# Presentation: 677436

## 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

**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

- 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

- A

- B

- C

- D

- E

- F

- 1

- 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

## RMS Emittance Growth vs. Horizontal Separation at LHC

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

- 0 
- 
- 
- 

## RMS Emittance Growth vs. Horizontal Separation at LHC

- 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

##        RHIC Physical Parameters

- 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

**Averaged Emittance Growth Rate vs. Vertical Separation**

- Case 3

- Case 2

- Case 1

## Vertical Emittance Growth without/with Chromaticity

**Vertical Emittance Growth without/with Chromaticity**

- With 6x6 linear map

- With 6x6 linear map + chromaticity kick

## Vertical Emittance Growth without/with Sextupoles

**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