Beam beam simulations with disruption (work in progress...)

1
Beam beam simulations with disruption(work in
progress...)

• M.E.Biagini
• SuperB-Factory Workshop
• Frascati, Nov. 11th, 2005

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Beam-beam

• Beam-beam interaction in a linear collider is
  basically the same Coulomb interaction as in a
  storage ring collider. But
• Interaction occurs only once for each bunch
  (single pass) hence very large bunch
  deformations permissible ? not for SBF !
• Extremely high charge densities at IP lead to
  very intense fields hence quantum behaviour
  becomes important ? bb code

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Disruption

• Beam-beam disruption parameter ? equivalent to
  linear bb tune shift in storage ring
• Proportional to 1/g ? large number for low energy
  beams
• Typical values for ILC lt 30, 100 gt SBF gt1000
• The bb interaction in such a regime can be highly
  non linear and unstable

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Scaling laws

• Disruption
• Luminosity
• Energy spread

Decrease sz decrease N Increase spotsize
Increase N Decrease spotsize
Increase sz decrease N Increase spotsize
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Kink instability

• For high Disruption values the beams start to
  oscillate during collision ? luminosity
  enhancement
• Number of oscillations proportional to D
• bb sensitive even to very small beam y-offsets

Simulation !
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Pinch effect

• Self-focusing leads to higher luminosity for a
  head-on collision
• The enhancement parameter HD
• depends only on the Disruption parameter
• HD formula is empirical fit to beam-beam
  simulation result ? good for small Dx,y only

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Disruption angle

• Disruption angle after collision also depend on
  Disruption
• Important in designing IR
• For SBF spent-beam has to be recovered !
• Emittances after collision have to be kept as
  small as possible ? smaller damping times in DR

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Beamsstrahlung

• Large number of high-energy photons interact with
  electron (positron) beam and generate ee- pairs
• ee- pairs are a potential major source of
  background
• Beamsstrahlung degrades Luminosity Spectrum

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SBF energy spread

• U(4S) FWHM 20 MeV ? beam energy spread has to
  be smaller
• PEP-II cm energy spread is 5 MeV, depends on
  HER and LER energy spreads, which in turn depend
  on dipole bending radius and energy
• For linear colliding beams a large contribution
  to the energy spread comes from the bb
  interaction
• Due to the high fields at interaction the beams
  lose more energy and the cm energy spread
  increases

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GUINEAPIG

• Strong-strong regime requires simulation.
  Analytical treatments limited
• Code by D. Schulte (CERN)
• Includes backgrounds calculations, pinch effect,
  kink instability, quantum effects, energy loss,
  luminosity spectrum
• Built initially for TESLA ? 500 GeV collisions,
  low rep rate, low currents, low disruption
• Results affected by errors if grid sizes and n.
  of macro-particles are insufficient

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Parameters optimization

• Choice of sufficiently good simulation
  parameters (compared to CPU time)took time
• Luminosity ? scan of emittances, betas, bunch
  length, number of particles/bunch
• Outgoing beam divergences and emittances
• Average beam losses
• Luminosity spectrum
• cm energy spread
• Backgrounds

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Luminosity sE vs N. of bunches at fixed total
current 7.2 A (6.2 Km ring)
Working point
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Working point parameter listfor following plots

• ELER 3.94 GeV, EHER 7.1 GeV (bg 0.3)
• Collision frequency 120 Hz
• bx 1 mm
• by 1 mm
• exLER 0.8 nm, exHER 0.4 nm ? DR
• ey/ex 1/100
• szLER 0.8 mm, szHER 0.6 mm ? Bunch comp
• Npart/bunch 4x1010
• Nbunch 24000 ? DR kickers
• Incoming sE 10-3 ? Bunch comp

LD 1.2x1036 cm-2 s-1
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Luminosity spectrum (beamsstrahlung contribution
only, incoming beams energy spread 10-4)
64 of Luminosity is in 10 MeV Ecm
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X - collision
x (nm)
z (micron)
red ? LER
HER ? green
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Y - collision
y (nm)
z (micron)
red ? LER
HER ? green
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Outgoing beam emittances

• LER
• exout 4.2 nm 5 exin
• eyout 2.9 nm 360 eyin
• HER
• exout 1.5 nm 4 exin
• eyout 1. nm 245 eyin

Damping time required 6 t For a rep rate 120
Hz ? t 1.5 msec needed in damping ring
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Outgoing beam phase space plots
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L vs energy asymmetry (bg)
Asymmetry helps L Chosen bg 0.3
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Hourglass effect

• Hourglass effect limits attainable Luminosity ?
  bunch must be shorter than b
• Short bunches ? smaller Disruption
• Long bunches ? smaller energy spread
• Solution travelling focus (Balakin) ?
• Arrange for finite chromaticity at IP (how?)
• Create z-correlated energy spread along the bunch
  (how?)

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Luminosity vs sz
Geometric L does not include hourglass For
shorter bunches LD increase but energy spread
also!
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L vs x-emittance
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L vs y-emittance (coupling)
1 coupling is OK (smaller L has a fall off)
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Comments

• Energy asymmetry can be compensated by asymmetric
  currents and/or emittances and bunch lengths
• Current can be higher or lower for HER wrt LER,
  with proper choice of emittance and bunch length
  ratios
• Increasing x-emittance the Disruption is smaller
  ? less time needed to damp recovered beams ? loss
  in luminosity could be recovered by collision
  frequency increase
• Increasing beam aspect ratio (very flat beams)
  also helps to overcome kink instability

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Outgoing beams, exLER 1.2 nm
? X
LER
y ?
? X
HER
y ?
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X collision, b aspect ratio 100
x (nm)
z (micron)
red ? LER
HER ? green
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Y collision, b aspect ratio 100
y (nm)
z (micron)
red ? LER
HER ? green
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Luminosity spectrumb aspect ratio 100
Luminosity is 60 lower Dy is smaller sE is not
affected by the interaction
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Outgoing beams, b aspect ratio 100
? X
LER
y ?
? X
HER
y ?
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Outgoing beam emittancesb aspect ratio 100

• LER
• exout 8 nm 10 exin
• eyout 0.05 nm 6 eyin
• HER
• exout 1. nm 2.5 exin
• eyout 0.02 nm 5 eyin

Damping time required 2 t With rep rate 360
Hz ? t 1.4 msec
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To do list

• Decrease cm energy spread
• Increase luminosity
• Increase X spot sizes aspect ratio ? very flat
  beams (R100) and bunch charge
• New parameter scan
• Increase precision ? n. of micro-particles
• Travelling focus
• .