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
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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
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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
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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
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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
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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
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