Analysis of beam-beam Analysis of beam-beam diffusion effects in RHIC and diffusion effects in RHIC and

the LHC the LHC

V. Ranjbar and T. Sen, FNALV. Ranjbar and T. Sen, FNAL

MotivationsMotivations To better understand the impact of beam-beam and to settle on To better understand the impact of beam-beam and to settle on

optics and compensation methods to minimize its negative effect in optics and compensation methods to minimize its negative effect in the LHCthe LHC

RHIC is a good test bed for the LHC as a result there are plans to RHIC is a good test bed for the LHC as a result there are plans to install a wire compensation scheme in RHIC and to benchmark install a wire compensation scheme in RHIC and to benchmark simulation codes against beam-beam experiments in RHIC.simulation codes against beam-beam experiments in RHIC.

There is now an effort underway to bring beam-beam modeling There is now an effort underway to bring beam-beam modeling results closer to experimental. However modeling beam-beam results closer to experimental. However modeling beam-beam effects in a realistic way including higher order fields can very effects in a realistic way including higher order fields can very computationally intensive using standard lifetime tracking methods. computationally intensive using standard lifetime tracking methods. Another approach is to consider Diffusion Coefficients as various initial Another approach is to consider Diffusion Coefficients as various initial

particle distributions. particle distributions. This approach coupled with the Fokker-Planck diffusion equation can This approach coupled with the Fokker-Planck diffusion equation can

provide lifetime estimates much faster however there are limits to the provide lifetime estimates much faster however there are limits to the validity of this approach. validity of this approach.

Validity of Diffusion DescriptionValidity of Diffusion Description

We assume a radomized phase or nearly random.We assume a radomized phase or nearly random. No global Chaos No global Chaos We require that the evolution of the distribution be We require that the evolution of the distribution be

described in terms of a Markov process in the Action.described in terms of a Markov process in the Action. Also if the system is Hamiltonian we can equate the Also if the system is Hamiltonian we can equate the

frictional and diffusion coefficients in the Fokker-Planck frictional and diffusion coefficients in the Fokker-Planck equation.[1]equation.[1]

Estimating beam lifetime from Estimating beam lifetime from Diffusion Coefficients Diffusion Coefficients

The approach is to first calculate the Diffusion The approach is to first calculate the Diffusion Coefficient as a function of Action D(J). This can be Coefficient as a function of Action D(J). This can be done by tracking a small number of particles at done by tracking a small number of particles at various actions and using:various actions and using:

To estimate the Diffusion at each Action.To estimate the Diffusion at each Action. Using the fit to the Diffusion an escape time can be Using the fit to the Diffusion an escape time can be

calculated using:calculated using:

Where Ja is the action at the aperture (we use 10sigma) Where Ja is the action at the aperture (we use 10sigma)

this provides a estimate of the lifetime. This is what this provides a estimate of the lifetime. This is what we present today. Of course ideally the FP equation we present today. Of course ideally the FP equation should be numerically integrated.should be numerically integrated.

dJJD

Jt

Ja

esc 0 )(

Preliminary lifetime Calculation using Diffusion Preliminary lifetime Calculation using Diffusion versus direct Lifetime tracking in RHICversus direct Lifetime tracking in RHIC

Relative Lifetime Calculations for Qx=0.68

0.00E+00

5.00E+00

1.00E+01

1.50E+01

2.00E+01

2.50E+01

0 2 4 6 8 10 12

Sigma beam Seperation

Rel

ativ

e L

ifet

ime

Lifetime from Tracking

Lifetime from Diffusion

RHIC Experiments and SimulationsRHIC Experiments and Simulations

Several experiments were Several experiments were conducted at collision energy in conducted at collision energy in RHIC RHIC April 5April 5thth – 1 bunch per beam, – 1 bunch per beam,

interaction at nominal locationinteraction at nominal location April 12April 12thth – 1 bunch per beam, – 1 bunch per beam,

interaction at IP6interaction at IP6 May 3May 3rdrd - ~10 bunches per beam, - ~10 bunches per beam,

interaction at nominal locationinteraction at nominal location May 24May 24thth - ~10 bunches per beam, - ~10 bunches per beam,

interaction at nominal location, interaction at nominal location, tune scan. Octupoles used to tune scan. Octupoles used to increase nonlinearities.increase nonlinearities.

May 30May 30thth - ~10 bunches per beam, - ~10 bunches per beam, interaction at nominal location, interaction at nominal location, operate near 0.75. Octupoles on. operate near 0.75. Octupoles on.

We consider the May 3We consider the May 3rdrd since since setup most closely resembles setup most closely resembles simulations.simulations.

Qx,QyQx,Qy (0.69,0.68)(0.69,0.68)

(0.72,0.73)(0.72,0.73)

Qx’,Qy’Qx’,Qy’ 2,22,2

B.B. ParB.B. Par 9.77E-39.77E-3

rms bunch rms bunch lengthlength

2 nsec2 nsec

x x , , yy 1515 mm-mrad mm-mrad

IntensityIntensity 2 – 1.5E+112 – 1.5E+11

rms momentum rms momentum deviationdeviation

3.11E-43.11E-4

RHIC resonance linesRHIC resonance lines

Tune footprints with sextupoles and single parasitic interaction at (1) 3 separation, (2) 10 separation. Blue beam base tunes = (0.68, 0.69). The closest resonances are the 3rd, 6th and 10th order resonances but the footprint is clear of these resonances at both separations.

10th Order

3rd and 6th Order

4 Sig

2 Sig

May 3rd Experiment Moving Yellow beam Q= .69,.70

BTF done at 4 Sig separation Qx=.0.6917, max= 8.313, Qy = .6964, max=209

BTF done at 2 sigma Qx= .6905, max= 8.34, Qy=.6959, max = 330.84- Qx went down by 1.2E-3 and Qy by 0.5E-3.- Power went up by 8 units in vertical and .5 in horizontal

0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

1.20E-01

1.40E-01

1.60E-01

1.80E-01

2.00E-01

0.25 0.27 0.29 0.31 0.33 0.35

X Sig2

Y Sig 2

X Sig4

Y Sig4

Simulated Results show change in tune of 10^-3 downAnd increase in vertical signal and decrease in horizontal signal

Loss Rate vs Beam seperationLoss Rate vs Beam seperation

Relative Lifetime Calculations for Qx=0.68

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

6.00E+00

0 2 4 6 8 10 12

Sigma beam Seperation

Rel

ativ

e L

ifet

ime

Lifetime from Tracking

1/Loss Rate

Conclusions from RHIC Conclusions from RHIC ExperimentsExperiments

Tunes:Tunes: BBSIM simulations show that both the vertical and horizontal tunes in the blue beam move BBSIM simulations show that both the vertical and horizontal tunes in the blue beam move

down by about 0.001 when the separation is decreased from 4 to 2 sigma by moving the down by about 0.001 when the separation is decreased from 4 to 2 sigma by moving the yellow beam. yellow beam. Observations: Measuring from 4. sigma to 2. sigma the horizontal tunes went down by Observations: Measuring from 4. sigma to 2. sigma the horizontal tunes went down by 0.0005 and the vertical tunes went down by 0.0012. In the horizontal plane the measured 0.0005 and the vertical tunes went down by 0.0012. In the horizontal plane the measured tune variation was probably within error of the tune measurement since measurements tune variation was probably within error of the tune measurement since measurements made at intermediate sigma separations yielded lower tune measurements. made at intermediate sigma separations yielded lower tune measurements. The magnitude and direction of the tune change agreed with BBSIM predictions in the The magnitude and direction of the tune change agreed with BBSIM predictions in the vertical plane. vertical plane.

Power in the Tune signalPower in the Tune signal BBSIM finds the power halves in the horizontal plane while the power doubles in the vertical BBSIM finds the power halves in the horizontal plane while the power doubles in the vertical

plane again when the vertical separation is reduced from 4 to 2 sigma. plane again when the vertical separation is reduced from 4 to 2 sigma. Observations: The peak power in the horizontal plane went up from 7.66 to 8.23 and the Observations: The peak power in the horizontal plane went up from 7.66 to 8.23 and the peak power in the vertical plane went up from 245 to 253. The power in the horizontal plane peak power in the vertical plane went up from 245 to 253. The power in the horizontal plane went in the opposite direction predicted by BBSIM. The power in the vertical plane matches went in the opposite direction predicted by BBSIM. The power in the vertical plane matches the direction of BBSIM prediction but not the size (assuming the BTF units are linear). the direction of BBSIM prediction but not the size (assuming the BTF units are linear). However here again the power fluctuated at each measurement while moving the yellow However here again the power fluctuated at each measurement while moving the yellow beam from 4 to 2. sigma, reaching a maximum of 330 at 2.8 sigma.beam from 4 to 2. sigma, reaching a maximum of 330 at 2.8 sigma.

Experimental Lifetime Estimates:Experimental Lifetime Estimates: Problematic since there was not enough time to sit and fit a lifetime cure at each separation. Problematic since there was not enough time to sit and fit a lifetime cure at each separation.

However we do have max loss rates which should correlate with lifetimes.However we do have max loss rates which should correlate with lifetimes.

LHC Simulations and Estimations LHC Simulations and Estimations of Diffusionof Diffusion

Consider Several Consider Several Optics optionsOptics options Baseline Baseline 64 LR BB 64 LR BB Quad 1Quad 1st st 64 LR BB 64 LR BB Dipole 1Dipole 1stst Interaction Interaction

32 LR BB 32 LR BB

LHC InjectionLHC Injection LHC FlattopLHC Flattop

Energy (GeV)Energy (GeV) 450450 70007000

Revolution Revolution Frequency Frequency (kHz)(kHz)

11.245 11.245

Synchrotron Synchrotron Frequency Frequency (Hz)(Hz)

61.861.8 21.421.4

rms bunch rms bunch length (nsec)length (nsec)

.37.37 .25.25

EmittanceEmittance 22.5 pi22.5 pi

Bunch Bunch IntensityIntensity

1e111e11

BB. ParBB. Par 3.4E-33.4E-3

TuneTune .31, .32.31, .32

Tune footprints for Optics optionsTune footprints for Optics options

ConclusionConclusion

Results from experiments in RHIC show some Results from experiments in RHIC show some agreement with BBSIM simulationsagreement with BBSIM simulations

Diffusion approach is a good first estimate of the Diffusion approach is a good first estimate of the impact of beam-beam effectsimpact of beam-beam effects There maybe be some promise in extracting lifetimes There maybe be some promise in extracting lifetimes

using this approach, however more work needs to be using this approach, however more work needs to be done in this vein done in this vein

Results from LHC simulations show clearly the Results from LHC simulations show clearly the negative impact due to beam-beam effects with the negative impact due to beam-beam effects with the Quad 1Quad 1stst option. option.

However a Dipole 1However a Dipole 1stst option in some instance maybe option in some instance maybe better than the Baseline.better than the Baseline.

[1] . A. J. Lichtenberg and M. A. Lieberman, “Regular and Stochastic Motion”, Springer-Verlag 1983