Collimation Depth Calculations for ILC BDS

Frank Jackson

Latest Versions ILC-BDS

• ‘FF9’ deck available at SLAC– http://www.slac.stanford.edu/~mdw/ILC/Beam_Delivery/20050316/

• 20 mrad and 2 mrad x-ing angle schemes

• Include energy spectrometers

• Bandwidth has been optimised

• Different designs for 2 mrad extraction– SLAC-EU collaboration, under development

Collimation Depth Calculation

• SR must pass through all apertures close to IR– IP beampipe, extraction quadrupoles or the

facing final doublet

• Use semi-analytic linear calculation routine DBLT by Oliver Napoly (SACLAY)– Calculates SR fan as function of collimation

depth– Constrain the fan to pass through IR

apertures, solve for collimation depth

DBLT (O. Napoly) Assumptions and Method

• Assumes minimal 2-phase collimation– Collimators in phase and

90O out of phase with IP• Assumes mono-

energetic halo particles• Track corners of

collimated phase space at IP back through final doublet

• Use many SR emission points in final doublet

x

x’

Collimated halo phase space at IP

DBLT Solutions

• Aperture constraint satisfied by ellipse of solutions in Nx, Ny space

• A different ellipse for every SR emission point in FD

• ‘Smallest’ ellipse defines collimation depth

Possible coll. depth solutions for one emission point

Aperture

SR profiles

x

y

Nx

Ny

X marks solution for square SR profile at

apertureFor more details see 15 Oct 04 talk

http://www.astec.ac.uk/ap/collider/collimmeet05Oct04/index.html

20 mrad Collimation IssuesAperture list

http://www.slac.stanford.edu/xorg/lcd/ipbi/lcws05/maruyama_backgrounds.ppt

Component Aperture (radius, mm)

S(entrance) (wrt IP)

S(exit)

(wrt IP)

IP 12 -0.06 0.06

QFEX1A 12 3.51 5.71

QFEX1B 17 6.01 7.72

QFEX1C 24 8.02 9.73

QDEX2A 30 10.03 11.50

QDEX2B 43 13.25 16.72

QDEX2C 43 17.03 20.51

QFEX3A 43 20.81 24.08

QFEX3B 46 24.38 27.66

QFEX3C 58 27.96 31.23

Last extraction quad is at 47m from IP, 71 mm aperture.

20 mrad Collimation Issues

• Extraction quads extend to ~50m from IP.• How far from IP should SR cleanly pass?

– Don’t have good feeling for background effects/back scattering

• For depth calculation choose 3 apertures for SR clearance– VTX beampipe at IP– QFEX1A exit (12mm, 5.71 m from IP)– QFEX1C exit (24mm, 9.73 m from IP)

20 mrad Collimation Solutions

VTX beampipe QFEX1A exit QFEX1C exit

QFEX1A exit solution Nx = 8.82 x Ny= 68.89 y

Compare with estimation by optics rescaling from NLC (A. Drozhdin), Nx = 8 x Ny = 57 y

Corresponds to spoiler gaps of ax = 1mm, ay = 0.5 mm

20 mrad SR Fan Envelope• Plot SR fan

envelope for 8.82x x 68.89y collimated halo

• Demonstrates SR clearance of constraining aperture

• Rays are not straight lines in r vs. s space!

FD VTX QFEX1-5

• Now non-symmetrical problem

• SR fan passes through one or more non-symmetrical apertures, then will hit beam pipe eventually

2mrad Collimation Depth

QD0

SR fan centroid

IP

QD0

Extracted Beam

2mrad Extraction (Daresbury/Orsay) 500 GeV

• What collimation depth to clear QD exit?

• Treat as symmetric problem and constrain SR fan with 22 mm symmetrical aperture – to do

QD

QD

1.6 mrad

5.4 m

8.8mm

31 mm

Distance of closest approach ~ 22 mm

Ignore everything afterwards

SR fan centroid

Other Issues

• SR from last bend before final focus may also constrain coll. depth

• Have been ignoring effect of local chromaticity correction sextupole

• Have been ignoring energy spread of beam halo

Conclusion and Future Work

• DBLT gives quick evaluation of collimation depth– Can use as first approximation for spoiler gaps

• Fine tuning of collimation depth requires simulation– For example, BDSIM cross check of DBLT

incorporating halo energy spread

• Broader collimation questions– Collimation performance of whole lattice

(STRUCT/BDSIM) – Machine protection issues