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/ 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

yxyx

z

yx

ND

,

,

Scaling laws• Disruption:

• Luminosity

• Energy spread:

yx

NL

2

yx

zN

D

zx

E

N

2

2

Decrease z + decrease NIncrease spotsize

Increase NDecrease spotsize

Increase z + decrease NIncrease spotsize

Contraddicting requests!

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

g

D

D LL

H

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

0

2 2

( )y yx x e e

z z x y x

DD Nr Nr

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

• (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

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

1400.00

1600.00

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

5000 10000 15000 20000 25000 30000 35000

Dy

LER

Dy

HER HD

Dy

HD

# bunches

15.7

Npart

(x1010

)

7.9 5.2 4 3.1

Luminosity & E vs N. of bunches at fixed total current = 7.2 A (6.2 Km ring)

5.0 1035

1.0 1036

1.5 1036

2.0 1036

2.5 1036

3.0 1036

0

20

40

60

80

100

120

5000 10000 15000 20000 25000 30000 35000

Lg

LD

cm E

# bunches

15.7

Npart

(x1010

)

7.9 5.2 4 3.1

Energy spread

Working point

D

Working point parameter listfor following plots…

• ELER = 3.94 GeV, EHER = 7.1 GeV ( = 0.3)• Collision frequency = 120 Hz• x = 1 mm• y = 1 mm• x

LER = 0.8 nm, xHER = 0.4 nm DR

• y/x =1/100• z

LER = 0.8 mm, zHER = 0.6 mm Bunch comp

• Npart/bunch = 4x1010

• Nbunch = 24000 DR kickers• Incoming E = 10-3 Bunch

comp LD = 1.2x1036 cm-2 s-1

64% of Luminosityis in 10 MeV Ecm

0.0 100

5.0 1031

1.0 1032

1.5 1032

2.0 1032

2.5 1032

3.0 1032

3.5 1032

4.0 1032

10.572 10.574 10.576 10.578 10.580 10.582

Luminosity spectrum

Ecm

(GeV)

Luminosity spectrum (beamsstrahlung contribution only, incoming

beams energy spread 10-4)

X - collision

z (micron)

x (nm)

HER green red LER

Y - collision

z (micron)

y (nm)

HER green red LER

Outgoing beam emittances

• LER: – x

out = 4.2 nm = 5 * xin

– yout = 2.9 nm = 360 * y

in

• HER: – x

out = 1.5 nm = 4 * xin

– yout = 1. nm = 245 * y

in

Damping time required: 6 For a rep rate 120 Hz = 1.5 msec

needed in damping ring

Outgoing beam phase space plots

LER

HER

X

X

y

y

L vs energy asymmetry ()

0.00

200.00

400.00

600.00

800.00

0

1

2

3

0 0.1 0.2 0.3 0.4 0.5

Dy

LER

Dy

HER

HD

Dy H

D

2.0 1035

4.0 1035

6.0 1035

8.0 1035

1.0 1036

1.2 1036

1.4 1036

0

5

10

15

0 0.1 0.2 0.3 0.4 0.5

Lg

LD

cm E

Asymmetry helps LChosen = 0.3

Hourglass effect• Hourglass effect limits attainable Luminosity bunch

must be shorter than *• 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?) *z y

Luminosity vs z

0.00

200.00

400.00

600.00

800.00

1000.00

0

0.5

1

1.5

2

2.5

3

0.4 0.8 1.2 1.6

0.3 0.6 0.9 1.2

Dy

LER

Dy

HER

HD

Dy

HD

z

LER (mm)

z

HER (mm)

5.0 1035

1.0 1036

1.5 1036

2.0 1036

2.5 1036

0

5

10

15

20

0 0.4 0.8 1.2 1.6

0.0 0.3 0.7 1.0 1.4

Lg

LD

cm E

z

LER (mm)

z

HER (mm)

Energy spread

D

Geometric L does not include hourglassFor shorter bunches LD increase butenergy spread also!

L vs x-emittance

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200.00

400.00

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800.00

1000.00

0

1

2

3

4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Dy

LER

Dy

HER

HD

Dy

HD

x

LER (nm)

x

HER (nm)

4.0 1035

8.0 1035

1.2 1036

1.6 1036

2.0 1036

0

5

10

15

20

0 0.2 0.4 0.6 0.8 1 1.2 1.4

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Lg

LD

cm E

x

LER (nm)

x

HER (nm)

Energy spread

L vs y-emittance (coupling)

0.00

100.00

200.00

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400.00

500.00

600.00

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16

Dy

LER

Dy

HER

HD

Dy

HD

y/

x (%)

2.0 1035

4.0 1035

6.0 1035

8.0 1035

1.0 1036

1.2 1036

1.4 1036

0

5

10

15

0 2 4 6 8 10 12 14 16

Lg

LD

cm E

y/

x (%)

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, xLER = 1.2 nm

LER

HER

X

X

y

y

X – collision, aspect ratio = 100

z (micron)

x (nm)

HER green red LER

Y – collision, aspect ratio = 100

z (micron)

y (nm)

HER green red LER

Luminosity spectrum aspect ratio = 100

0.0

5 1031

1 1032

1 1032

2 1032

10.576 10.578 10.580 10.582 10.584

aspect ratio = 100

Ecm

(GeV)

Luminosity is 60% lowerDy is smallerE is not affected by the interaction

Outgoing beams, aspect ratio = 100

LER

HER

X

X

y

y

Outgoing beam emittances aspect ratio = 100

• LER: – x

out = 8 nm = 10 * xin

– yout = 0.05 nm = 6 * y

in

• HER: – x

out = 1. nm = 2.5 * xin

– yout = 0.02 nm = 5 * y

in

Damping time required : 2 With rep rate 360 Hz = 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

• ….