15/ 12/93 OCR Output

eva, Switzerland

briefly evaluated.required LEAR hardware modifications is presented. Special features of a dedicated ring arelighter ions with highest possible luminosity is also discussed. A first analysis of theLimitations and expected performances for lead ions are examined in detail. The case of

and optimized for this purpose.considerations also apply to the case of a new "LEAR-like" accumulation ring specially builtusing the Low Energy Antiproton Ring (LEAR) "in situ" is described, but most of thelinac. This report presents a first feasibility study of this idea. To be specific the scheme ofaccumulate and cool the ions in a small storage ring at 4.2 MeV/ u, the output energy of theTo reach the required luminosity for Pb-Pb collisions in the LHC, it has been proposed to

Abstn

P. Lefévre, D. M6h1

(A FEASIBILITY STUDY)

A LOW ENERGY AC TION RING OF IONS FOR LHC

CERN-PS-93-62 \ C V- , 1+ § uci 5 LD "/*IllIlllllllIIIIIIllllllllllllllllllllllllllll

LHC N°‘°”°

/ CERNQS g3.6g (DI)CERN LIBRARIES, GENEVA

- PS DIVISION

EUROPEAN ORGANIZATION FOR NUCLEAR RES

ACKNOWLEDGEMENTS OCR Output

CONCLUSIONS

COMPATIBHJTY WITH ANTIPROTON OPERATION

3.2.3 Storage in the PS

3.2.2 Full stripping at the exit of LEAR

3.2.1 Charge states at the LEAR entrance

3.2 Low charge states in LEAR

3.1 Lead scheme applied to lighter ions

OTHER IONS

2.8.3 Preliminary conclusions on the basic scheme for Pb53

2.8.2 Injection into the PS

2.8.1 Transfer lines

2.8 Transfer lines and PS injection

2.7.3 Fast extraction from LEAR

2.7.2 Magnet power supplies and ramping

2.7.1 RFparameters

2.7 Acceleration and extraction

2.6.5 Longitudinal stability limits

2.6.4 Transverse space charge limits

2.6.3 Intra-beam scattering

2.6.2 Recombination with cooling elecuons

2.6.1 Stripping by residual gas

2.6 Beam lifetime limitations in LEAR

2.5 Electron cooling dmc

2.4 Aperture and stachng considerations

Linac performance assumed2.3

2.2.2 Number of bunches and total luminosity

2.2.1 Performance limitations

2.2 LHC requirements for lead ions

2.1 Overview

THE BASIC SCHEME FOR LEAD IONS

INTRODUCTION

TABLE OF CONTENTS

dense cooled stack. They are transferred into the stack by the electron cooling system OCR Outputtypically 50 mm to 0 amplitude at the septum. Up to 20 turns are injected around thescheme with an orbit bump decreasing in about 50 tts (i.e. over 20 turns) from(E0) and injection line (E2), Fig. 1. The injection is a classical horizontal multitumUsing LEAR in situ the transfer to the accumulation ring proceeds via the existing loopenergy is 4.2 MeV/u. The charge state, 28+, is stripped to 53+ at the exit of the linac.

The Linac 3 is assumed to deliver ions with a repetition rate of 10 stl. The output

2.1 Overview

2. THE BASIC SCHEME FOR LEAD IONS

The definitions and units used in this report, are summarised in Appendix 1.

lator could be built. Most of the following considerations apply to both alternatives.wound up in a few years from now. In the opposite case a new dedicated ion accumuAccumulator Ring. This is a possibility only, should the antiproton programme be

To fix ideas we consider the conversion of LEAR "in situ" into a Low Energy

improvements and consider the performances to be expected with ions lighter than lead.acceleration will be examined. In a second part, we point out altematives and possibleimplications related to injection/ejection, beam transfer, as well as bunch formation andappropriate for fast cooling and stacking will also be mentioned. Then hardwarethe stacking procedure, cooling times and beam lifetime limitations. Optical setting

To address the feasibility of this scheme, we discuss intensity and density limits,

value of 2 1027 cm·2 s·1·LHC. Then with about 500 bunches per ring the total luminosity is close to the designenough bunches to reach the luminosity limit of 3.6 10cmsper bunch in the24 ‘2 ‘1with a stack of up to 1.2 109 ions per batch of 4 bunches. The goal is to provide densescheme". It is based on the accumulation of Pb53"‘ at 4.2 MeV/u in the cooling ringRing in more detail, than was possible in [1] and [2]. We will first discuss the "basic

lt is the object of the present report to present the Low Energy Accumulation

gaining back these factors by means of cooling and accumulation.and luminosity are of the order of 30 and 103 respectively. The stacking scheme aims atconstruction for fixed target experiments at the SPS. The missing factors in intensitybeams like those foreseen for the standard CERN Heavy Ion Facility [4], underHowever the corresponding phase space density cannot be reached with conventionalthe beam—beam interaction [3]. This leads to an upper limit for the luminosity per bunch.the requirement to have a sufficient beam lifetime ir1 the presence of nuclear effects inan order of magnitude. In fact the operation of the LHC with Pb ions is constrained byduring the time of a PS cycle thus increasing the intensity to be accelerated via the PS bystrong electron cooling to cool and accumulate the pulses from the heavy ion Linac 3alternatives has been discussed in [2]. The basic idea is to use a ring like LEAR withthe LHC project proposal [1]. The proposed solution together with a number of

The accumulation of heavy ions at low energy is part of the scheme adopted in

Fig. I : Ian scheme forLHC with accumulation in LEAR

\ LEAR OCR OutputE3

c\ ‘T ‘Q \Z 0ns

EX ‘¥

16i/\@ /

E1

lx \`\R€’6

PSB

42

(ref. [5]). Thereafter the acceleration continues at h = 16. OCR Outputfrequency is gradually stepped down from h = 32 to 28, 24, 20 and finally 16To achieve this uansfonnation with minimum blow-up, a procedure is used where thetransferred into the buckets of a lower frequency rf-voltage (fdr = 4.75 MHz, h = 16).where the limit (fr; = 9.5 MI-lz) of the RF-system is reached, the 4 bunches are(fl-f = 2.7 MHz, corresponding to h = 32 in the PS). After acceleration to 258 MeV/u,

The train of the 4 bunches is transferred into matched PS buckets

Fig. 2 : Overview of the lead transfer schemes

/\/VV\ Strnpng

•···*•· Transfer scnene for SPS faxed target Ion physics

Possible alternative schene

B¤s•C transftf Schené

129.5 2sa.0

T/A MeV/u

14.a s4.4 | 149.5 I sore

tsso for 0=2a> caauo for ¤=e2>

ser u=sa asc eso iaac 1 2140 | isaacP/0 MeV/c per charge 1990

LINAC

tax

c·ss

ELEAR

r ········ 1 ·········· 1···t··BUDSTEIR

PS •»=a2 I •·.=1e ¤»—. 32 I ¤=1e NIV) lm¤=a2

SPS

justify the extra cost. Fig. 2 illustrates the different transfer schemes.i.e. the maximum that LEAR can hold, has been excluded as the gain does not seem tobeam transport is required. ’I`he extreme of 2 GeV/c per charge (125 MeV/u for Pb53"‘),of LEAR. Then, however, an upgrading of the LEAR ejection, the PS injection and theRF gymnastics, and - for operation with lighter ions · to permit full stripping at the exitinteresting to reduce losses due to interaction with the residual gas in the PS, to simplify

We note that u·ansfer energies higher than 14.8 MeV/u, e.g. 64.4 MeV/u look

altematives.

a length of 3.6 s; other PS cycles with 2.4 or 4.8 s duration can be considered asacceleration is about 1 s. The full LEAR-cycle is matched to a standard PS-cycle withenough to the present 609 MeV/c used for antiproton transfer. ’l'he time available foraccelerated and transferred to the PS at 654 MeV/c per charge (14.8 MeV/u), closeis reached and the beam is bunched at harmonic number 4 (frf · 1.4 MHz),

After 2 sec of stacking the required intensity of 1.2 109 ions (6.4 1010 charges)

100 ms must be obtained.

before the new pulse arrives. Cooling times fast enough to accomplish this during

(ejection from LEAR - LHC at interaction energy) of about 1/3. Hence we require an OCR OutputAn analysis of the transfer losses [2] leads to an expected overall efficiency

the injector systememittance, retaining the life-time of 10 h). But this leads to more difficult conditions foraccepted (increasing the intensity and the luminosity per bunch proportional to the

In principle higher luminosity could be obtained if larger emittances could be

Table 1 : LHC parameters for operation with 208Pb82

nsBunch spacin 134.7

660Bunch harmonic number

GeV/u 1 18Iniection ener

3.1Collision energy [TeV/u]

0.8[eV · s/ u]ark

[eV · s/ charge] | 2-01.5€v* [uml

1.5[um]

Normalised emittances at collision

Luminositv/bunch [cm‘s2 ‘1 3.6 1024Number of ions/bunch 0.94 108

limits given in table 1.These assumptions lead to the intensity (about 108 ions/bunch) and luminosity

protons.

ii) the same physical beam emittances in the transverse planes as for operation withsection of = 280 barns for beam loss;

i) a luminosity half-life of 10 h in the presence of nuclear effects with a total cross

requirements [3]The performance limits for Pb-Pb collisions in the LHC follow from two basic

2.2.1 Performance limitations

2.2 LHC requirements for lead ions.

to the 24 minutes time constant for blow-up by intra-beam scattering [3].(3078 MeV/u). The holding time of about two minutes is sufficiently short compared

Prior to acceleration in the SPS 32 PS-batches are stored at injection energy

496 as discussed in section 2.2.2 below.

systems and to facilitate RF acceleration in the SPS. Then a realistic bunch number isHowever several gaps are needed to avoid loss during the rise and fall of the kickerprinciple 165 such batches with a total of 660 bunches would fit into the LHC.The bunch chain, which filled 1/4 of the PS circumference, has a length of 157 m. Inbetween consecutive bunches) · and the bunch harmonic number of 660 in the LHC [3].matches both - the 200 MHz RF structure in the SPS (leaving 26 empty bucketscharge after stripping). At this energy the bunch separation (135 ns at the B = 0.97)

Ejection and full stripping to Pb82+ are done at 3078 MeV/u (= 10 Gev/c per

considered. OCR Output

"LHC injection and dump·kicker—gaps" are marginal and will therefore not be furtherbunch mode respectively, whereas gains obtainable by shortening the "RF-gap " andto about 100 ns fall is of the order of 20% and 50% for the four-bunch and the twotable 2. The gain in bunch number and luminosity obtainable by speeding up this kicker

Possible improvements by upgrading the SPS injection kicker are also given in

are prepared.details are given in table 2, including a mode where only two bunches per LEAR cyclecycle and 10 s for acceleration in the SPS the filling time per ring is then 8.1 min. More

This leads to a total of 496 bunches per LHC ring. With a 3.6 s LEAR and PS

filled bunch places are underlined.summarised by the formula: 660 = [(4 + 1) 32 + (5)] 3 + [(4 + 1) 28 + (25)] where the

The disuibution of the 660 bunch places in LHC for the 4 bunch basic scheme is

28 PS batches, instead of the 32 used for the three other SPS fillings.LHC dump kicker. This gap is created by filling the fourth SPS pulse with onlyFinally a single gap of 3.2 us is required in the LHC beam to permit rise of the

160 consecutive bunch places, leaving 5 &ee places corresponding to 943 ns.LHC comprises 165 bunch places and one SPS batch (32 PS batches) occupies(26659 m) is almost 4 times the SPS circumference (6911 m); one quarter ofaccommodate the fall of the LHC injection kicker. The LHC circumferenceA gap of 940 ns is needed between consecutive SPS batches in the LHC, to

occupying 160 bunch places and leaving an addiuonal ll bunch places free.bunches each separated by an empty bunch place are lined up in the SPS,the beam velocity (B = 0.97 at injection). To leave this gap, 32 PS batches with 4SPS RF -syszem [6] once per tum to re-synchronise the travelling wave system toA gap of about 1.75 us is required to "switch the phase" of the Hxed frequency

left between consecudve PS-batches stored in the SPS.additional gap of 135 ns, corresponding to one empty SPS bunch place has to beThe free space of = 120 ns separating the PS bunches is not sufficient, and anA gap of 220 ns is required to accommodate the fall of the SPS injection kicker.

in the SPS [3];loss during rise or fall of the kicker systems and to facilitate the RF-gymnasdcs required

Some of the 660 bunch spaces in the LHC have to remain unoccupied to avoid

2.2.2 Number of bunches and total luminosity

efficiency.and 4 respectively have been admitted for in the esdmation of the overall transferemittance increases in the horizontal, vertical and longtudinal plane by factors of 1.5, 2and to leave room for blow up during acceleration, transfer and RF-gymnastics. In fact,collision energy in table 1. This is to respect acceptance limitadons in the injector chainnormaliscd cmittanccs at low cncrgy have to be smaller than the values given forintensity of 3 108 ions/bunch in LEAR i.c. 1.2 109 pcr batch of 4 bunchcs. The

used in [4]. OCR Outpute and Ap/p are then smaller by a factor of 4 and 2 respectively than the 2 rms values

, _defined as the full area of the bunch (see appendix l for more details). The numbers forEx= (oxy2/BXN) [pm] and Ap/p = Gp E o(dp/p); the longitudinal emittance is ldefined with reference to one standard deviation (ox, oy, o(dp/PD viaconventions the transverse emittances and the momentum spread in the present work areare the same as those assumed in [4]. For consistency with the LEP and LHCemittances and the momentum spread of the beam at the Linac 3 exit as given in table 318% at 4.2 MeV/u, is obtained from the formulae by E. Baron et al. [8]. Thewe take a transmission of 90% each as in CHIF. The efficiency of stripping to Pb53+,

For the Radio Frequency Quadrupole (RFQ) structure and the subsequent linac

process, as a safety factor.will keep this possible improvement , which would clearly ease the accumulationLEAR, up to the theoretical limit where the total charge per burst is constant [7]. Weindications that higher currents can be reached during the shorter pulses needed forpulse length up to 400 ps as required to fill the 4 PS booster rings. There areperformance [4] of the Electron Cyclot1·on Resonance (ECR) source for CI-IH: with awith a length up to 100 tts and at a rate of 10/s . The current of 80 ILA is the present dayrepetition rate. In fact we assume that the source produces pulses of 80 |.1A of Pbzgfixed target experiments at the SPS - except that we need shorter pulses but fasterthose of the CERN Heavy Ion Facility (CHIF), [4] — presently under construction for

The performances which we take for the source and the Linac 3 are the same as

2.3 Linac performances assumed.

Table 2 : Bunch numbers, filling times and initial luminosity ( one insertion)

Tk ~ 220 ns at present).

(135 ns spacing), it requires however an upgrading of the SPS injection kickers.

a rise time Tk S 120 ns permits rise of the kicker field between two consecutive PS bunches

Filling time per LHC ring [minutes] 8.1 I 9.1 I 13 I 18.5

Imam tummosi ¤m·2 s -11 x 1027I 1.8 I 2.2 I 1.5 I 2.2

Number of bunches per LHC rin 496 I 608 I 412 I 616

Number of PS cvcles to iill one LHC ring I 124 I 152 I 206 I 308

BASIC

SPS kicker rise time 220 I 120* I 220 I 120*

Number of SPS cvcles ver LHC rin

3.6PS cycle duration [s] 3.6

Number of bunches per PS-cvcle

multitum injection [9] as shown on Fig. 3. Then, to improve the efficiency, some OCR OutputThe 20 turns are injected around the stack in much the same way as in a classical

Table 4 : LEAR acceptances

:i:3momentum, Ap/p [10*3] [ :+:5

vertical, Av [

horizontal, Ah [ 200 150

Acceptances Theoretical I Practical

the vertical acceptance, too, has to be used for multitum stacking.50%, about 20 tums are needed to reach the intensity gain of 10. Thus to some extentabout 10 turns fit into the horizontal acceptance. In reality, with an overall efiiciency ofaccommodate each incoming turn. Then from tables 3 and 4 one concludes that ideallyacceptance in phase space of 9 times the rms emittance of the beam) is required totion and stacking with cooling an effective space of at 3 standard deviations (i.e. an

The acceptances of LEAR are given in table 4. We assume that for multiturn injec

2.4 Aperture and stacking considerations

Table 3 : Source and UNAC parameters.

Momentum spread Gp after debunching [10*3] [ <0.2normalised e*h = e*v [pm] 0.2

physical eh = ev [um] 2.1

Transverse emittances (lo)Corresponding tlux [ions/tts] | 2.6 106Pulse current (after suipping) [pA] 22

Beam at injecdon to LEAR

Stripping eHiciencv 28+ to 53+ 18 %Charge state selected after stripping 208pb53+

Stripping foil ( Carbon)

Transmission efHcienc 0.9

[MeV/u] 4.2Output energy

LNAC

Transmission efiicienc 0.9

[keV/u]Output energy 250

ions/usCorresponding flux dN/dt 1.8 107[IJ-A]Pulse current 80

Transverse emittances (16), normalised [Hm] 0.07

[keV/U] 2.5Output energyIon species 208pb28+

Ion source

Repetition rate 10s·1[ns]Pulse length S 100

General Parameters

lattice. OCR Output

replace the transverse scheme will be investigated, together with the optimization of thefmal position of the injection elements. Longitudinal stacking which could improve or

The study of the injection scheme will be pursued in the coming year to decide the

envisaged to design new electrostatic elements.mechanics and the 150 kV power supplies. Concerning the fast bumpers it could also bemodification of the current sheet itself (profiled septum), but hopefully using the sameexisting electrostatic septum used for ultraslow extraction could be used afterefficiency could be obtained by using a thin elec¤·o-static septum (S 0.1 mm). Theinjection efficiency will suffer due to the magnetic septum thickness (9 mm); a higherin SS42 or SLI and the DC magnetic septum in SL1 [Fig. 4]. However, the multiturnfast bumpers to be relocated in section SSll and SSl2 with the addition of a third one

In principle, the injection can be achieved with the existing elements, namely the

contained in an rms phase space area ofa few mm mrad.into the stack. After 100 ms, when the next pulse is available the particles must be

The electron cooling system is working continuously to merge the injected beam

Fig. 3 : Multizurn injection (far QH - 230)

stacked cooled circulating beanMultlturn Injected bean around the

Bump

Decreasing

at the septun posltlon

Horizontal phase plane

···—H·—-l · -—• X

Incoming bean

septumCooled bean ¤

H2, ><’

quadrupoles.provided by the solenoidal fields of the electron cooling device and possibly by skewedvertical phase plane, where "spare" acceptance is available. The coupling can becontrolled amount of coupling is used to uansfer particles from the horizontal into the

Q = 53, A=208 the charge- and mass number of the ions,

and electrons,

k (= 0.16) a constant, depending on the distribudon of ions

with:

c

1 () OCR Output1/ = L}. L L ° I kATlc crerpw

write the cooling rate aslarge amplitude have to be transported into the centre. To estimate the time for this wesomewhat different from the cooling of a normal beam as pulses injected at a relatively

The cooling times to be expected are discussed in ref. [10]. The problem is

2.5 Electron cooling times

Fig. 4 : Modified layout of LEAR for ion accumulation and cooling

SL3$$32 $$31

BNH20BHNSO

Electron cooling

$$22N l $$41 % rest Kicker - ew Q Qments

M Relocatecl elements

Fast Kickers

RFteuigewSLAsteLEAREJECTIDN _ seems

RFMagnetic

(DC)

Septum

Magnetic

$$21$$42(DC)

Bumpers Sgpfum BumpersF¤St electrostatic \ F¤St

Magnetic orEBQBHN40 BHN10

$$12$$11SLI

E2INJECTIDN

EE

10 OCR Output

same k-value has been taken here for the "flattened" ion beam where the cooling iswhere the cooling is dominated by the electron velocity spread (Bc > Bi). Thewhere the influence of the solenoidal field can be neglected). This is the situation,k = 0.16 applies for a flattened but non-magnetised electron beam (i.e. a beam

iv) Finally there are uncertainties about the value of the "constant" k of Eq. (1);

up by the "flattened distribution"- and "the magnetised" electron effects [10].possibility to obtain very small effective temperatures is, to some extent, openedbeam is smaller than 4 mr, corresponding to about 0.1 eV beam temperature. The

iii) To have fast cooling it is important that the angular spread (Qc) of the electron

the electrons into account.

A careful optimisation is necessary, taking the imperfect overlap of the ions with

provide at the same time, zero dispersion in order to favour fast cooling.of the optics is under study to increase this value, perhaps up to 10 m, and tosettings the horizontal beta at the LEAR cooler is as small as bh = 2m. A changeThus a relatively large beta function is advantageous. With the present optical

injected pulse and stack, Gi = d/Bb.dominated by the large horizontal beam size as given by the distance (d) between

ii) The angle of 4 mr taken above is the effective ion beam divergence. It is

scaling assumed above is valid.("cold ion limit") a QL5 scaling holds whereas in the "hot ion beam limit" the Q2Darmstadt [12] indicate that for highly charged ions with small velocity spreadestablished, to Pggi;. Recent measurements done at Heidelberg [11] andorder of magnitude from ions with Q/A = 1, for which cooling rates are well

i) The Q2/A dependence taken in Eq. (1) implies an extrapolation by more than an

Several remarks are now in order :

given in parentheses) we obtain a time constant of 65 ms.With the numbers indicated above (where those specific to the present case are

the angular spread between the electron and the ion beam.9 (= 4 mr)

the elementary charge ande = 1.6 10*19 C

trons/cm3],ding to a volume density nc = j/(ebc) E 0.45 108 elecbeam cross section) for the new LEAR gun correspon

j (= 0.02 A/cm2) : the current density of the electron beam [0.55 A/(30 cm2 e

_ -r° ` 2'8 IO Cm i the classical electron and proton radii,13 16 rp = 1.5 l0` cm

Lc 2 10 the Coulomb logarithm,

device,

the fraction of the circumference occupied by the coolingTlc(= 0-018)

1 1 OCR Output

estimated &om the Betz and Schmelzer formula as quoted in [13]Here the equilibrium charge state, Q for the ions, QT for the residual gas is

(Y_1)(Y_1) Q.0 5-2-2" 3.5 l0-2-2 Q " o= Z 'QQ -.= ;and cl=—-——-——QQ();cm2/atom (2) ¤ 2 2 T 2 O.5 T [ ](Q)Q2 10-24 (—18+x)

[13] for the electron capture and loss cross-sectionsTo estimate charge exchange with the residual gas, we use Franzke's formula

2.6.1 Stripping by the residual gas.

2.6 Beam lifetime limitations in LEAR.

Table 5 : LEAR batch ( coasting beam) at the end of stacking.

momentum spread, coasting beam Gp [10*3] 0-5

[eV · 5 / u] 0.05

0,19[eV·s/charge]0.5[um]

[uml

normalised emittances

number of ions 1.2 109

Beam properties expected at the end of stacking are summarised in table 5.

the transverse one, but this fact is not needed for the stacldng scheme.to about 14 instead of 8 minutes. The longitudinal cooling is expected to be faster thanLEAR and PS cycle of, say 6 instead of 3.6 s. This would increase the LHC Hlling timea first phase one might use a slower filling rate, e.g. with a linac pulse every 0.2 s and aand vertical cooling in about 0.1 s, to clear space for the new pulse, can be achieved. In

Based on present day understanding of electron cooling we expect that horizontal

the ions.strongly cooled beams, has to be upgraded for the even more demanding operation with

The present transverse damping system, necessary to ensure the stability of

will also have to be studied together with the lattice modifications.An increase of the cooling length from the present 1.5 m to 2.5 or 3 m in LEAR

stability and to reduce the effective temperature.neutralisation of the cooling electron beam looks promising to improve the beamprovide the required high density and low temperature of the electron beam. Controlledhighly charged ions. Parallel to this, improvements of the hardware are indicated, totheoretical and experimental work is necessary to determine the limiting cooling rates for

In summary : the required fast cooling and stacking is a challenging as, both

Tc < 0.1 eV as discussed above).dominated by the large horizontal ion spread (and where 9] > Sc provided that

12 OCR Output

level.

3-5 times higher vacuum pressures can be accepted before the losses exceed the 10%losses are compiled in table 6. One concludes that these losses are negligible and thatsimplicity approximate this by a pure N2-atmosphere with P = 10*12 torr. The resultingcomposition as measmed during oxygen storage tests is given in Appendix 2. Let us forgases like N2, CO... with a partial pressure of about 0.5 10*2 torr. An example of the90% of H2 molecules with a partial pressure of 5 10*12 torr and of 10-20% of heavier

To apply these relations, we note that a good vacuum in LEAR consists of 80

AN/N=ln(Ng/N)=ncoBAt=At/it

yielding for the special case of storage:

AN/N=ln(Ng/N)=nc]oBdt

The losses during storage and acceleration are obtained by integrating Eq. (4)

0* /[molecule] = 2 0 /[atom]

diatomic gases like H2 or N2the assumption that the influence of the constituents is simply additive such that e.g. for

Thus the cross sections per molecule are needed. Usually these are obtained with

= _ n 3.6 10 jon] ~ 2.7 10 —i[mbaI]16 P16 P

expressed by the number of molecules/cm3 of the residual gas is related to the pressurewhere 6 = oc + 01 is the total charge changing cross section. The volume density

1/1=—=nGBc%%

The beam lifetime is obtained from the cross section via

including measurements with oxygen ions in LEAR.Appendix 2 where we compare results with a collection of data extracted from literatureoverestimate the cross sections (up to a factor 20 for hydrogen). This is discussed inheavy ions (Z > 32) in gases like N2. For lighter residual gases, the formula tends tofor projectile energies in the range of 1 to 10 MeV/u. The tits give good results for

We note, that the cross-sections, Oc and ol were derived by fitting measurements

b=_4< , = . O r 0711 (z)¤rQ Q X l $10, t Q>6 ¤r b=_2_3

1·5°=4F2

B= v/c in both cases. ’I`he other quantities entering into Eq. 2 aregas atoms respectively. The relative ion - atom velogity is given by the beam velocity

where we insert the atomic numbers Zj =Z and Z·=ZT for the ions and the residual

13 OCR Output

times for three dzjferent situations on the 42 Mev/u injection flat top.Table 7: Beam conditions, resulting maximum tune shifts and intra beam scattering

19ms growth time I img [S] I 11

0.009 0.033 0.084Maximum tune shift | AQ.,

0.84 0.95 0.92correction factor IFTune shift

0.4Bunching factor | Bf

0.5Momentum spread | gn [10-3]Ev 2.1

Emmanees eh [uml 2.1 1010

Intensi 1.2 1091.2 108 I 1.2 109

iniection I coasting I hunchedAfter stackingBeam at T/A = 4.2 Mev/u I After

negligible compared to the electron cooling times and thus of no concem.situauons summarised in table 7. Although the growth times are short, they arebeam. We have used the computer code NTRAB [17] to make estimates for the 3

Growth times and equilibrium depend critically on the three emittances of the

2.6.3 Intra beam scattering.

capture.

indications that these would increase the loss rate significantly compared to radiativelike e. g. resonant dielecuonic capture or three body reactions [16], but there are no

There are other charge changing mechanisms in the elecuon-heavy ion interaction

the losses reach 10% during 2 s of coolingproportional to the cooling rate. Even then, there is still a factor of 10 in hand, beforedensity and hence the recombination rate may increase by a factor of about 2,Pb53+, all other parameters kept equal. With the new electron gun [15] the elecuonScaled with Q2 this corresponds to 2.8 10‘3/s (i.e. to a beam lifedme of > 350 s) forLEAR the recombination rate (dN/dt)/N observed (and calculated) is less than 10‘6/s.

The corresponding cross-section scales (roughly) with Q2 [14]. With protons in

XQ+ + e‘—> X(Q‘1)+ + hv

dominant mechanism can be assumed to be radiative recombinadon

For the density of the cooling beam in quesdon (about 0.5 108 electrons/cm3) the

2.6.2 Recombination with cooling electrons.

14.8 MeV/u.during a LEAR cycle with 2 s stacking at 42 MeV/u and 1.6 s acceleration toTable 6 :Ly‘erime and particle losses for a Pb’3* beam at 4.2 Mev/u, 14.8 Mev/u and

cle 150 s average I < 2%/cycle

0.2%/stixed 14.8 MeV/u I 500 s

1.1%/sf1xed 4.2 MeV/u I 90 s

ener lifetime I loss/unit time

14 OCR Output

GD 2 1.5 l0‘4 which is safely below the 5 10‘4 of the cooled coasting beam. On theobserved. Then with 1.2 109 Pb53+ ions at 4.2 MeV/u the stability limit is satisfied for

In LEAR, impedances of the beam environment with Zn/n ==100 Q have been

momentum distribution by twice the rms i.e. we take (Ap/p)FwHM == 26For practical calculations we approximate the full width at half maximum of the

= "impedance/n at f = tifm,"

Bc/21cR : "rev.f1equency"frev

931.5 MeV : "rest energy per mass unit"with : eU()

(8,2 2 (a) Z ;.<a.N..=. fa P Fwrm UO A B Y “

the low momentum spread coasting beams. 'I`he criterion requires:We use the criterion of Rugiero-Vaccaro and Keil-Schnell to examine stability of

2.6.5 Longitudinal stability limits.

been started to explore the space-charge limits of LEAR in detail.focusing functions which vary strongly around the ring. Experiments with protons havenecessary due to the particularities of LEAR which has a low periodicity lattice andacceleration is safely below that obtained in accelerators. Some caution is howeverwith the suong tune shift is short). The tune shift of the bunched beam duringring limit (and even slightly above, which however looks permissible as the time spent

One concludes that the coasting beam at the end of stachng is close to the storage

AQ ~ 0.5milli-seconds in the space-charge regime:accelerators (PS, booster...), with dwelling dmes ofin storage rings (ISR), with storage dmes of hours: AQ = 0.03

maximum permissible tune shifts (again quoted for G = 2 ) areexperienced in existing machines. As a rule of thumb: to preserve beam quality, the

We can now compare the tune shifts given in table 7 to the "empirical" limits

AQ calculated here.for constant transverse projected distribudon (G = 1). Thus AQ is half the maximum

We note that the "u·aditional" value for AQ called the Laslett tune shift is calculated

listed

the correcdon factor Fc (see Appendix 1) evaluated for the present LEAR lattice is alsoThe maximum tune shifts for different situations are included in table 7 where

The incoherent space charge tune shift is dehned and detailed in Appendix I.

2.6.4 Transverse space charge limits

15 OCR Output

safety factor of 1.4. At ejection a gap of 100 ns in the beam has to be provided for theprogramme is designed in such a way, that the bucket area exceeds the bunch area by azero to 1.5 - 3 kV and the stable phase does not exceeds 6 degrees. The voltagecreate problems with the space charge limit. Concurrently the RF voltage rises frommaximum dB/dt of 0.5 - 1 Tesla/s is reached without too tight bunching which would

At the end of the injection flat top, the magnetic Held is smoothly raised so that the

harmonic number h=4 .

Table 8 : RF parameters for Pb53+ at injection and ejection flat tops in LEAR, for

2.2Bucket/bunch area I A/E1

Bunch area (per bunch) I S1 [cvs/ul I 0.012 I 0.012 I 0.012

0.4Beam bunching factor 0.4 0.32

Full Bunch duration 225420Atb Ins]

1.2RF- voltaze 1.2[kV]

700 185374RF - period Ins]

RF · freuuenc 1.44 I 2.69 I 5.4[MH:]

RF - harmonic Nr

{rev 2.8Revoludon dme 1.49 I 0.74[us]

Off-momentum factor =· 0.9q = 1/y2·11y,2 | = 11.0045 I 1.015 I 1.0691

Relativistic parameters 0.096 I 0.1762 I 0.3537

Maznetic rizidi 1.16 I 2.18 I 4.57Bp [Tm]

Momentum/charge [MeV/cQ] I 347.6 [ 654.3 [ 1387.3

Energy/nucleon 14.8 I 64.4T/A [MeV/u] l 4.2

0.0125 eV.s/u (0.05 eV.s/charge) for each of the 4 buckets.flat tops. The numbers refer to the case of harmonic number 4 with an area of

Table 8 summarises the RF-parameters for the injection and two possible ejection

2.7.1 RF parameters.

2.7 Acceleration ramping and extraction

seems to be the case at present.self bunching provided that the real part of the coupling impedance is well controlled, as

In summary we can assume that the stack with on = 5 10*4 will resist longitudinal

"Keil-Sclmell circle".capacitive impedance the stability zone is much larger than predicted by the simplerequired by Eq. (8) have been obtained, in full agreement with the fact that forwith electron cooling in LEAR, space charge impedances several times larger than

8 KQ and would need a momentum width GD 2 1.3 10‘3 to satisfy Eq. (8). However

n W. . . . . other hand thc d1rectlong1tud1nal space charge xmpedance · - 1s as large asZnx 750 :2

16 OCR Output

strongly dependant of the final lattice for which the optimisation of the position of theThe fast extraction scheme is sketched in fig. 5. The extraction parameters are

2.7.3 Fast extraction from LEAR

645 MeV/u. Injection at 42 MeV/u, B = 0.279 T, IM = 0.792 kA.rebuilt to solve the pyralene problem and to meet the rise rate for ejection atbe used in its present state Q‘ the ejection is at 14.8 MeV/u. The supply R5 has to beTable 9 : Magnet cycle and power supplies for bending magnet. The supply R22L can

VNNormal voltage 120 I 380

4.81.5Normal current

R22L, pres. I R5. mod.Power suppl

3 .6 3.6cle time

tq I sAccumulauon time

Am Is 0.05 0.05Eiection flat

0.750.65Descent to iniection Held I Atl Is

0.9 0.8AtT lsAcceleration time

2.3560.695AIDifference to iniection

1.492 3.148Excitation current

0.246 0.829DiH`erence to iniection Held I AB

0.525 1.108LEAR magnetic field

4.57B 0 [Tm 2 . 1 8Maznetic rizidi

14.8 | 64.4Eiecdon energy/nucleon I T/A [MeV

correcdon elements) all seem capable of following the 1.6 s cycle.The other converters (the supplies for the quadmpoles (R21L), and for the

pyralene used in this supply.fast enough cycle. A partial reconsuuction is necessary in any case to replace theMeV/u in 1.6 s. For the higher energy alternative the R5 has to be upgraded to assure aobtain a rate of rise with dB/dt = 0.3 T/s which will permit the cycle 4.2 - 14.8 — 4.2ejection at 14.8 MeV/u, the R22L can be used; it needs only minor improvement tois employed for high momenta (2.0 Tm S Bp S 6.7 Tm). For the basic ion scheme withcovers the low momentum range (Bp S 2.03 Tm at present), and the R5 supply, whichLEAR bending magnets are fed by two different sets of supplies : the R22L whichPb53+ ions with 14.8 and alternatively with 64.4 MeV/u ejecdon energy. At present the

In table 9 the basic parameters of the magnetic cycle are recalled pertaining to

2.7.2 Magnet power supplies and ramping

ICSPCCGVCIY (RPS = BRLEAR!).hps = 32 or hps = 16 permitting bunch to bucket transfer of 4 or 2 LEAR bunchesto the lower frequency limit of 2.7 MHz in the PS if the harmonic number chosen ismatching to the PS buckets. The exuaction energies of 14.8 or 64.4 MeV/u correspondwith a voltage up to 6 kV each. This leaves a comfortable margin for acceleration andtwo LEAR cavities will be modified to cover the frequency range of 0.7 to 5.4 MHzsomewhat higher voltage may be required to match the bunches to the PS·buckets. Thebunches become sufficiently short. At 64.4 MeV/u this requires about 3 kV. Arisc of thc cxtracdcn kicker. This is obtained by raising the RF-voltage so that the

18 OCR Output

charge) the strength of the PS elements have to be doubled; a second tum can be addedthe p/Q = 650 MeV/c per charge, ions. For the high momentum (p/Q = 1387 MeV/c perantiproton fast exuaction channel (septum SMH26 - kicker KFH28) in the PS to inject

For the same reasons as discussed above, there is no difficulty to use the existing

2.8.2 Injection into the PS

1387 MeV/c per charge) some power supplies have to be exchanged.momentum (p/Q = 650 MeV/c per charge) but for the high momentum option (p/Qtransfer antiprotons of p = 609 MeV/c. There is no problem for the lower ejection

The present elements of El, the line that connects E2 to the PS, are able to

previously used for H‘ injection into section 4 of LEAR.the common injection/ejection line E2 will be consuucted with the existing elements1l6° bending magnets of the E0 loop. The E3 line which connects the ejection point toprotons; the only delicate point is an increase of 12% of the magnetic field of the twomomentum p/Q = 350 MeV/c per charge is close to the present p = 309 MeV/c for the

Concemin g the non common part of the injection line (E0), the transfer

Fig. 6 : Current in the transfer line (Q) elements

C -..--.--- - Pulsed e iectlon level

().l._-T-X----!-——-——• `li

DC injection level

l I ~ 5 to 10 ms

(diodes and self) to reach the ejection current level.opposite polarity will be added in parallel, with the necessary protection elements

The present DC power supplies will be kept and pulsed power supplies of the

lattice has been chosen.

quadrupoles instead of 10. A detailed study will be made when the optimum LEARoptics has to be found, hopefully with an easier matching (D ~ 0) but with 12 or 13coil diameter of 130 mm instead of the present 200 mm. As a consequence, a newnew quadrupoles developed for the Booster-Isolde line; these quadrupoles have an innerkept for the bendings. For the pulsed quadrupoles it is proposed to use the design of theelements have to be changed for new laminated elements; the existing coils could bepulsed in the opposite polarity during the 1.4 us ejection (fig. 6). The massive corequadrupoles operating in a DC mode during the 2 s accumulation time, have to beLEAR and the extracted LEAR beam to be injected into the PS. The 5 dipoles and 10

As shown on fig. l, the line E2 is common for the Linac 3 beam to be injected in

2.8.1 Transfer lines

OCR Output2.8 Transfer lines and PS injection

19 OCR Output

ejiciency of % as assumed above).bunches and corresponding stored intensity per bunch required in LEAR (overallTable 11 : Intensity limit per bunch in LHC, total initial luminosity for about 500

*** limited bv the count rate in the detector

** limited by Intra Beam Scattering in LHClimited by nuclear effects

16I 8 M110,,,*H 31 210 10 310 Il00

Ca I 40 I 20 I 2.4 109** I 1.2 1080 0.8 1010 I 251.8 109Nb I 93 I 41 I 5.4 108** I 610288 108Pb I 208 I 82 I .94 108* I 1.8 1027

LHC LHC bunchElement I A I Z I N/bunch in I L I N stored in LEAR I Ngm/Nlgb

to be an important effect for lead, will be even more difficult for lighter ions.Hence in a design pushed to these limits, the space charge in LEAR, which tumed out

The resulting intensities increase strongly with decreasing atomic number [20].

parameters and in particular assume a horizontal IBS growth time limit of 10 h.table 11. Theses numbers are based on a set of assumptions about the LHC beambeen calculated by D. Brandt [19] for several typical ion species and are recalled inbecomes the dominating luminosity limit. The corresponding intensities per bunch havelarge A [19]. Finally, for very light ions, the count rate acceptable in the detectorlower luminosity limit than the nuclear beam—beam effects, which dominate for very

For lighter ions (roughly for A < 190) intra-beam scattering in the LHC imposes a

with this more general case.will therefore outline some possible extensions of the scheme discussed so far to deal

Recently interest has been expressed for ion species lighter than lead [18]. We

3. OTHER IONS

open.

determinant advantage for the lighter ions (section 3), justifying to keeping this option14.8 MeV/u. Nevertheless, it will be shown that the higher energy scheme has a64.4 MeV/u. This advantage is marginal, so the "best" transfer energy for Pb ions isefficiency is raised from 80% to 86% by increasing the injection energy from 14.8 toshown that for the pressure of 10*9 mbar, i.e. 0.75 10·9 Torr (Ng equivalent), the PSresidual gas. An estimation made by the same method as used in the section 2.6.1, hashigher injection energy in the PS is to reduce the losses due to the stripping by thethe exception of the pulse length of the LEAR ejection kicker. The advantage of the

The "high energy" (64.4 MeV/u) transfer level to the PS is more complicated with

2.8.3 Preliminary conclusions on the basic scheme for Pb$3+

can be foreseen for the pulsed septum magnet keeping the existing power supply.to the kicker which will be powered by a new 70 kV generator; a new magnetic circuit

20 OCR Output

2.2.2). The transfer of one bunch per LEAR and PS cycle is not considered (strongaccount due to the reduction of bunch number in the LHC in the 2 bunch mode (section

In addition, a reduction of 17% of the initial luminosity has to be taken into

charge detuning as for Pb ions.4.2 MeV/u. Relative number of ions per LHC bunch in LEAR with the same spaceTable 12 .· Charge state Q after stripping for optimum stripping ejficiency at

8 I 0.5 I 68% I 4 3.4 I 7.817 I 0.42 I 37% I 7 1.9 I 3.8

Nb 32 I 0.34 I 24% I 10.9 1.24 I 2.48

Pb 53 I 0.25 I 18% I 13.5

A I efficien 4b mode I 2b mode_ I _

6/AElgmcnt | Optimum charge state and efficiency I 2 · N§’“/ Ngbtripping at 4.2 Me

favourable 2 bunch mode.

limit in LHC (table 11) indicates a missing factor from 2.5 to 13, even in the more

"b'l`he ratio N I$/ Ng(table 12) compared to the intensity ratio to reach the IBS

factor of 2.

because compared to the 4 bunch scheme the intensity stored in LEAR is reduced by aclear that from the point of view of space-charge the 2 bunch mode is preferable,the 2 and 4 bunch modes (respectively 2 and 4 bunches per LEAR and PS cycle). It is

"' bper bunch in LHC Ng, relative to the number of Pb ions, Ng, can be estimated forIf we accept the same space charge tune-shift as for Pb ions, the number of ions

formula [8].(Q = Q) at 4.2 MeV/c calculated with C. Hill's programme [21] using E. Baron’snumbers are included in table 12 where the charge state is the optimum after suippingspecies, the space charge tune—shift in LEAR scales like N Q2/A. The corresponding

With the hypothesis that Linac 3 accelerates to 4.2 MeV/u independent of the ion

3.1 "Lead Scheme" applied to lighter ions

sections.

injection into the PS. These points will be discussed in more detail in the followingenergy in LEAR and perhaps use one Booster ring to raise the energy further prior tobunches in the PS. To this end it is advantageous to accelerate to the highest possiblecombined with full stripping at the exit of LEAR, which permits stacking of up to 16

In addition, except for very heavy ions, these measures can profitably be

profit from the A/Q2 dependence of the space chargeii) the use of lower charge states during stacking and acceleration in LEAR, to

batch by the corresponding factor;4 assumed for Pb, are prepared per LEAR cycle. This reduces the intensity per LEAR

i) the use of a 2 or 1 bunch mode where only 2 or 1 LHC bunches, instead of the

charge limit in LEAR :In principle two different ingredients can then be combined to improve the space

2l OCR Output

Calcium already with the 4 bunch mode.improvement of N{,°"/N? (table 11) is satisfied for Q/A = 0.125 for Niobium andparameter is indicated in table 13. One concludes from the table that the requiredoptimised for Q/A = 0.125. The space charge limits in LEAR scale as Q2/A. This

Low charge states are favourable for the source and Linac 3 performances,

3.2.1 Charge states produced by the ion source

LEAR.

Fig. 7 : Overview of the "light" ion transfer scheme with full stripping at the exit of

() are values of P/0 vs MeV/c per charge-·-—--· alternative through Booster

possible schene for D and Co

expected schene

42 14.8 23.9 50 64.4 400 3078T/A MeV/u

Q Ec<14¤0>(350)

•25U¤" ca ‘°‘ n¤°° LEAR

<15s0><·•*¤>LINAC | .a¤u

LEARCe" NbW <59¤><111¤>

Source I °150LEARc¤" N¤"°

<710><1330>

•IZ5D" C¤" N¤“‘, LEAR

0/A

Full stripping -•

wuz |l00Z |84% |10¤z

-- --- - ...... J w lzm 4`4i• +•%100>BUDSTER htcc1]b#;4b

PS

<7aoc> ub SPS ,_.....***

<as0¤>¤'* c¤¤’•

several possible charge states.ex¤·action energy from LEAR. Details are given in table 13 for the typical ions and forindependent parameters to be chosen, namely the charge state hom the source and the

An overview of the proposed scheme is shown in fig. 7, illusuating the two

exuaction with a good emciency, except for very huvy elements.ionscanbeaccelexatedinLEARtoanenergywheiettieycantlienbefully suippedafterstate into LEAR directly from the Linac 3, without stripping at the Linac exit. These

To further improve the space charge limit, one soludon is to inject low charge

3.2 Low charge states in LEAR

luminosity increase compared to ladsadsfy the user requirements for the lightest ions, even if it permits a nodceablelong Elling time). In consequence, the "lead" scheme is not considered as able to fullyrcducdon of the number of bunches in LHC with the present SPS injecdon Hcker, and

22 OCR Output

present Linac 3 to LEAR transfer line can handle p/Q S 350 MeV/c per charge.charge (p/Q) gives the "equivalent proton momentum" at injection into LEAR. Thethe same space charge detuning in LEAR as for the Pb scheme. The momentum perTable I3 : Charge states from Linac and relative number of ions per LHC bunch with

7090.125 I 0.25 I 54 I 108 I(216!)

48 96 4720.1875I 0.s6I 2416,. I 326 520.250 3541 I 13

0.125 88 7090.625 I 22

0.150 30 5900.9 I 1520“I 6

170.200 34 4431.6 I 8.5

10 0.250 10 20 3502.5 I 5

17.4 34.80.129 6901.5 I 8.741°" I 12

0.150 12.8 25.6 5902.1 I 6.493... I 144.823 0.247 9.6 3505.7 I 2.4

ev/c4b lb2b

U ll1¤j.m1.EARIon I Q QA | Q2/A N§?“/N{"

will start during the coming months.measure the source performances with several different charge states, for typical ions,

Studies on the modihcation of the bending magnets are going on; experiments to

accumulation in the PS) this solution could satisfy the LHC limits.focusing optics. In conjunction with the one bunch mode (with the necessity ofrequire a modiicadon of the existing ll6° bending magnet, with smaller gap, and a new

Finally, an intermediate solution looks promising using Q/A ~ 0.2 to 0.18; it will

the PS bucket length (h = 16).high extraction energy and by voltage increase (2 cavities) matching the bunch length toon h = l at 4.2 MeV/u (fl-; = 0.36 MHz) or capture on h = 2 then merging on h = 1 atmatching. Two soludons can be envisaged, modi5cation of one LEAR cavity to capturebe expected for the transfer of one bunch Hom LEAR to PS concerning the longitudinalaccumuladon in the PS of the fully stripped ions (section 3.2.3). Some dimculties are toContrary to the situation discussed in section 3.1, the one bunch mode can be used withshown in table 13, the one bunch mode has to be used to satisfy LHC requirements.drastic change of the 116° magnet and hence Q/A << 0.25 in LEAR is excluded then, asdrawback of this situation is that it is less favourable for the space charge in LEAR. If asupplies to push the existing magnet into the saturation region (B = 1.46 T). Thep/Q = 350 MeV/c per charge and will demand a modest improvement of the power

Opposed to this, Q/A = 0.250, close to the Pb situation, corresponds to

to be built with a small bending radius (p = 0.8m), which is far from simple.increased. Instead a new superconducting magnet to operate around 2.5 T would have(Bp = 2.4 Tm). As the space in the tunnel is limited, the bending radius cannot below charge states, these magnets have to transfer ions with p/Q = 709 MeV/c per chargeline (E0 loop) (iig. 1) designed for protons of p = 309 MeV/c. To make full use of thehigh Held required in the two 116° bending magnets of the LNAC to LEAR u·ansfer

The main inconvenience of the operation with low charge states comes from the

23 OCR Output

unlikely solution of superconducting E0 elements is adopted or if a new machine isenough charge states (Q/A > 0.135) to make the altemative worthwhile. Only if theenergy and good at Booster energy. Simply because a Pb source cannot produce highPb ions, even though the efficiency of full stripping for Pb is still finite at high LEARstripping at the LEAR or Booster exit and stacking in the PS do not look attractive for

We have to note that the schemes without stripping after the linac but with a full

monoturn bunch to bucket transfer. This has to be studied in more detail.new injection in the Booster ring 3 has to be implemented to permit high energyto the PS at higher energy. To this end a new short beam line is necessary (tig. 1) and aat 64.4 MeV/u in the PS, namely to inject from LEAR into the Booster, and from there

Finally a further option can be considered in case of difficulties with the stacking

time.

on the accumulation time through both the source performance and the electron coolingthe duration of the LEAR cycle. The LEAR cycle cart be short but is strongly dependantIn this way 4 to 16 bunches can be stored in the PS depending on the ion species andobtained using the antiproton ejection elements which are designed for p = 609 MeV/c.

The injection momentum p/Q = 700 to 800 MeV/c per charge will be easily

beam blow-up due to the field imperfections in the PS will be smaller at higher fields.transfer the LEAR bunches directly into the PS buckets on harmonic h = 16. Finally thein favour of high energy stacking in the PS for all ion species is the possibility totime the high energy option T/A = 64.4 MeV/u is necessary for Nb. Another argumentFrantzke's formula [13] are listed in table 14. It appears that to have a long enough lifeenergies with a PS residual gas of N2 with 10*9 mbar pressure computed frompressure because the electron capture cross section is small. The life time for several

The fully snipped ions can be stored in the PS despite the relatively high vacuum

3.2.3 Stacking in the PS

T/A > 12 MeV/u).Baron's formula used for the stripping ejiciency is not well established for energiesfully stripped ions in the PS for a residual gas of N; with 10*9 mbar pressure (note thatTable 14 : Rough estimates of the ejiciency for full stripping and 1/e We time of the

100100 22 230

10070

> 9093Nb 20

t tseff (% t (s) I eff (%T/A = 64.4 MeV/uElement l T/A = 14.8 MeV/u

fliciency for full stripping and beam life time in the PS at

large atomic mass (Nb) it is necessary to accelerate to and extract at T/A = 64.4 MeV/u.Nevertheless it is clear that to reach a stripping efficiency close to 100% for ions ofBaron's formula [8] is well established only for energies, below 12 MeV/u.typical energies (table 14) and are included in fig. 7. These values are approximations as

'l`he efficiencies for full stripping have been calculated from E Baron‘s formula at

24 OCR Output

LEAR but could be justified by the improved performance.The cost of a dedicated machine is definitely higher than the modification of

bunches for LHC in a shorter filling time.the new machine could be short to ease the accumulation in the PS, and provide more

Combined with a faster acceleration system and shorter cooling times, the cycle of

the (Q/A ~ 0.125) leading to favourable space-charge conditions.at the machine exit. The injection line can allow transfer of very low charge states frommachine is a free parameter which can permit the full stripping of all ions including leadfor a high performance electron cooling device. The maximum energy of the newdepend on the outcome of this study, but there must be room for a long straight sectionconstraints due to the existing infrastructure and buildings. The shape of the ring willbut a preliminary study has to be made to establish the feasibility and to determine thebends and with Booster-PS injection line, look easy. Much civil engineering is requiredthe PS ring (fig. 8) where the communications with the Linac 3 beam line without sharp

A new dedicated accumulator ring could be located in a favourable situation inside

build a new "LEAR-like" machine for ion stacking and cooling.the LHC era, which is not envisaged at this time, the most reasonable solution is to

If it is ftuther decided to keep a wider programme of antiproton physics alive in

experiments.

be located in the LEAR South Hall after the removal of some high energy LEARmomenta p > 609 or 309 MeV/c has also to be envisaged. Such a small ring could easilyprogramme is envisaged, the construction of a new simple antiproton ring for low

This possibility has to be carefully studied; however, if such a long term

and during other long periods for antiprotons.scheduling problem could be solved if LEAR runs during periods of months for ionsrequired for a possible long term antihydrogen physics programme. In such a case theextraction of low energy antiprotons to feed Penning Traps. This lcind of operation is

The only compatible operation could be to keep in LEAR the possibility of fast

accumulation.seen from fig. 4 which illustrates the main rearrangement of the LEAR layout for ionwith the operation with internal jet target and with ultra slow extraction. This can beLHC operation. 'l`he main reasons are the incompatibility of the rearrangement of LEARphysics programme around LEAR is wound up 3 or 4 years before the begirming of the

The use of LEAR (in situ) for the LHC ion programme is valid if the antiproton

4 . COMPATIBILI'l`Y WITH ANTIPROTON OPERATION

species of interest.ingredients mentioned above will per·mit to reach the required luminosities for all the ion

More study is needed but it appears on first sight that the combination of the

3.3 Conclusions for ions lighter than lead

including Pb.envisaged (section 4), can the above scheme also be profitable for the very heavy ions,

25 OCR Output

Implementation of a dedicated machine.lighter than Pb;Performances of the ion source and the Linac 3 for different charge states and ionsAnalysis of transfer efficiencies;Electron Cooling and stackingMultitum injection in LEAR;machines;Linac 3-LEAR and LEAR-PS transfer lines and matching between the differentoptimisation of the LEAR lattice;

work is necessary to reach the level of a design study concerningpossibility to obtain the desired luminosity with lead and also with lighter ions. More

The use of LEAR or a LEAR-like machine with suong elecuon cooling opens the

s. CONCLUSIONS

Fig. 8 : Possible dedicated ion cooling and storage ring

1.mAC 3

w LINALZ 2 \ ELEM

\ ®·\

sm /)

BUUSTER

26 OCR Output

advice and contributions.

J. Gruber, G. Heritier, K. Metzmacher, D. Simon and M. Thivent for their preciousquoted in the references, we would like to thank M. Brouet, J. Buttkus, P. Gourcy,study. They will be more involved for the design study. In addition to the colleagues

Many hardware and machine specialists have been consulted for this feasibility

6. ACKNOWLEDGEMENTS

performances) but would obviously be more expensive than "LEAR in situ"A new dedicated ion ring could be optimised more freely (situation and

further studies.

extraction at 64.4 MeV/u and stacking in the PS looks promising but needs manyinjection from the Linac 3 of charge states corresponding to Q/A ~ 0.200 to 0.18 withejection at 14.8 MeV/u looks quite feasible. Concerning the lighter ions, the direct

The use of LEAR in situ for Pb$3* with stacking and cooling at 4.2 MeV/u and

27 OCR Output

Q Mi Q= = 300 Bp in MeV / charge$2

being the bending radius in a magnetic field B) byThe momentum per charge is related to the beam rigidity Bp in T.m (p

M1 Mi ’ Mi Mi Mi

Energies and momentum per ion mass are expressed in MeV/u and related

¤ = 2.9979108 m $-1.with Eg = Mi Eu, Eu = 931.502 MeV (the atomic mass unit) and

E=T+E0 =x/(P¢)+E02

interrelated byThe total energy E, the kinetic energy T and the momentum p of the ions are

207. 955 1>b28*Fm Mpb 4 = 207. 94 1>b”+

Mi = 207_ 925 amu Pb(nucleus mass)82*

me : .0005486 amu (eleeuon mass)M-Qmc (neglecting electron binding energy)

ion mass in amu

82For Pb, M = 207.97 amu = 193.72 GeV / c

208

Note that in chemisuy it is defined as 1/12 of the atomic mass of HC).(1 amu : 931.502 MeV/c2 is defmed as 1/16 of the atomic mass of 160.Atomic mass in amu (atomic mass unit)Charge state (Q = Z for fully stripped ions)Mass number (number of nucleons)Atomic number (number of protons)

Ion notation _I

SOME NOTATIONS AND DEFINITIONS

APPENDIX 1

28

the RMS value.

for a Gaussian distribution we use : A-= 4 o(T/A), where o(T/A) isK';]Mi OCR Outputspread;

'trcv is the revolution period and A = Bly Eu 2 is the total energyL M1

ef=A - tm, ineV.s/uIM1

Coasting beam (area in (AT, At) plane).

Longitudinal emittance

The acceptances Ah and Ay are also defined as areas in phase plane devided by rc.

Normalised emittances: ef, = B7 eh , ez = Bye`,

respectively and Bh, By the horizontal and vertical Twiss parameters).(oh and ov are the RMS of the projected horizontal and vertical distribution

BvB.,oi, 0; . 8 = —— , 6,, = —— 111 “

Transverse emittances (S11I’f8CCS in phase plane/1:)

(also called MeV/nucleon).Mi == M (in amu) = A, and write T/A ·== T/Mi and cp/A === cp/Mi in MeV/u

In agreement with notations used in other reports we will use:

<1.5 lOfor Pbfor 20<A <214 AM<.03 AM `4

AM = O by definition for 12C (or 160) and for A = 20 and 214AM = M - A is the mass excess in amu.

Note : M expressed in amu is close to A

E0 E., Mi: 2 — 1 : 2- : BY W

E0 Eu MiT 1 T 'Y — 1 : -—· : --—

E0 Eu Mi

The related relativistic parameters are given by

29 OCR Output

have to be used. Thus

machine circumference, and tune shifts averaged around the ring (<>)The lattice function (Bb, BV, D) are strongly changing along the

a{,= ehlih + D2 of, instead of t-:h|3h (D being the dispersion function).

in a quadratic way, which becomesThe dispersion term has to be included in the horizontal beam size (ah)

Fc is a correction factor due to two effects of importance in small machines

N is the total of number of ions.

rp = 1.54 10*18m is the classical proton radius.

G and Bf are listed in table A1-1 for several typical distributions.

Bf = 1 for a coasting beam.Bf = < I >/l ratio between mean intensity and peak intensity so that

Bf is the bunching factor given by the longitudinal distribution and defined by

G is a geometrical form factor given by the shape of the uansverse disuibution.

Fi is an image factor, Fi = l for low energy machines.

41: A E@(1+,/eh /8,,) BfAQ _L1_ 21 N GEF; l V P 2

Space charge vertical detuning

Q Q. e = —A — At in eV.s/charge, which is —l-~ — times the e in eV.s/ u ‘‘

M- ATC T 4 (Q)

Sometimes one uses

ri = 4 G p

aussian distribution we approximate the total momentum sBr ad to'I`he relative momentum spread is represented by its rms value Gp = O for a

to be parabolic.At (s) is the full btmch duration - the line charge density of the bunch is supposed

=—A-At ineV.s/u1£ ;

Bunched beam (area of the bunch in (AT, At) plane)

30 OCR Output

intensity per bunch).periods (1,,,, = h 1,f), m the number of full buckets, N = mNb (N total intensity, Nbthe RMS bunch duration, h the harmonic number, 1,,,, and 1rf revolution and RFI = is the full bunch length, Atb the full bunch duration, 07 is the RMS bunch length, 0}type of real distributions (projected phase plane distributions).Table A1 .1 Transverse geometrical form factor (G) and bunching factor (Bj) for several

4 21tR 4 h T,-f

,/2,, ,,,.401 : ,/2,, BigGaussian

22,:11 3 h T,2x 2 FKT) 6/5 I 2_.m* - EEE;Parabolic

ZTCR h {rf

Uniform 1 I ml = Elgin

Distribution in real space | G

‘°Sl°°a = 20},, b = 26,, into Las1ett's formula). Then G = 1 and AQ, = 2 AQi,the detuning in the center of a beam with a uniform projected distribution (insertingthe center of a Gaussian beam. Frequently the expression "Laslett tune shift" is used for

In the body of this report, we use G = 2, thus refering to the tune shift (AQ) in

1+ Bheh + D‘o/ [$,,:2,,g)F _

1+ ,/eh /e,,

3 1 OCR Output

[23].theory for various gas compositions, including the case where hydrogen predominates

Recent measurements at the GSl—S1S on Au53"‘ show a good agreement with

than predicted by the formula.which consisted of 90% H2, the measured beam lifetime was longer by a factor of 7-10results of which are detailed in table A2·2. For the residual gas composition of LEAR

Similar conclusions can be drawn from the oxygen storage test [22] in LEAR,

formula with measured values extracted from literature.Table A2-1 Comparison of total charge exchange cross section from F ranzke’s

1.lOE-164.7 Pb54+ 2.20E-16 2.0

2.40E-18 7.00E-18 2.98.4 Ar18+

1.70E- 17 5.7Arl7+ 3.00E-188.4

l. 10E-16 0.9Pb54+ 1.00E- 164.7

1.22.40E-17 2.80E-1710.0 U63+

5.70E·17 1.8Pb55+ 3.10E-175.9

2.90E-17 2.40E-17 0.85.9 Pb40+

1.4Pb54+ 7.00E-17 1 .0OE- 164.7

1.16.00E—17 6.30E- 17Pb54+4.7

1.20E-18 1.30E- 17 10.8Pb54+4.7

7.75.20E-19 4.00E-18U63+10.0

1.11 .30E-18 1.40E-18U40+7.8

1.60E-17 26.76.00E-194.7 Pb59+

6.10E-19 1.50E-17 24.64.7 Pb58+

1.50E-17 22.16.80E·l94.7 Pb57+

6.9OE-19 1.40E-17 20.3Pb56+4.7

1.40E-17 21.96.40E-19Pb5 5+4.7

20.01.30E- 176.50E·19Pb54+4.7

19.41.30E- 176.70E—l9Pb53+4.7

17.51.20E-176.85E-194.7 Pb52+

13.37.50E-19 1.00E-17Pb5 1+4.7

20.05.005-20 1.00E-18Ar17+8.4

T (MeV/U)

¤1¤u1a¤1Im1c/measEnergy|Ion|Target|n®¤·edBeam and target conditions | Total sigma for charge exchange

omparison of Franzke's formula with measurements

factor up to 15-20.whereas for light gases like Hg the formula tends to overestimate the cross section by aMeV/u. One concludes that the agreement is satisfactory for gases like N2 or heavierare compared with the results of Franzke's formula for energies ranging from 4.7 to 10

In table A2-1 the total cross sections for different ions and targets (residual gas)

Comparison of Franzke‘s formula with measurements.

APPENDIX 2

32 OCR Output

06+ and 08+ Storage in LEAR [20].F ranzke ’s formula and corresponding beam Metime as calculated and measured during

Table A2·2 : Residual gas composition, charge exchange cross sections from

sigc Fr¤ me-20I 1.sE-1<> I 4.4s-19 I sts-to I sae-10 I me-Ia

Element H1.1 I Hem I c¢,12 I N7,14 I oa.1c> I AnaA0

Cross sections oer atom used above

meas/calc I 7.4memured I 36000 Isec

Ltletime: calculated I 4837.4 Isec

Sum->I 2.1 E-045.8 5-12Total

1.8 E-062.2 E-021.3 5-188.0 5-15

4.3 E-052.2 E-021.0 E-182.4 5-13N2

1.9 E-052.2 5-027.3 5-191.5 5-13H20

4.6 5-062.2 E-027.3 5-193.6 5-14CH4

2.2 5-02 8.5 E-071.5 E-19He 3.3 E-14

1.4 5-042.2 E-W1.5 5-195.3 5-12H2

(sec/\-1)(torr) (cm/\2)

total capture/lossl 1 /tauMolecule I Pressure

Resldud Ga Cross-sectlon/ moleculeldecay const.

Franzl<e‘s formulaMeasured

Beta 0.1557

Ener 11.5 IMeV/ugglualion al LEAR 08+ experiment

sic/sigl 0.022 I 0.022 I 0.022 I 0.022 I 0.022 I 0.022sig?. Frc 2.8 E~18 I 5.65-18 I 1.7 E—l7 I 2.0 E—l7 I 2.2 E-17 I 4.7 E-17Element gl Q ,| He12 I C6,l2 I N7,14 I 08,16 I Ar18AO

Cross sections per atom used above

meas/calc I 9.4mexured I 1500 Isec

l]1Hi@ calculated I 158.9 Isec

Sum—>| 6.3 5-035.8 5-12Total

5.3 5—052.2 E-M4.7 E-178.0 E-15

1.3 5-032.2 E-024.0 E-172.4 5-13N2

5.8 E-O42.2 E-O21.5 E-I3 2.8 E-17

2.2 E-02 1.4 E-043.6 E-I4 2.8 E·17CH4

2.6 E-052.2 E-025.6 5-183.3 E·I4H•

4.2 E-032.2 E-025.3 E-I2 5.6 E-18

(sec/\-U(torr) (cm/\2)

.tota| capture/howl 1/tauMolecule I Pressure

Rasldud Ga grass-sectiam moleculeldecay const.Fran zke‘s formulaMeasured

0.1237Betc7.2 |MeV/u

Evcluction of ILEAR 06+ experimcnt

33 OCR Output

Science, Vol. NS—24, No.3, June 1977, p. 1390.

the 1977 Particle Accelerator Conference, IEEE Transactions on Nuclear.Efficiency in A.G. Synchrotrons by Means of Skew Quadrupoles, Proceedings of

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34 OCR Output

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