Emittance Growth from Elliptical Beams and Offset Collision at

LHC and LRBB at RHIC

Ji Qiang

US LARP Workshop, Berkeley, April 26-28, 2006

Outline

• Strong-strong simulation of elliptical colliding beams at LHC

• Offset beam-beam interactions at LHC• Long-range beam-beam effects at RHIC

Elliptical colliding beams at LHC

• Using Dipole first with doublet focusing• Focuing is symmetric about the IP• Less magnets and lower nonlinear fields at IP• Increase of luminosity

Computational Model

• Two collision points (no parasitic collisions)

• With 0.212 mrad half crossing angle

• Linear transfer map between IPs

• Tunes (0.31, 0.32)

• Beta* (0.25, 0.25) vs. (0.462,0.135)

• One million macroparticles for each beam

• 128 x 128 x 1 for strong-strong beam-beam force calculation

RMS Emittance Growth with Round and Elliptical Colliding Beams at LHC

X elliptical

Y elliptical

Y roundX round

Offset Beam-Beam Collisions at LHC

Beam energy (TeV) 7

LHC Physical Parameters for the Beam-Beam Simulations

Protons per bunch 10.5e10

* (m) 0.5

Rms spot size (mm) 0.016

Betatron tunes (0.31,0.32)

Rms bunch length (m) 0.077

Synchrotron tune 0.0021

Momentum spread 0.111e-3

Beam-Beam Parameter 0.0034

IP1

IP5

AB

C D E

F1

2

3 4

5

6

A Schematic Plot of LHC Collision Scheme

One Turn Transfer Map

M = Ma M1 Mb M2 Mc M3 Md M4 Me M5 Mf M6

M = M6-1 Mf M6 Ma M1 Mb M1-1 M1 M2 M3 M3-1 Mc M3 Md M4 Me M4-1 M4 M5 M6

Here, Ma and Md are the transfer maps from head-on beam-beam collisions; Mb,c,e,f are maps from long-range beam-beam collisions; M1-6 are maps between collision points.

• Linear half ring transfer matrix with phase advanced:

• 90 degree phase advance between long-range collision

points and IPs• 15 parasitic collisions lumped at each long-range

collision point with 9.5 separation

p

66.292;655.312x y

RMS Emittance Growth vs. Horizontal Separation at LHC(No Parasitic Collisions)

0

0

RMS Emittance Growth vs. Horizontal Separation at LHC(With 60 lumped Parasitic Collisions)

Long-Range Beam-Beam Effects at RHIC

• Study the effects of long-range beam-beam (LRBB) at RHIC for the coming wire compensation experiment and find the maximum signal-to-noise ratio setting subject to some limits

• The effects of LRBB subject to • Separation• Tunes• Chromaticity• Sextupole nonlinearity• etc

Beam energy (GeV) 100

RHIC Physical Parameters

Protons per bunch 2e11

* (m) 1

Transverse Emittance [ mm-mrad] 15

Rms bunch length (m) 0.7

Tunes case 1 (28.68,29.69) and (28.73,29.72)

Momentum spread 0.3e-3

Tunes case 2 (28.68,29.69) and (28.68,29.69)Tunes case 3 (28.73,29.72) and (28.73,29.72)

Computational Model

•4 x 4 linear transfer map (146 linear map between sextupole)

•Sextupole nonlinearity (144 thin lens kicks)

•Self-consistent strong-strong beam-beam

•1 Million macroparticle for each beam

•128 x 128 x 1 mesh grid

Averaged Emittance Growth Rate vs. Vertical Separation

Case 3

Case 2

Case 1

Vertical Emittance Growth without/with Chromaticity

With 6x6 linear map

With 6x6 linear map + chromaticity kick

Vertical Emittance Growth without/with Sextupoles

With 6x6 linear map

With 4x4 linear map + sextupoles

Summary

• Initial simulations indicate larger emittance growth from the elliptical colliding beams than the round colliding beams at LHC

• The effects of static offset beam-beam collisions on emittance growth is weak without parasitic collisions at LHC. It can be large with the including of parasitic collisions.

• LRBB at RHIC— Significant emittance growth for beam-beam separation below 4

sigmas— Emittance growth show some dependent on the machine tunes.

For some tunes, the emittance growth shows a linear dependent on separations; Other shows nonlinear dependence. However, beyond 6 sigmas, the emittance growth is no longer sensitive to the machine tunes.

— The effects of chromaticity depends on the machine tunes and becomes weaker for larger separation.

— Stronger sextupole strength might help to improve the signal-to-noise ratio at large separation.

Future Studies

• Study of emittance growth including parasitic collisions and nonlinear longitudinal map

• Study of emittance using an updated LHC lattice parameters with distributed parasitic collision model

• LRBB at RHIC— Including both chromaticity + sextupole + LRBB in the simulation— Systematic comparison with experiment data— Wire compensation