Simulations of LHC LongRange BeamBeam Compensation

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Simulations of LHC Long-Range Beam-Beam
Compensation with DC and Pulsed Wires
U. Dorda F. Zimmermann CERN AB/ABP
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Long range beam beam interaction (LR)
LHC Nominal bunch 120 LR encounter Extreme
Pacman bunch 60 LR encounter
The nonlinear beam-beam force causes an amplitude
dependent tune-shift which leads to beam-blow up
and reduces the lifetime and limits the
luminosity of LHC
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The forces of the LR-interaction and the wire
LR force caused by the strong beam
Center of weak (studied) beam
wire
Within limits the force originating from the wire
is very similar to the LRs one.
In the weak-strong simulation model the strong
beam is assumed to stay unchanged while its
presence influences the weak (studied) beam
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Location of the compensation wires around the IP
Ip1 Ip5 The wires are positioned on both sides
104.93 m from the IPs in a region where the two
beams are separated ßw1760 m, sw0.9 mm
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• The compensation cannot work perfectly due to
• Phase advance between LR-IP and wire-position
• Force is similar but not the same (especially
  close to the wire)
• The wire cannot be positioned in the perfect
  position (9.5 sigma)
• but behind the collimators (11 s)
• Assumption round Gaussian beam
• Not all LR-IPs are at the same distance

wire
The beam-beam separation d varies from 7 to 13 s
The average phase-advance from LR-IP to wire is
2.6º
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Weak-strong simulated footprints for LHC
Long range
The linear tune shift scales with the inverse
square of the beam-beam-separation
Nominal tune
Long range Head On
Wire
Initial particles are launched on a square grid
(0-10 s)
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Long range Head On Wire
Ideal wire current
The wires compensate for the long range
interaction nearly completely
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What about adding other nonlinearities
? Example Adding one weak sextupole
The wire proves to be still effective
Corresponding x-x-phasespace
Sextupole only
LR HO
LR HO sextupole
Stable up to 25 s
Stable up to 7.5 s
Stable up to 2.5 s
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Pacman bunches
The tune spread of the extreme PACMAN bunch is
half that of the nominal one, because the former
experiences only half the number of long-range
collisions.
Pacman (extreme case)
Pacman (extreme case) Head On
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Compensation for Pacman bunches
Pacman (extreme case) HO nominal wire
Pacman (extreme case) HO adjusted wire
The adjusted wire reduces the tune spread almost
to the one of HO only.
The wire is overcompensating
The wires current needs to be adjusted to the
specific bunches in order to compensate each one
perfectly.
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Individual compensation requires pulsing of the
wire current
If pulsing is not exact it causes more trouble
than it solves e.g Jitter causes an emittance
growth
A jitter of 4mA causes a 10 emittance growth
within 20 h.
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Demands on the current supply
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Wire compensation experiment in SPS
Experiment Excite the beam with wire 1 and
compensate for it with another one further
downstream (phase advance 1º)
No excitation
Both wires on
Only wire 1 on
Within a certain tune range the 2nd wire is able
to compensate nearly completely for the first one.
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Parameter scans for the SPS
Simulated sensitivity to positioning
Optimal position
Sensitivity to the current of wire nr. 2
Experiment
Simulation
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Regions of stability
Stable regions are in blue, unstable ones in red
One wire only
Both wires
Liaponov stability-criterion Inspect the
increase of the phase-difference between two
initially close particles with time.
Small amplitude
large amplitude
0.014
0.02
0.7
3.2
Linear Detuning with amplitude, stable
Exponential growth, unstable
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• Summary
• The simulated wire compensation shows promising
  behavior
• The experiments in the SPS confirm this idea
• The simulation tends to exaggerate the effects
  and further improvement modeling the
  other nonlinearities is needed but they reproduce
  the experimental results qualitatively.
• A pulsed wire option is strongly recommended but
  the demands on the hardware are challenging.