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.

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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

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

Ji Qiang

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


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

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

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


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

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


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

RMS Emittance Growth with Round and Elliptical Colliding Beams at LHC

X elliptical

Y elliptical

Y round

X round


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

Offset Beam-Beam Collisions at LHC


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

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


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

A Schematic Plot of LHC Collision Scheme

IP5

3

4

C

D

E

2

5

B

A

F

1

6

IP1


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

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


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

RMS Emittance Growth vs. Horizontal Separation at LHC

(No Parasitic Collisions)

0 s

0.1 s

0.2 s

0.4 s


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

RMS Emittance Growth vs. Horizontal Separation at LHC

(With 60 lumped Parasitic Collisions)

0 s

0.1 s

0.2 s

0.4 s


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

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


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

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)


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

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


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

Averaged Emittance Growth Rate vs. Vertical Separation

Case 3

Case 1

Case 2


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

Vertical Emittance Growth without/with Chromaticity

With 6x6 linear map

With 6x6 linear map + chromaticity kick


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

Vertical Emittance Growth without/with Sextupoles

With 6x6 linear map

With 4x4 linear map + sextupoles


Summary

Summary

  • 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.


Emittance growth from elliptical beams and offset collision at lhc and lrbb at rhic

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


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