1

Initial Beam-Beam studies

January 20, 2014

2

Contents

• The beam-beam code and the two parameter sets used.

• The beam-beam effects on the phase space of the proton beam.

• Effects of shifting the waist of the beam.• Effects on the spent beams.• Effects on the phase space of the spent

electron beam.

3

Beam code and Parameters• The code in use is Guinea pig, two versions are

used for the different simulations, the C version, guinea 1.4.4 and the c++ version guinea_pig++

Value Nominal Parameters

High Luminosity

Particle number (ion/electron) 1010 17/0.3 22/0.2

β* ion mm 100 50

β* electron mm 120 32

ϵx,y ion mm mr 3.75 2

ϵx,y electron mm mr 50 50

4

Transverse EffectsNominal High Luminosity

5

Longitudinal Effects

Nominal High Luminosity

6

Longitudinal Effects

7

Luminosity Measurements with Offsets

Nominal Parameters High Luminosity

Lum

inos

ity m

-2s-1

Horizontal Offset x/σ Horizontal Offset x/σ

Lum

inos

ity m

-2s-1

8

Angles With Offsets (Protons)

Horizontal Offset x/σ Horizontal Offset x/σ

Mea

n An

gle

μr

Mea

n An

gle

μr

9

Angles With Offsets (Electrons)

Horizontal Offset x/σ Horizontal Offset x/σM

ean

Angl

e μr

Mea

n An

gle

μr

10

Trajectories with offsetsNominal Parameters High Luminosity

Head-on

1σ offset

11

Luminosity Measurements with TrackingLu

min

osity

m-2

s-1

Turns x10Turns x10

Lum

inos

ity m

-2s-1

Turns x10 Turns x10

Nominal Parameters High Luminosity

12

Induce an instability

Attempt to induce instability in recirculating proton beam by matching the electron beam to always hit with a set offset at the same section of the beam, based on the horizontal tune.

13

Induced Instability

• Red= nominal without longitudinal motion• Green=nominal with longitudinal motion• Blue=HL without longitudinal motion• Purple=HL with longitudinal motion

Turn

Horiz

onta

l Pos

ition

m

14

Induced Instability (cont’d)

Red lines indicate no longitudinal motion, green lines indicate longitudinal motion

Nominal Parameters High Luminosity

Turn Turn

Nor

mal

ized

Emitt

ance

Nor

mal

ized

Emitt

ance

15

Waist ShiftsNominal Parameters High Luminosity

1.1% increase 18.7% increase

16

Waist Shifts Combined with OffsetsNominal Parameters High Luminosity

Wai

st S

hift

Wai

st S

hift

Offset Offset

17

Trajectories with offsets and waist shiftNominal Parameters High Luminosity

Head-on

1σ offset

30,000 μm

18

Spent Electron BeamNominal Parameters High Luminosity

Red particles show the beam without beam-beam effects, green particles show the electron beam with beam-beam effects.

19

Spent Electron Beam (At Max Luminosity Waist Shift 0.6 σz)

Nominal Parameters High Luminosity

Red particles show the beam without beam-beam effects, green particles show the electron beam with beam-beam effects.

20

Conclusions

• The beam beam effects on the ion beam are rather small

• The beam beam effects on the electron beam are quite large

• The effects on the spent beam are of particular importance in the high luminosity parameter set

• Could have a nonlinear response to offsets

21

Backup 1

22

Backup 2

Horizontal Offset x/σ Horizontal Offset x/σ

STDE

V An

gle

μr

STDE

V An

gle

μr

23

Backup 3

Horizontal Offset x/σ Horizontal Offset x/σ

STDE

V An

gle

μr

STDE

V An

gle

μr