October 1, 2004 1

Beam beam simulation

S.Isaacman, A.Long,E.Pueschel,D.Rubin

October 1, 2004 2

Weak-strong simulation

- Strong beam is fixed - Weak beam consists of N macro particles. - Track weak beam macro-particles through lattice

• Guide field includes all magnetic elements• Third order map for wigglers• RF cavities• Synchrotron radiation damping and excitation• Beam beam elements at each of parasitic crossing points and at IP• Beam beam element is 2-d. Represent longitudinal extent of strong bunch at IP with 2-d slices

October 1, 2004 3

Single beam scan

Before/after sextupole optimization toMinimize energy dependence of beta …

October 1, 2004 4

Weak-strong simulation

- RationaleIn CESR, nonlinearities associated with wigglers, pretzel,

multiple parasitic crossings, impose the beambeam current limit

Conjecture - Coherent beam beam effects do not contribute because the threshold is even higher

October 1, 2004 5

Simulation Initialization

SpecifyHorizontal, vertical, synchrotron tunesBunch currentBunch pattern

Long range beam beam ineractions- Identify locations of parasitic crossings- Split elements at pc’s- Reverse separator polarities and compute closed orbit, twiss parameters of strong beam-Insert beambeam element at splits using coordinates of closed orbit to set x,y offset, and twiss parameters and emittance to set beam size

Beam beam interaction at IP - Compute orientation and profile of strong beam at IP (depends on beta*, coupling parameters, emittances) - Insert beam beam element and set offsets, and sizes

October 1, 2004 6

Collision assurance

Strong beamThere is no symmetry to ensure that the closed orbit at IP is zero and in general it is not - Imperfect closure of L3 vertical separation bump - lattice/ pretzel asymmetry - field errors

Weak beam Closed orbit depends on current in strong beam And bunch pattern - parasitic crossings

7

Collide Beams

Close pretzel- Adjust voltage of separators 8E/8W (pretzing 13) to zero differential horizontal offset at IP For each voltage setting

• Update closed orbit for strong beam• reset offsets for beambeam elements for parasitic crossings• Compute closed orbit for weak beam

Close vertical - Adjust vertical phase advance between vertical separators and vertical separator voltage asymmetry to zero differential vertical offset and angle at IP

• Update strong beam closed orbit and beambeam element offsets

Set tunes - Qtune (arc quads) to specified horizontal and vertical tunes. - Cavity voltage -> synchrotron tune

Repeat

October 1, 2004 8

BEAMBEAM_SCAN: Initially Qx = 0.528012985254068 Qy = 0.579040001964802 Closed orbit 0.2793E-03 -0.3422E-02 0.2171E-05 -0.1985E-03-------------------------------------------------------------

BEAMBEAM_SCAN: After parasitic interactions added 2.0mA/bunch Qx = 0.516058248861953 Qy = 0.589267022102283 Closed orbit 0.2587E-03 -0.3285E-02 0.1570E-05 -0.1663E-03

Strong beam: sigma_x = 0.3976E-03 sigma_y = 0.4613E-05 sigma_z = 0.1202E-01 Pitch : x= 0.3720E-02 y= 0.6893E-03 Offset : x= -0.8405E-03 y= -0.2156E-05 Tilt = -0.2317E-03

BEAMBEAM_SCAN: After beambeam added 2.0mA/bunchQx = 0.511007131744029 Qy = 0.589754109234780 Closed orbit 0.2597E-03 -0.3258E-02 0.1577E-05 -0.1665E-03

9

close_pretzel: 0 8W(mr) = 0.202 8E(mr) = -0.297 dx,dxp,dy,dyp (mm) = -1.0900 6.9724 -0.0038 0.8493 1 8W(mr) = 0.311 8E(mr) = -0.188 dx,dxp,dy,dyp (mm) = -1.0900 6.9724 -0.0038 0.8493 2 8W(mr) = 0.310 8E(mr) = -0.188 dx,dxp,dy,dyp (mm) = 0.0027 6.9600 -0.0041 -0.0027 Qx = 0.5323 Qy = 0.6061 Qz = -0.0980

CLOSE_VERT 0 48W(mr) =-1.185 48E(mr) =-1.185 dx,dxp,dy,dyp (mm) = 0.0000 6.9597 -0.0041 -0.0006 1 48W(mr) =-1.184 48E(mr) =-1.186 dx,dxp,dy,dyp (mm) = -0.0001 6.9564 0.0001 0.0102 2 48W(mr) =-1.184 48E(mr) =-1.186 dx,dxp,dy,dyp (mm) = -0.0001 6.9565 0.0000 0.0000

Qx = 0.5323 Qy = 0.6063 Qz = -0.0980 Closed orbit -0.2920E-03 -0.3259E-02 -0.2679E-06 0.2583E-03 BEAMBEAM: turn off beam beam at IP

Qtune with pretzel and vert closed but beam beam at IP off: Qx = 0.5161 Qy = 0.5891 Qz = -0.0980 CLOSE_VERT: 0 48W(mr) =-1.184 48E(mr) =-1.186 dx,dxp,dy,dyp (mm) = -0.0007 6.9809 0.0002 -0.0052 1 48W(mr) =-1.184 48E(mr) =-1.186 dx,dxp,dy,dyp (mm) = -0.0007 6.9811 0.0000 0.0000

qtune to Qx = 0.5161 Qy = 0.5891 Qz = -0.0980

Turn Beambeam on Qx = 0.529667621152411 Qy = 0.608165434304978 dx,dxp,dy,dyp (mm) = -0.0008 6.9816 -0.0001 0.0053

October 1, 2004 10

Generate weak beam distribution

- Calculate equilibrium normal mode emittances - Generate random distribution in “horizontal”, “vertical” and longitudinal phase space - Transform to lab coordinates - Shift centroid of distribution to coordinates of closed orbit at IP - Tilt distribution to match angles of closed orbit

October 1, 2004 11

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Track weak beam macro particles

- Track through guide field that now includes beambeam elements at parasitic crossings and at IP - Particles do not communicate with each other

Every N turns (~500)

- Luminosity•Calculate luminosity

- Update size of strong beam•Fit gaussians to x-y-z distribution of weak beam•Set size of strong beam to match weak beam

- Is the distribution of the weak beam gaussian?

October 1, 2004 13

Distribution after200,000 turnsIb=1.25mA

October 1, 2004 14

χ2 vs turnFor fitted gaussian toweak beam distribution

-> weak beam remains gaussian

October 1, 2004 15

Convergence in ~ 10 Damping times (200,000 turns)

200k turns 1000k turns

October 1, 2004 16

Dependence on number of macro-particles in weak beam

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Parallel processing

After weak beam distribution is generated, track particles on independent nodes Every N (500) turns send particle coordinates back to central processor

Linux clusters in use CHESS - Sirius, Feynmann (

October 1, 2004 20

Tune scan200 particles200k turns 1.5mA 9X4

equilibrating strong beam

October 1, 2004 21

D266.200422-sep-048X4, 1.89GeV

200 particles200k turns 9X4

October 1, 2004 22

October 1, 2004 23

5.3GeV9X4

D062.2001

Red - equilibratingStrong beam size

Green - fixed strong beam0.5% emittance coupling

October 1, 2004 24

1.89GeV200k turns200 particles

Red -Skew errors from9-sep-27 characterization

Green - No skew errors

October 1, 2004 25

Efffect of parasitic crossings1.89GeV

Single bunch

9X4

October 1, 2004 26

Summary - Status

-Measured vs calculated tunes Is relevant tune with/without parasitic interactions? How does it depend on current?-Number of macro particles in weak beam More macro particles -> higher luminosity Perhaps 200 is not enough to identify 3 gaussian distributions-How to introduce emittance coupling without prejudice?

-Contintue investigation of effect of long range interactions

Use tune scan to find operating point and compare with measurements To date weak beam bunch 1. Is there some bunch dependence?

-Simulate head on conditions and compare with measurements

- Tune simulation - Any/all lattice parameters/groups can be tuned

- More computers?

October 1, 2004 27

CESR-c

Electrostatically separatedelectron-positron orbitsaccomodate counterrotating trains

Electrons and positrons collidewith ±~3 mrad horizontalcrossing angle

9 5-bunch trains in each beam(768m circumference) Beam

October 1, 2004 28

Open squares are calculation

Red points are data

October 1, 2004 29