Beam beam simulations with disruption (work in progress...) M.E.Biagini SuperB-Factory Workshop Frascati, Nov. 11th, 2005

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

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 < 30, 100 > SBF >1000 The bb interaction in such a regime can be highly non linear and unstable

Scaling laws Disruption: Luminosity Energy spread: Decrease sz + decrease N Increase spotsize Increase N Decrease spotsize Contraddicting requests! Increase sz + decrease N Increase spotsize

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 !

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

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

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

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

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

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

Luminosity & sE vs N. of bunches at fixed total current = 7. 2 A (6 Luminosity & sE vs N. of bunches at fixed total current = 7.2 A (6.2 Km ring) Working point D Energy spread

Working point parameter list for 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

Luminosity spectrum (beamsstrahlung contribution only, incoming beams energy spread 10-4) 64% of Luminosity is in 10 MeV Ecm

X - collision x (nm) z (micron) HER  green red  LER

Y - collision y (nm) z (micron) HER  green red  LER

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

Outgoing beam phase space plots LER HER  X y 

L vs energy asymmetry (bg) Asymmetry helps L Chosen bg = 0.3

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?)

Luminosity vs sz D Geometric L does not include hourglass For shorter bunches LD increase but energy spread also! D Energy spread

L vs x-emittance Energy spread

L vs y-emittance (coupling) 1% coupling is OK (smaller L has a fall off)

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

Outgoing beams, exLER = 1.2 nm y   X HER y 

X – collision, b aspect ratio = 100 x (nm) z (micron) HER  green red  LER

Y – collision, b aspect ratio = 100 y (nm) z (micron) HER  green red  LER

Luminosity spectrum b aspect ratio = 100 Luminosity is 60% lower Dy is smaller sE is not affected by the interaction

Outgoing beams, b aspect ratio = 100  X LER y   X HER y 

Outgoing beam emittances b 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

To do list… Decrease cm energy spread Increase luminosity Increase X spot sizes aspect ratio  “very flat” beams (R=100) and bunch charge New parameter scan Increase precision  n. of micro-particles Travelling focus ….