Beam-beam simulations with crossing anlge + crab-

waist

M. Biagini, M. Zobov, LNF-INFNP. Raimondi, SLAC/INFNI. Koop, D. Shatilov, BINP

E. Paoloni, Pisa University/INFN

SuperB III Workshop, SLAC, 14-16 June 2006

BB simulations

• New “crossing angle + crab waist” idea has solved disruption problems related to collisions with high current, small sizes beams back to two “conventional” rings

• With very small emittances and relatively low currents (comparable to present B-Factories values) a Luminosity of 1036 cm-2 s-1 is reachable without large emittance blow-up

Vertical waist has to be a function of x:

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

Z= x/ for particles at + x (x/2 at low current) Crabbed waist realized with a sextupole in phase with

the IP in X and at /2 in Y

2Sz

2Sx

z

x

2Sx/

2Sz*

e-e+Y

Crabbed waist removes bb betratron couplingintroduced by the crossing angle

Luminosity considerationsIneffectiveness of collisions with large crossing angle is illusive!!!Loss due to short collision zone (say l=σz/40) is fully compensated by denser target beam (due to much smaller vertical beam size!) cross

2 2 cross xz

lN N l 2 /

Number of particles in collision zone:

1 2 0

x y

N N fL

4

e 2 y

1yy x y

r N

2 ( )

1y 1 0 y 1y34 36 2 1

e y x y

N f E(GeV) I(A)L 1 2.167 10 1.2 10 cm s

2r (cm)

No dependence on crossing angle! Universal expression: valid for both, head-on and crossing angle collisions!

I. Koop et al, BINP

Tune shiftsRaimondi, Shatilov, Zobov:(Beam Dynamics Newsletter, 37, August 2005)

2 2 2x z xtan ( / 2)

e xx

2 2 2 2 2 2z x z x y

yey

2 2 2y z x y

r N

2 tan ( / 2) tan ( / 2)

r N

2 tan ( / 2)

SuperB:

e xx 2 2

z

yey

y z

2r N0.002

r N0.072

2 2 2z x xtan ( / 2) 100 m 2.67 m

2 2 2z x

y

tan ( / 2)8000!!!

One dimensional case for βy >>σx/θbut with crabbed waist for βy <σx/θ also!

I. Koop et al, BINP

“Crabbed” waist optics

1x x

x x x x1 1 11x x x xx x

y y y1 1 1y y y y

y y y y y

u 0 1 0u 0T T T T

F u 2u F 1F u

u F 0 F 1 0T T T T

F 0 F u 2u F 1

Appropriate transformations from first sextupole to IP and from IP to anti-sextupole:

IP

Δμx=πΔμy=π/2

Δμx=πΔμy=π/2

x,yT x,yT+ks -ks

Sextupole lens Anti-sextupole lens

Synchrotron modulation of ξy (Qualitative picture)

ξy(z-z0)

Relative displacementfrom a bunch center

z-z0

Head-on collision.Flat beams. Tune shiftincreases for halo particles

Head-on collisionRound beams ξy=const

Crossing angle collision.Tune shiftdecreases for halo particles

Conclusion: one can expect improvements of lifetime of halo-particles!

I. Koop et al, BINP

ξy increase caused by hourglass effect

For Super-B parameters set: Increase of ξy only by 26%

Dependence of ξy on βy for constant beam sizes at IP

2

y yy

1 zg(x(z)) dz

4

I. Koop et al, BINP

Collisions with uncompressed beamsCrossing angle = 2*25mradRelative Emittance growth per collision about 1.5*10-3

yout/y

in=1.0015

Horizontal Plane Vertical Plane

SuperB parameters

GuineaPig modifications

• With the large crossing angle scheme and long bunches the actual collision region is very short

• The code solves Poisson equation for all the volume occupied by the particles very long computing time, not needed !

• Modification of the code to perform fields calculation in the collision region only

• Computing time was reduced by a factor 10!!

GuineaPig modifiedE. Paoloni, Pisa

Luminosity vs Number of particles /bunch

Crab-waist simulations

• The new idea 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

Ohmi’s weak-strong code

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

Luminosity Vertical blow-up

DANE (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, by = 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 bunches

M.Zobov, LNF

Luminosity with shorter bunch, smaller x

With the present achieved beam parameters (currents, emittances, bunchlenghts etc) a luminosity inexcess of 1033 is predicted.With 2A+2A L> 2*1033 is possibleBeam-Beam limit is way above the reachable currents

Luminosity scan

Without Crab Focus

Vertical Size blow-up scan

M. Zobov

With Crab Focus

Beam-Beam Tails Without Crab

WaistWith Crab Waist

Bunch core blowup

also reduced

Ay = 90

Ay = 45

Vertical tails growth Greatly reduced

(A is the amplitude in number of beamsize )

D.Shatilov, BINP

Beam size and tails vs Crab-waistSimulations with beam-beam code

LIFETRAC Beam parameters for DANE2

An effective “crabbed” waist map at IP:0 0

0

Vy y xy

y y

Optimum is shifted from the “theoretical” value V=1 to V=0.8,since it scales like z/sqrt((z2+x

2)D.N. Shatilov, BINP

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

Very weak luminosity dependence from damping time given the very small beam-beam blow-up

0

0,2

0,4

0,6

0,8

1

0 5 104 1 105 1,5 105 2 105 2,5 105

x^(-0.37)

x^(-0.48)

x^(-0.56)

x^(-0.50)

y0/y

turns

(0.057,0.097,-0.01)(0.057,0.097,+0.01)

(0.11,0.19,-0.01)(0.11,0.19,+0.01)

Wigglers off

DANE Wigglers

SC Wigglers

M. Zobov,LNF

0,5

1

1,5

2

2,5

3

3,5

5 104 1 105 1,5 105 2 105

(0.057,0.097,-0.01)(0.057,0.097,+0.01)(0.11,0.19,-0.01)(0.11,0.19,+0.01)

turns

L, 10^33

Wigglers offSC Wigglers

DANE Wigglers

Vertical blow-up Luminosity

Preliminary results on Super PEPIIx = 20 nmy = 0.2 nmx = 14.4 my = 0.4 mz = 10 mmE = 7x10-4

x = 10 mmy = 0.8 mms = 0.03C = 2.2 kmfcol = 238 MHz = 2 x 14 mradx = 35 msN1 = 1.3x1011

N2 = 4.4x1010

I1 = 5 AI2 = 1.7 A

First approach with new parameters,weak-strong code

M. Zobov, D. Shatilov

L = 1.65x1035 cm-2s-1

Tune scan for Super-PEPII

M.Zobov, D.ShatilovSynchrobetatron resonances

Coupling resonance

crab focus on

crab focus off

Coupling resonance disappears

No dependence on tunes !!

Tails growth

M.Zobov, D.Shatilovn/= 0 n/= 0.6 n/= 1

x = 0.5325, y = 0.5775

x = 0.54, y = 0.5825

Crab OnCrab Off

30 y

10 y15 y

40 y

15 y

20 y

L=1.5x1035 L=1.65x1035L=1.64x1035

Conclusions

• The “crossing angle with crab waist” scheme has shown big potentiality and exciting results LNF, Pisa, 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