CARE-HHH APD BEAM’07

Optics considerations for PS2

W. Bartmann, M. Benedikt, C. Carli, B. Goddard, S. Hancock, J.M. Jowett, A. Koschik, Y. Papaphilippou October 4 th , 2007

Outline

     

Motivation and design constraints for PS2 FODO lattice Doublet/Triplet Flexible (Negative) Momentum Compaction modules

 High-filling factor design  Tunability and optics’ parameter space scan

PS2-SPS transfer line optics design Summary and perspectives

Y.P. - 4/10/2007 Optics Considerations for the PS2 2

Motivation – LHC injectors’ upgrade

 Upgrade injector complex.

R. Garoby, BEAM’ 07

 Higher injection energy in the SPS => better SPS performance  Higher reliability

Present accelerators Future accelerators Linac2 50 MeV 160 MeV Linac4 1.4 GeV 4 GeV 26 GeV 50 GeV PSB PS (LP)SPL PS2 (LP)SPL:

(Low Power) Superconducting Proton Linac (4-5 GeV)

PS2: High Energy PS (~ 5 to 50 GeV – 0.3 Hz) SPS+:

Superconducting SPS (50 to1000 GeV)

SLHC

: “Super-luminosity” LHC (up to 10 35 cm -2 s -1 )

DLHC

: “Double energy” LHC (1 to ~14 TeV)

SPS 450 GeV 1 TeV SPS+ LHC / SLHC 7 TeV ~ 14 TeV DLHC

3

  

Design and optics constraints for PS2 ring

Replace the ageing PS and improve options for physics Integration in existing CERN accelerator complex Versatile machine:   Many different beams and bunch patterns Protons and ions

Basic beam parameters PS2

(~0.2) Constrained by incoherent space-charge tune-shift Injection energy kinetic (GeV) 4 Improve SPS performance Extraction energy kinetic (GeV) Circumference (m) Transition energy Maximum bending field Maximum quadrupole gradient [T/m] Maximum beta functions [m] Maximum dispersion function [m] Minimum drift space for dipoles [m] ~ 50 1346 ~10/10i 1.8

17 60 6 0.5

Analysis of possible bunch patterns: C PS2 = (15/77) C SPS Longitudinal aspects Normal conducting magnets Aperture considerations for high intensity SPS physics beam Space considerations Y.P. - 4/10/2007 4

Layout

PS2 PSB     Racetrack: Integration into existing/planned complex:    Beam injected from SPL Short transfer to SPS Ions from existing complex All transfer channels in one straight Minimum number of D suppressors   High bending filling factor Required to reach 50GeV Y.P. - 4/10/2007 Optics Considerations for the PS2 SPL Linac4 PS 5

FODO Lattice

 Conventional Approach:  FODO with missing dipole for dispersion suppression in straights  7 LSS cells, 22 asymmetric FODO arc cells, 2 dipoles per half cell, 2 quadrupole families   Phase advance of 88

o

, γ tr of 11.4 7 cells/straight and 22 cells/arc -> in total 58 cells   Q H,V = 14.1-14.9 Alternative design with matching section and increased number of quadrupole families Y.P. - 4/10/2007 Optics Considerations for the PS2 6

Dispersion suppressor and straight section

Cell length [m] Dipole length [m] Quadrupole length [m] LSS [m] Free drift [m] # arc cells # LSS cells: # dipoles: # quadrupoles: # dipoles/half cell: 23.21

3.79

1.49

324.99

10.12

22 7 168 116 Extraction 2 Fast Injection H -Injection MTEBK MS2 MS1 Y.P. - 4/10/2007 ES MTEBK BD DuK ExtK InjK 7 cells Optics Considerations for the PS2 InjS H 0 S H InjS 7

Doublet and Triplet arc cells



y



y

10

D x

10

D x



x



x

  Advantages  Long straight sections and small maximum ß’s in bending magnets (especially for triplet) Disadvantage  High focusing gradients Y.P. - 4/10/2007 Optics Considerations for the PS2 8

Flexible Momentum Compaction Modules

 Aim at negative momentum compaction   Similar to and inspired from existing modules (e.g. J-PARC, many studies) First approach (one module made of three FODOs):  Match regular FODO to 90 o phase advance   Reduced central straight section without bends, re-matched to obtain phase advance (close to three times that of the FODO, i.e. 270 o ) Disadvantage: Maximum vertical β above

80m



x



y

10

D x



y



x

10

D x

regular FODO 90 -> zero dispersion at beginning/end Y.P. - 4/10/2007 o /cell reduced drift in center, average 90 γ tr ~ 10i o /cell -> negative dispersion at beginning/end Optics Considerations for the PS2 9

    

FMC modules with high filling factor

Improve filling factor: four FODO per module Dispersion beating excited by “kicks” in bends Resonant behavior: total phase advance < 2π Large radii of the dispersion vector produce negative momentum compaction High phase advance is necessary ß x 5D ß y

C. Carli et al. PAC07

In red: real lattice Phase advance with shorter drifts Optics Considerations for the PS2 10 Y.P. - 4/10/2007

 

Improving the high filling factor FMC

The “high-filling” factor arc module  Phase advances of 280

o

,320

o

per module   γ t of 8.2i Four families of quads, with max. strength of 0.095m

-2

   Max. horizontal beta of

67m

and vertical of 43m Min. dispersion of -6m and maximum of 4m Chromaticities of -1.96,-1.14  Total length of

96.2m

Slightly high horizontal β and particularly long module, leaving very little space for dispersion suppressors and/or long straight sections Y.P. - 4/10/2007  Reduce further the transition energy by moving bends towards areas of negative dispersion and shorten the module Optics Considerations for the PS2 11

   

Alternative FMC module

1 FODO cell with 4 + 4 bends and an asymmetric low-beta triplet  Phase advances of 320

o

,320

o

module per       γ t of

6.2i

Five families of quads, with max. strength of 0.1m

-2

Max. beta of

58m

in both planes Min. dispersion of -8m and maximum of

6m

Chromaticities of -1.6,-1.3 Total length of

90.56m

Fifth quad family not entirely necessary Straight section in the middle can control γ t Phase advance tunable between

240 o

and 330

o

Y.P. - 4/10/2007  Main disadvantage the length of the module, giving an arc of around

510m

Optics Considerations for the PS2

560m

(5 modules + dispersion suppressors), versus for the FODO cell arc 12

 

The “short” FMC module

Remove middle straight section and reduce the number of dipoles 1 asymmetric FODO cell with 4 + 2 bends and a low-beta doublet    Phase advances of 280,260

o

module γ t of

9.4i

Five families of quads, with max. strength of 0.1m

-2

per     Max. beta of around

60m

both planes Total length of

72.84m

in Min. dispersion of -2.5m and maximum of

5m

Chromaticities of -1.1,-1.7  Considering an arc of 6 modules + 2 dispersion suppressors of similar length, the total length of the arc is around

510m

Y.P. - 4/10/2007 Optics Considerations for the PS2 13

300 

y [ o ]

290 280 270 260 330 320 310

“Tunability”

 250 220 240 260 280 300 320 340 360 380 400 420 horizontal and between 250

o



x [ o ]

Phase advance tunable between 240

o

and 320

o

and 420

o

in the in the vertical plane Y.P. - 4/10/2007 Optics Considerations for the PS2 14

Transition energy versus horizontal phase advance

30 20 10 

t

0 -10 -20

imaginary

-30 220 240 260 280 300 320 

x [ o ]

340 360 380 400 420 Y.P. - 4/10/2007 Optics Considerations for the PS2 15

Dispersion versus transition energy

30

imaginary

20 

t

10 0 -10 -20    -30 -30 -20 -10 0 

xextr

10 20 30 Almost linear dependence of momentum compaction with dispersion min/max values Higher dispersion variation for γ t closer to 0 Smaller dispersion variation for higher γ t Y.P. - 4/10/2007 Optics Considerations for the PS2 16

Transition energy versus chromaticity

30 horizontal vertical 20

imaginary

10 

t

0 -10 -20    -30 -3 -2.5

-2 -1.5

-1

Chromaticity

Higher in absolute horizontal chromaticities for smaller transition energies Vertical chromaticities between -1.8 and -2 (depending on vertical phase advance) Main challenge: design of dispersion suppressor and matching to straights Y.P. - 4/10/2007 Optics Considerations for the PS2 17

  

PS2 – SPS Transfer Line design goals

Keep it short!

Matched optics (



,

a

,D,D’

) at both ends (PS2, SPS)

2700 2600

Survey Plot CCS coordinates

TT12

~21m 

Get dispersion D function under control!

2500

PS2 SPS L cell

[m] 64

b max

[m] 110

b min

[m] 19

Match space/geometry

location of PS2) 8 requirements (Transfer Line defines   15m separation between TT10/TI2 and PS2 beam axis and same between PS2 and any other beam axis

Length limits for TT12 + tight geometry constraints!!!

2400 2300 2200 700 800 900 1000 1100 X [m] 1200

TI2

1300

SPS

~15m

1400

TT10

 Use normal conducting NC (dipole, quadrupole) magnets 

Low

 insertion for ion stripping  Emittance exchange scheme  Branch-off to experimental areas

1500

 No need for vertical bends, PS2 will be level with SPS

PS2 – SPS Transfer Line optics

SPS injection region Matching section Achromat 1 Achromat 2 PS2 extraction region PS2 LSS regular cells   Matching section (with low  insertion) near SPS 2 bending sections (opposite direction) as achromats

(D=D’=0 at each end)

Low-





Summary

Different lattice types for PS2 optics investigated

  FODO type lattice a straightforward solution  FMC lattice possible alternative   no transition crossing challenge: matching to straights with zero dispersion

Perspectives:

 Complete the lattice design including chromaticity correction and dynamic aperture evaluation  Detailed comparison based on performance with respect to beam losses  Collimation system  Non-linear dynamics  Collective effects Y.P. - 4/10/2007 Optics Considerations for the PS2 20