Beam-beam simulations

M.E. Biagini, K. Ohmi, E. Paoloni, P. Raimondi, D. Shatilov, M. Zobov

INFN Frascati, KEK, INFN Pisa, SLAC, BINP

April 26th, 2006UK SuperB Meeting, Daresbury

Outline

• GuineaPig simulations & Automatization

• 2 beams scheme with asymmetric energies

• Crab waist simulations:– DANE– SuperB

BB simulations

• Evolution of the SuperB layout is a consequence of the beam-beam studies

• Both luminosity and beam blow-up are the parameters to “watch”: figure of merit is now L/log(blowup/)

• Optimization of beam parameters must include Damping Ring optimization and Final Focus design

First simulations• An extensive campaign of beam-beam

simulations has been carried out to find the best beam parameters set

• GuineaPig code by D. Schulte (CERN) has been used (same as ILC studies) in this first phase

• Optimization of beam parameters for round beams case was performed interfacing GuineaPig with Mathematica

• Round and flat, 2 and 4 beams studied

GuineaPig to Mathematica

E. Paoloni, 2nd SuperB LNF Workshop

Round case test• Tested first with round beams• Search of maximum L with a scan of

parameters space

Scan of the x,x plane

Optimum region

L/log(blowup/)

Scan of the x,z plane

L/crossing

E. Paoloni, 2nd SuperB LNF Workshop

4 Beams tests

• 4 beams are more unstable than 2 beams, highly disrupted, with larger emittance blow ups and give lower luminosity

• Not exhaustive analysis not excluded we can find better working parameter set in the future

• Shorter beams seem to work better• Larger horizontal beam size is better• Higher energy definitely works better

Possible choice for ILC !!!!

2 beams

4 beams

Flat Casecomparison with

4 beamsPhase space after collision

(x,x’), (y,y’), (z,E/E)

x,x’ z,E/Ey,y’

x,x’ x,x’z,E/E z,E/Ey,y’ y,y’

2 beams asymmetric energies

• Studied the 2-beams scheme with asymmetric energies for 4x7 GeV case:– Npart = 2.x1010

– I = 1.6 A (for a 3Km ring, 6000 bunches)

– x = 2.670 m

– y = 12.6 nm

– z = 4. mm

– x = 2.5 mm

– y = 80. m

– = 2x25 mrad

Symmetric E

Y emittance blow-up: 3x10-3

Asymmetric E (4x7 GeV)

Y emittance blow-up: 4 GeV 5x10-3

7 GeV 3x10-3

Study of emittance blow-up

Asymmetric energies (4x7 GeV)

with transparency condition (I)

Y emittance blow-up: 4 GeV 3.5x10-3

7 GeV 3.6x10-3

Np(4 GeV) = 2.65x1010

Np(7 GeV) = 1.51x1010

I(4 GeV) = 2.1 AI(7 GeV) = 1.2 A

Asymmetric energies (4x7 GeV)

with asymmetric bunch lengths

Np(4 GeV) = 2x1010

Np(7 GeV) = 2x1010

I(4 GeV) = 1.6 AI(7 GeV) = 1.6 A

z(4 GeV) = 3.02 mm z(7 GeV) = 5.29 mmY emittance blow-up: 4 GeV 4x10-3

7 GeV 4x10-3

Crab-waist simulations

• The new idea by Pantaleo is being checked by several beam-beam codes:– Guinea-Pig: strong-strong , ILC centered– BBC (Hirata): weak-strong – Lifetrack (Shatilov): weak-strong with tails

growths calculation– Ohmi: weak-strong (strong-strong to be

modified for long bunches and large angles)

Sto

rag

e

rings

Vertical waist has to be a function of x:

Z=0 for particles at –x (- x/2 at low current)

Z= x/2 for particles at + x (x/2 at low current)

x

2Sz

2Sx

z

2Sx/

2Sz*

e-e+

GuineaPig

Collisions with uncompressed beamsCrossing angle = 2*25 mrad

Relative Emittance growth per collision about 1.5*10-

3

yout/y

in=1.0015

DANE case (M.Zobov, LNF)• Hirata’s BBC code simulation

(weak-strong, strong beam stays gaussian, weak beam has double crossing angle)

• Np = 2.65x1010, 110 bunches

• Ib = 13 mA (present working current)

• x = 300 m, y = 3 m

• x = 0.3 m, y = 6.5 mm

• z = 25 mm (present electron bunch length)

• = 2x25 mrad• YIP = y+0.4/(x y’) crabbed waist shift• Lo=2.33x1024 (geometrical)• L(110 bunches,1.43A) = 7.7x1032

• Lequil=6x1032

(Geometric) Luminosity

Takes into account both bb interactions and geometric factor due to crab waist

0,5

0,6

0,7

0,8

0,9

1

1,1

1,2

0 0,2 0,4 0,6 0,8 1

L/Lo

n x [1/angle]

n/

Peak around 0.3/

M.Zobov, LNF

Scan vs crab waist n/

Vertical Tails(max amplitude

after 10 damping times)

Vertical Size Blow-up

2

4

6

8

10

12

14

16

0 0,2 0,4 0,6 0,8 1

Ay/y0

n x [1/angle]

n/

0,5

1

1,5

2

2,5

3

0 0,2 0,4 0,6 0,8 1

y/y0

n x [1/angle]

n/

M.Zobov, LNF

Present WP:x = 0.11y = 0.19

Possible WP:x = 0.057 y = 0.097

0

0,5

1

1,5

2

2,5

0 5 10 15 20 25

(0.11,0.19)(0.057,0.097)Theory

I [mA]

L [10^33]

Luminosity vs bunch currentfor 2 different working points

M.Zobov, LNF

0

2

4

6

8

10

12

14

0 10 20 30 40 50

200um,20mm200um,15mm100um,15mm

I [mA]

L [10^33]

110 bunchesM.Zobov, LNF

Luminosity with shorter bunch and smaller x (preliminary)

0,5

0,6

0,7

0,8

0,9

1

1,1

1,2

0,06 0,08 0,1 0,12 0,14 0,16

Qx

L/L0 at Qy = 0.09

Some resonances

0

0,2

0,4

0,6

0,8

1

1,2

0,06 0,08 0,1 0,12 0,14 0,16

no crab focus0.25/teta0.40/teta

Qx

L/L0 at Qy = 0.05

M.Zobov, LNF

2Qx = 2Qy1Qx = 2Qy

(present with crossing angle only)

No crab waist

Crab waist

Beam-Beam Tails (D.Shatilov, BINP)

Without Crab Waist

With Crab Waist

Bunch core blowup

also reduced

Ay = 90

Ay = 45

Vertical tails growth Greatly reduced

(A is the amplitude in number of beamsize )

SuperB Luminosity Ohmi’s weak-strong code

K2 is the strength of the sextupolar nonlinearity introduced to have crab waist

SuperB vertical blow-up Ohmi’s weak-strong code

Conclusions

• For the asymmetric energies “equal blow up” can be obtained with transparency condition (asymmetric I, or z)

• The “crab waist” scheme has shown big potentiality and exciting results LNF, BINP and KEKB physicists are working on the bb simulation with different codes to explore its properties and find the best set of parameters

• This scheme is promising also for increasing luminosity at existing factories, as DANE, KEKB and possibly PEPII