm long targets the copper yield would then exceed that from tungsten by about 10%. Included in fig. 26 is the effect of the target length for tungsten in the lithium lens geometry . A target length of 6 cm is indicated as in the Fermilab case. For both acceptances one expects to collect about 1.5 times theoptimumnumber of p with the linear horn collector. The calculated fraction of accepted p due to secondary interactions is shown in fig . 27 . 5.2.2. Horn current

Fig. 28 compares CERN data (241 with calculations for the 0 yield from a 11 cm long, 0.60 cm diamet :r

C Hojuut, A. Vcn Gin7teken / Antiproton yields 1 15,0

.

1

._

(_ .. . 1 _

I

7

I

10.0

5.0

v

o.o

E X

-5.0

-10.0

I -2.5

-15.0

1

I _ i -1.5

I -2 .0

I -LO

~

I -0.5

1

I 0 .0

~

1 0.5

1

I L0

I L5

I 2.0

I 2 .5

X (Cm) Fig. 24 . Predicted distribution in phase space at the horn exit for all p transmitted (unnormalizedl .

Z5 6.0 4 .S ~

072

,7

v ^

LS

1_

0.0

x

-1.5 0

-4.5 0

2

:a "T

05n 0i~n4RNJt\9>59~4

\29t " 7

7 7 24i450 5 02

5Fn

" 17 ~4e2" 44ôi~Y4?ijÔ7774915]F 770 " 2o tilv " 9~17v "~~8 77 5^ y4 S92'5N9941559_t SYCS t0N55"7q 45 457 7! " 7V775\I09 75955>SYFIRY\Y5007472~5i77770074 u575o.S0z4"" `9 7 7 7777C579 97a0404 q >RT>0oi9S574705Y77Fp5579JRN N+4 27>"4 0 5Yt "52`n4490V7974filNYN777R777l97 5l4G0 50> SNfl559504 95400Y>9 F 0at^? +Y " W" ~ .>5t9n225h49E5979R'titvYâo2ia Y 59J540n57C7Yti7SN>2117 ` 474179`9n745Y95755F774774 955'i02 9\ 9Hr .FRS750Y7>W >050 a9 YF7 , "54Y9775gp7974F547944g92429V255i747959\77I99 77604q 755 5 " 7 é007 >71'J00509924J74900n05R?9F747740754059Y7205N Ufl7Yra 7.7C7R175 75C .7+^;H9gy7fl7975z~i2729574r5pi0J7r'~5Y7x ; : ;~7 ;R2974,Y99Rt,R5~i 02Y5 5 .ti~,57 44 Y259i\i~> 4 5 799S07C79F0n.N2FiCV7 C5Y9 5.7759yS F 0 Y ~4nY700 ~VY597245\)F5RC5NR\~iEg~~~57Lt~42fn 4 955" 4Y 5497 F 529Fß4J4997747GFY4R']7\7HP99g227C5~0JRYYN-7C V >R099779 u J 7N051977!l592?5H>9C7Y7 R2$57R9Y99R5F4Y \F995S 444 fs Sé0\00FG7051547r,4G972579g 500447 7 4F57CFfl4759757Y952907550 Ft570^ 77V7>4Y00gn0~4700qF047470i " 507774FS7751Y72>045YN\K9R9 J0~0707Y "F " 9q 5 F J474YFif77l7? ;5>779Y475545+0FVIF>49595r9E070749 9P ' "5g5iS7Y5F7r.77iG72Y 75! 747$ 0257 72572YSTF795o17Lr05lYS509RY272 51 2 " 4774>m"55ngi o5579 "W '7 2>!14t17171RIY4>S" FF U499YY<\"1 9" 2C 7`4 " 4,77 " 2 4 ti 4 W722 " 7>9YMW77gYR79H094oyY79'7 0 5 z50 74o7is > " 1" ÔYY'VJo{\NftY27i"Y41.+0,1dh77.~t1" s2 7, 70 " 0 72772±5 Wf7?" ~579077 " 7 n ~l 5+7707 050 2Y0+V 777740 0u444 FF7451991 y2 7 :7570' 5 1 " 00 1, > .

i4

a

~

l05 +

'z"ivsoi'

H

-6.0 -~ 5 I -2 .5

I 1 -2.0

1

I -1.5

1 -L0

I

1

-0.5

I

I

I

00

0.5

L0

I

15

I

1

20

2 .5

x (cm) Fig . 25 . Predicted distribution in phase space at the horn exit within IlM)a mm~mrad (onnurmalized).

82

C. Hojmt, A. VanGinneken /Antiproton yields +

CERN DATA

w 10s 2 O O A. z

ro' l

0

I 120.

I 1.0. HORN

I 160.

,

CURRENT x

I 190.

,

I200.

103 (A)

Fig. 28 . Comparison of CERN data of p yield within dplp = 0.015 as a function of homcurrent with calculations.

I 6

1 I 9 ' b

I I I , 12 , la , 16 TAROT LENGTH (cm)

,

Fig. 26 . Calculated yield of p as afunction or target length for CERN hom andfor lithium lens geonetries. copper target, assuming a transverse acceptance in both plan of 85w mm - mrad. There is good agreement for the larger values of the horn current but the optimum yield occurs at significantly different values of the current. Thecalculated optimum yield is larger by a factor of two. Although the distribution of p in transverse phase space at the horn exit for the nominal hom current of 146 kA is consistent with an upright ellipse, for a 170kA current there appears to be aconverging p beam with an ellipse angle given by tan j_ -0.48 rod m-1 . 5.2.3. Accepfatee The calculated p yield as a function of the acceptanceis presented in 6g. 29. For thelinear homgeome-

try both 11 cm long tungsten and copper targets are shown along with a 6cm tungsten target and lithium lens geometry. Comparison is made with data available from the CERN Antiproton Accumulator staff (251. For the larger of the measured yield curves there is good agreement for acceptances below 25rr mm - mrad but the calculation predicts larger yields than are observed at the larger acceptances. For comparison the design value for the CERN 10

0 0

na

6 CALCULATED YIELDS 0 W-6cm Li LENS + W-11cm HORN x Cu - llcm HORN v W-Il cm DESIGN (Ref. 4)

'6 1

V 2 nâ

w '61

F 03- .

a û

0p ".

w " TUNGSTEN " COPPER

^ O.IO4L.

I 6

-L 8

I 10 ' 12 114 TARGET LENGTH (cm)

16

1

Fig. 27. Calculated fraction of p originating from secondary interactions fa the CERN hangeometry.

Fig. 29. Comparison of experimental andcalculated yield of p within dp/p s 0.015 vs. acceptance for the CERN horn geometry. The predicted yield for the CERN lithium lens geometry is also shown.

C. Hojcat, A . Van Ginneken / Antiproton yields

References

Table6 Fermilab -CERN comparison .

P production < 60 mead p collected per proton Max. no. of protons per second P collected per second

83

Fermilab

CERN

Ratio

2.19 x10'3

1 .21 x 10 -"

17.4

4.90x 10' s

1 .42x 10 -°

34 .5

1 .50X 1012

5.00 x 10"'

0.30

7.35 x 107

7 .10x 106

10.4

project [4] of 2.5 x 10 -6 P per proton is also indicated . This valueis close to the predictions for the lithium lens geometry. 6. Summary Perhaps the most significant figure of merit of a P source is the rate at which P are accumulated. This relates directly to the average luminosity of the collider andhence to the event rates observed in experiments. Table 6 compares calculated results of the P collection rate for the Fermilab and CERN designs. The standard parameters are used with the choice of tungsten as target material in both cases . It can be observed in table 6 that the kinematical region and the lithium lens colto^tion system of the Fermilab design offer substantial advantages . Die larger proton intensity at CERN partially offsets t'oese advantages . Theproton intensity ) .n theFermilab design is limited by the rotation of theproton bunches prior to targeting (to minimize the ',P longitudinal emittance) which precludes loading the Main Ring with more than a single Booster batch. Without' this limitation the proton intensity could be increased by about a factor of seven although such again would impose presently unrealistic requirements on the P collection device and the stochastic cooling system. Further improvements arepossible both at Fermilab and at CERN . The MC progri .m described above can be a valuable aid in studying tt~e effects of many such improvementschemes in a quantitative way. We thank the staff of the CERN Antiproton Accumulator and the Institute of Nuclear Physics, Novosibirsk, for many fruitful discussions. One of us, C.H ., wishes also to thank these institutions for their warm hospitality.

(I] G.1 . Budker, At . Energy 22 (1961) 346 ; Sov. 1. At. Energy 22 (1967) 438. 121 S. van den Meer. Report CERN/ISR-PO/72-31 (1972). 13] A.N . Skrinsky et al., 8th Inc . Conf. on High energy accelerators, Geneva (1971) p. 72 ; C. Baltay, 6th Inc . Conf. on High energy accelerators, Stanford (1974) p. 572 ; D. Cline et al ., Fermilab Report TM-687 (1976) ; T. VsevoMzskaja et al ., INP-Novosii, irsk 80-182 (1980) and Fermilab p tote 185(1981). 141 CERN, Design Study pp facility CERN/PS/.4A 78-3. [51 See e.g., B.V. Chirikov et at., Nucl . Insu. and Meth . 144 (1977) 129 ; F. Krienen and J. MacLachlan, IEEE Trans. Nucl. Sci . NS-28 (1981) 2711 . 161 A. VanGinneken, Fermilab FN 272 (1975). [71 C.W . Akerlof, Phys. Rev. D3 (1971) 645; J.V . AIlaby et al ., CERN Report 70-12 (1970); B, Alper et A, Nucl . Phys. 11100 (1975) 237; 1. Baider et al Phys. Leu. 3911 1197:) 414; L.M. Bark- et al., Serpukhor Reoo,t IHI P 79.92 (1979) ; W. Bouoli, Nucl . Phys. 1114(1 (19781 271 ; D. Dekkers et al ., Phys. Rev. 137B (1965) 962; A.N. Diddenc et al., Nuovo Cirri, 31 (1964) 961; T. Eichten et al., Nucl . Phys . 1144 (1972) 333; H.1 . Frsch et al ., Phys. Rev. Let, . 44 (1980) 511; K. Guettler et al ., N.I. Phys. B1 16 (1476) 77; P. Garbincius (Fermilab SAS group), private communication; J.C . Sen,, private communication; M.A .J . Bctje, Thesis, Utrecht (1980) ; A.O. Vaisenberg et al., Zh . Eksp . Theor. Fiz. 29 (1979) 719 . 18] D.C. Carey et al., Phys. Rev. Leu. 33 (1974) 327; D.C. Carey et al., Phys . Rev. D14 (1976) 1196; F.E. Taylor et al., Phys . Rev. D14(1976) 1217 ; J.R. Johnson et al ., Phys. Rev. D17(1978) 1292 . 191 See e.g ., J. Hebert e, al., Phys. Rev. DIS (1977) 1867 . 110] S.J . Brodsky et al., Phys. Rev. Lett . 39 (1977) 1120. fill L.M . Barkov et ai., Serpukhov Report, IHEP 81-107 (1981) . [12] R. Hagedorn and J . Ranft, Suppl. Nuovo Cim. 6 (1%8) 169. [131 Seee.g., J .G. Rushbrooke and B.R. Webb,:, Phys. Repu . 44 (1978) 1 . [ 14] B. Rossi, High energy particles (Prentice Hall, N.J ., 1952) . 1151 Fermilab Antiproton Source Design Report, Fermilah (February 1982). [161 B.F . Bayanov et al ., 10th Inc. Conf. on High energy accelerators, Protvino (1977) vol . 2, p. 103 . (17] T.A. Vsevolozskaya et al., Zh. Teor. Eksp. Fiz. 45 (1975) 2494; B.F. Bayanov et al ., Zh. Tmr. Eksp. Fi,. 48 (1978) 160 ; E.P . Cotton, Fermilab P Note 120 (March 1981) . [181 B.F. Bayanov et al ., Fermilab Report TIN-1000 (August 1980) ; B.F. Bayanov et at., Nue. Instr . and Meth . 190 (1981) 9: G.N . Silvestrov, private communication . 119] High intensity targeting Workshop, Univ. of Wisconsin Report, Fermilab (April 1980). (201 F. Krienen and F. Mills, Fermilab PNote 70 (May 1980) : T. Vsevolozskaya et al ., Fermilab Report TM-10411(1981). 1211 Sho Ohnuma, Fermilab Internal Report, unpublished. 1221 S. vanden Meer, private- communication. 123] E. Jones et al ., CERN Report PS/AA/ME,/Note 10 (February 1982). 124] R.P. Johnson, private communication . 1251 H. Ko6ol, CERN Report PS/AA/ME/Note 4 (December 1981) .