Beam-Beam Interaction in Novel,

Very High Luminosity Parameter Regimes

Mikhail Zobov

LNF INFN, Frascati, Italy

The 1st International Particle Accelerator Conference

Kyoto, Japan, 23-28 May 2010

Acknowledgments

1. Theoretical and numerical studies of beam dynamics in

crab waist collision have been carried out in close

collaboration with P.Raimondi, C.Milardi (INFN LNF,

Frascati, Italy), D.Shatilov, E.Levichev, P.Piminov (BINP,

Novosibirsk, Russia), K.Ohmi (KEK, Tsukuba, Japan),

Y.Zhang (IHEP, Beijing, China)

2. I am very grateful to the DAFNE Collaboration Team and

Operation Staff for providing the experimental data and

the help in performing dedicated experiments essential

for the crab waist collision studies.

• Present Generation Lepton Factories:

Standard Collision Scheme and Its Limitations

• Crab Waist Collision Scheme:

Concept and Beam Dynamics

• Experimental Test at DAFNE:

Principal Beam Dynamics Results

• Comparison with Numerical Simulations

OUTLINE

FactoriesDesign

Luminosity

Achieved

Luminosity

KEKBB-Factory

KEK, Japan1.0 x 1034 2.1 x 1034

PEP-II B-FactorySLAC, USA

3.0 x 1033 1.2 x 1034

DAFNEphase I

F-FactoryFrascati, Italy

1.0 x 1032 1.6 x 1032

DAFNE upgrade

F-FactoryFrascati, Italy

5.0 x 1032 4.5 x 1032

BEPCIIC-Tau-Factory

Beijing, China1.0 x 1033 3.3 x 1032

Parameters PEP-II KEKB DAFNE

LER HER LER HER e+ e-

Circumference, m 2200 2200 3016 3016 97.69 97.69

Energy, GeV 3.1 9.0 3.5 8.0 0.51 0.51

Damping time, turns 8.000 5.000 4.000 4.000 110.000 110.000

Beam Currents, A 3.21 2.07 1.70* 1.25* 1.40 2.45

Beam Current Records at Factories

Maximum positron

beam current

Maximum currents

with SC cavities Maximum electron

beam current* 2.00 A and 1.40 A

without crab cavities

Conventional Strategy

***,

*,

,

2

*

*

*2

2

0**

2

0

2

14

yxyx

yxeyx

x

y

ye

xyxb

yxb

Nr

rfN

NfNL

- Small beta function at the IP y*

- Higher number of particles per bunch N

- More colliding bunches Nb

- Larger beam emittance x

- Round beams x* = y*

- Higher tune shift parameters x,y

- Small crossing angle q << 1

- Small Piwinski angle F = ztg(q/2)/x < 1

Flat beams x* >> y*

for DA requirements

To avoid parasitic

crossings (PC)

To reduce strength of

SB resonances

Standard Collision Scheme Limitations

1. Hour-galss effect limits minimum beta function at IP y* z

2. Drastic bunch length reduction is impossible:

bunch lengthening, microwave instability, CSR

3. Further multibunch current increase would result in:

coupled bunch instabilities, HOM heating, higher wall plug power

4. Higher emittances conflict with

stay-clear and dynamics aperture limitations

5. Tune shifts saturate, beam lifetime drops due to

beam-beam intearction

New Collision Concepts

1.Round Beams

2.Crab Crossing

3.Large Piwinski Angle

4.Strong RF Focusing

5.Traveling Waist

6.Crab Waist

Tested at VEPP2000, CESR

Tested at KEKB

Tested at DAFNE

Design concept for the next

generation lepton factories

SuperB @ LNFL >1036 cm-2s-1

8 x 1035 (cm2s)-1

BINP Tau-Charm Project(Novosibirsk, Russia)

Injection facility exists

Tunnel for the linac and the technical

straight section of the factory is ready

From 1033cm-2s-1(BEPCII) to >1035cm-2s-1

E.B.Levichev

Against Standard Logic?

1.Small emittance x

2.Large Piwinski angle F >> 1

3.Larger crossing angle q

4.Longer bunch length z

5.Strong nonlinear elements (sextupoles)

Parameters BEPCII SuperC-Tau

Energy E, GeV 1.89 2

Circumference C, m 238 767

Damping time tx/ty/tz, ms 25/25/12.5 30/30/30

Beam current I, A 0.91 1.68

Bunches nb 93 384

Energy spread E 5.16x10-4 7.1x10-4

Bunch length z, cm 1.5 0.9

Beta functions x*/y*, m 1/0.015 0.04/0.0008

Emittances x/y, nm-rad 144/2.2 8/0.04

Beam sizes (IP) x/y, mm 380/5.7 17.9/0.179

Crossing angle q, mrad 11x2 30x2

Powinski angle F 0.435 15.1

Tune shifts y/x 0.04/0.04 0.13/0.0044

Luminosity L, cm-2s-1 1.0x1033 1.1x1035

1. Large Piwinski’s angle F = tg(q/2z/x

2. Vertical beta comparable with overlap area y 2x/q

3. Crab waist transformation y = xy’/q

Crab Waist in 3 Steps

1. P.Raimondi, 2° SuperB Workshop,

March 2006

2. P.Raimondi, D.Shatilov, M.Zobov,

physics/0702033

m

m

x

y2

m

m

x

y2

Crabbed Waist Scheme

x

x

yy

K

q

*

*

1

2

1

Sextupole (Anti)sextupole

20

2

1yxpHH

q

Sextupole strength Equivalent Hamiltonian

IP

yx , yx ,** ,yx

*

2* /

y

yyxs

q

2z

2x

q

z

x

4x/

q

z*q

e-e+

Y

2z

2x

q

z

x

4x/

q

z*q

e-e+

Y

1. Large Piwinski’s angle

F = tg(q/2z/x

2. Vertical beta comparable

with overlap area

y 2x/q

3. Crabbed waist transformation

y = xy’/q

Crabbed Waist Advantages

a) Luminosity gain with N

b) Very low horizontal tune shift

c) Vertical tune shift decreases

with oscillation amplitude

a) Geometric luminosity gain

b) Lower vertical tune shift

c) Suppression of vertical

synchro-betatron resonances

a) Geometric luminosity gain

b) Suppression of X-Y betatron and

synchro-betatron resonances

F

F

F

2222

2

012

;12

;14

1 NrNrNfnL

x

xex

xy

ye

y

yx

b

Large Piwinski’s Angle

P.Raimondi, M.Zobov, DAFNE

Technical Note G-58, April 2003

O. Napoly, Particle Accelerators:

Vol. 40, pp. 181-203,1993

If we can increase N proportionally to F:

1) L grows proportionally to F;

2 y remains constant;

3 x decreases as 1/F;

F is increased by:

a) increasing the crossing angle q and increasing the bunch length z for LHC

upgrade (F. Ruggiero and F. Zimmermann)

b) increasing the crossing angle q and decreasing the horizontal beam size x

in crabbed waist scheme

y

yyx

ye

yx

ye

y

yyyx

b

yx

b

NrNr

Nfn

NfnL

F

F

F

F

22

2

2

02

2

0

1212

1

14

1

14

1

Low Vertical Beta Function

Note that keeping y constant by increasing the

number of particles N proportionally to (1/y)1/2 :

2/31

y

L (If x allows...)

Vertical Synchro-Betatron Resonances

D.Pestrikov, Nucl.Instrum.Meth.A336:427-437,1993

tune shift

Synchrotron amplitude in z

Resonance suppression factor Angle = 0.00

0.0025

0.0050

0.01

Suppression of X-Y Resonances

ym

ym

y

y

Performing horizontal oscillations:

1. Particles see the same density and the same

(minimum) vertical beta function

2. The vertical phase advance between the sextupole

and the collision point remains the same (/2)

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

X-Y Resonance Suppression

Typical case (KEKB, DAFNE etc.):

1. low Piwinski angle F < 1

2. y comparable with z

Crab Waist On:

1. large Piwinski angle F >> 1

2. y comparable with x/q

Much higher luminosity!

nx nx

ny nyCrab OFF Crab ON

Frequency Map Analysis of Beam-Beam Interaction

E.Levichev, D.Shatilov and E.Simonov,

e-Print: arXiV:1002.3733, also IPAC10, THPE075

Crab = 0.0

Crab = 0.1

Crab = 0.2

Crab = 0.3

Crab = 0.4

Crab = 0.5

Crab = 0.6

Crab = 0.7

Crab = 0.8

ny

nx

Crab Sextupoles Off

Crab Sextupoles On

Bunch Current

Beam Blowup and Tails in SuperB

..and besides,

a) There is no need to increase excessively beam

current and to decrease the bunch length:

1) Beam instabilities are less severe

2) Manageable HOM heating

3) No coherent synchrotron radiation of short bunches

4) No excessive power consumption

b) The problem of parasitic collisions is automatically

solved due to higher crossing angle and smaller

horizontal beam size

Energy, GeV 0.51

Circumference, m 97.69

RF Frequency, MHz 368.26

Harmonic Number 120

Damping Time, ms 17.8/36.0

Bunch Length, cm 1-3

Emittance, mmxmrad 0.34

Coupling, % 0.2-0.3

Beta Function at IP, m 1.7/0.017

Max. Tune Shifts .03-.04

Number of Bunches 111

Max.Beam Currents, A 2.4/1.4

DAFNE Parameters(KLOE configuration)

0.931.91.8y, cm

1.700.340.44F

1.72.22.5z, cm

502525q, mrad

0.250.820.71x, mm

0.252.01.5x, m

0.250.340.34x, mm mrad

June 2009Apr. 2007Sept. 2005Date

SIDDHARTAFINUDAKLOEParameter

DAFNE IP Parameters

OLD

NEW

New Interaction Region

DAFNE Peak Luminosity

NEW COLLISION

SCHEME

Desig

n G

oa

l

CRAB OFF CRAB ON

y = 398 mm

y = 143 mm

103 colliding bunches

Transverse Beam Profile Measurements

Parameter KLOE FINUDA SIDDHARTA

Date Sept. 2005 Apr. 2007 June 2009

Luminosity, cm-2 s-1 1.53x1032 1.60x1032 4.53x1032

e- current, A 1.38 1.50 1.52

e+ current, A 1.18 1.10 1.00

Number of bunches 111 106 105

x, mm mrad 0.34 0.34 0.25

x, m 1.5 2.0 0.25

y, cm 1.8 1.9 0.93

y 0.0245 0.0291 0.0443(0.089)

DAFNE Luminosity and Tune Shifts

0

1 1032

2 1032

3 1032

4 1032

5 1032

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

L CW sextpoles OFF Feb. 9 th 2009

L March 15 th 2009

L March 13 th 2009

Lu

min

osity

[c

m-2

s-1

]

I+ * I - [A2]

0

1 1028

2 1028

3 1028

4 1028

5 1028

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Lspecific

CW Sextupoles OFF Feb. 9 th 2009

Lspecific

March 15 th 2009

Lspecific

March 13 th 2009

Sin

gle

Bu

nch

Sp

ecif

ic L

um

ino

sity

[cm

-2 s

-1 m

A-2

]

I+ * I- [A2]

Crab on/off Luminosity

vs Current Product

Crab on/off Specific

Luminosity

vs Current Product

Lifetime limit

Numerical Codes Used

1. BBC (K. Hirata, Phys.Rev.Lett.74, 2228 (1995))

2. LIFETRAC (D. Shatilov, Part.Accel.52, 65 (1996))

3. BBWS (K. Ohmi)

1. MAD (DAFNE lattice model)

2. ACCELERATICUM (P. Piminov, 6D symplectic tracking)

Weak-Strong Codes

Strong-Strong Codes

The codes have been successfully used for e+e- factories:

KEKB, DAFNE, BEPCII and colliders: VEPP4M, VEPP2000.

For Nonlinear Studies We Use

1. BBSS (K. Ohmi, PRSTAB 7, 104401, (2004))

2. SBBE (Y. Zhang, K. Ohmi, PAC2005)

Bea

m-b

eam

+ n

onlin

ear

latt

ice

Weak-Strong Simulations

Advantages:

1. Very fast (in comparison with strong-strong):

suitable for optimization, luminosity scans etc.

2. Special techniques are used for non-gaussian tail

simulations and lifetime determination (LIFETRAC)

Limitations:

1. Strong beam remains gaussian, no

blow up due to beam-beam interaction

2. Crab waist transformation is applied

only to the weak beam

D. Shatilov : crabbed distribution for the strong beamNew

Feature

Ax/x

Ay/y

Crabbed Strong Beam (DAΦNE parameters), Pictures: Log (dens)

Gaussian, Z=0

Crabbed, Z=0

Crabbed, Z=1 cm

Crabbed, Z=2 cm

D.S

hatilo

v, X

Su

perB

Work

shop,

Octo

ber

2009

Weak-Strong Simulations

(Crabbed Strong Beam)

Crab OFF Old program New program

Optimal Crab

crab=0.5 vs

crab=0.5

crab=0.8 vs

crab=0.8

gauss vs

crab=0.5

gauss vs

gauss

ny = 0.0894

L = 1.36E+32

Strong-Strong Simulations

Advantages: better reproduce collisions scheme:

1. 6D, fully self-consistent, both beams can be blown

up, non-gaussian

2. Crab waist transformation can be applied to both

beams

Limitations: very long CPU time due to

long damping time (DAFNE) and many

longitudinal slices required (SuperB)

due to

1. Dense collision area is much smaller

than bunch length

2. Beta function redistribution over this

small area

K. Ohmi : PIC simulations for the central dense area +

Gaussian approximation for tail slices!New

E. Paoloni

Tentative strong-strong simulation

• PIC collision if the separation of two slices is closer than 5x, otherwise Gaussian approximation

• 6000 PIC, 34000 Gaussian approximation per collision (200x200 slices)

K.Ohmi, IPAC2010

SuperKEKB

5x

Strong-Strong Beam-Beam Simulations (K. Ohmi)

Single Bunch Luminosity

Crab Waist On

Crab Waist Off

about 20% lower

(Damping time = 110.000 turns)

105 bunches

4.53E+32

1523 1002

Other Factors Affecting Luminosity

1. Electron cloud (beam size blow up, tune spread)

2. Lattice Nonlinearities

3. Ions of residual gas (incoherent effects, trapped ions)

4. Wake fields (single and multibunch effects)

5. Gap transients (different bunch synchronous phases)

6. Feedback noise (and also in other devices)

7. Low lifetime (not enough time for fine tuning)

8. Space charge effects

9. Touschek scattering

10.Other effects

1.0210 => 1.22

Yuan Zhang (IHEP, Beijing)

Strong-Strong Simulations of Weak-Strong Experiment

turns

turns turns

<10%

4 mm

10 mm

Horizontal size

Vertical size

SB Luminosity

DAFNE Dynamic Aperture Scan

(6D, p/p = 0 %)

No harmful resonances in the vicinity of the working point

DAFNE Dynamic Aperture

for (5.1065, 5.1750)

p/p = 0%

p/p = +0.3% p/p = -0.3%

takes into account the QDO

fringe field sextupoles

0

1 1032

2 1032

3 1032

4 1032

5 1032

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Luminosity [cm s ]-2 -1

I I [A ]2+ -

Crab OnOn

Crab Off

OFF

Dyn

am

ic A

pe

rtu

re 8

0

y

AxAx

AyAy

Beam-Beam interaction in

DAFNE nonlinear lattice

LIFETRAC + ACCELERATICUM

CONCLUSIONS

1.Experimental measurements at DAFNE prove

that the Crab Waist Concept works as

predicted by theory and numerical simulations

2.Benchmarking shows that numerical codes

are very reliable in predicting and reproducing

the experimental results and observations

This makes us more confident that very high

luminosities can be achieved in future colliders

Thank you !