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

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 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


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.


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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