Emittance Growth from Elliptical Beams and Offset Collision at LHC and LRBB at RHIC

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Emittance Growth from Elliptical Beams and Offset Collision at LHC and LRBB at RHIC

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Emittance Growth from Elliptical Beams and Offset Collision at LHC and LRBB at RHIC

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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

- 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 round

X round

Offset Beam-Beam Collisions at LHC

LHC Physical Parameters

for the Beam-Beam Simulations

Beam energy (TeV) 7

Protons per bunch 10.5e10

b* (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

A Schematic Plot of LHC Collision Scheme

IP5

3

4

C

D

E

2

5

B

A

F

1

6

IP1

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 M1-1M1 M2 M3

M3-1 Mc M3 Md M4 Me M4-1M4 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 s separation

RMS Emittance Growth vs. Horizontal Separation at LHC

(No Parasitic Collisions)

0 s

0.1 s

0.2 s

0.4 s

RMS Emittance Growth vs. Horizontal Separation at LHC

(With 60 lumped Parasitic Collisions)

0 s

0.1 s

0.2 s

0.4 s

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

RHIC Physical Parameters

Beam energy (GeV) 100

Protons per bunch 2e11

b* (m) 1

Transverse Emittance [ mm-mrad] 15

Momentum spread 0.3e-3

Rms bunch length (m) 0.7

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

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 1

Case 2

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

- Initialsimulations 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