Crab Waist Approach:

from DAFNE to SuperB

M. Zobov, INFN LNF, Frascati, Italy

for DAFNE Collaboration Team

and SuperB Accelerator Team

XXII Russian Particle Accelerator Conference RuPAC-2010

27.09 – 01.10.2010, Protvino, Russia

DAFNE Collaboration Team: D.Alesini, M.E.Biagini, C.Biscari, A.Bocci, R.Boni,

M.Boscolo, F.Bossi, B.Buonomo, A.Clozza, G.O.Delle Monache, T.Demma, E.Di Pasquale,

G.Di Pirro, A.Drago, A.Gallo, A.Ghigo, S.Guiducci, C.Ligi, F.Marcellini, G.Mazzitelli, C.Milardi,

F.Murtas, L.Pellegrino, M.A.Preger, L.Quintieri, P.Raimondi, R.Ricci, U.Rotundo, C.Sanelli,

M.Serio, F.Sgamma, B.Spataro, A.Stecchi, A.Stella, S.Tomassini, C.Vaccarezza, M.Zobov

(LNF INFN); M.Schioppa (INFN,Cosenza); M.Esposito (La Sapienza); P.Branchini (INFN,

Rome 3); F.Iacoangeli, P.Valente (INFN, Rome); E.Levichev, P.Piminov, D.Shatilov, V.Smaluk

(BINP, Novosibirsk); N.Arnaud, D.Breton, L.Burmistrov, A.Stocchi, A.Variola, B.F.Viaud (LAL,

Saclay); S.Bettoni (CERN, Geneva); K.Ohmi(KEK, Tsukuba); D.Teytelman(Dimtel Inc., USA)

SuperB Accelerator Team: M.E.Biagini, R.Boni, M.Boscolo, B.Buonomo,

T.Demma, A.Drago, S.Guiducci, G.Mazzitelli, L.Pellegrino, M.A.Preger, P.Raimondi, R.Ricci,

C.Sanelli, M.Serio, A.Stella, S.Tomassini, M.Zobov (LNF INFN); K.Bertsche, A.Brachmann,

A.Chao, R.Chestnut, M.Donald, C.Field, A.Fisher, D.Kharakh, A.Krasnykh, K.Moffeit,

Y.Nosochkov, A.Novokhatski, M.Pivi, J.Seeman, M.K.Sullivan, A.Weidemann, J.Weisend,

U.Wienands, W.Wittmer, M.Woods (SLAC); A.Bogomiagkov, I.Koop, E.Levichev, S.Nikitin,

I.Okunev, P.Piminov, S.Siniyatkin, D.Shatilov, P.Vobly (BINP); F.Bosi, S.Liuzzo, E.Paoloni

(Pisa University); J.Bonis, R.Chehab, O.Dadoun, G.Le Meur, P.Lepercq, F.Letellier-Cohen,

B.Mercier, F.Poirier, C.Prevost, C.Rimbault, F.Touze, A.Variola (LAL); B.Bolzon, L.Brunetti,

A.Jeremie (LAPP, Annecy); M.Baylac, O.Bourrion, J.M.DeConto, Y.Gomez, F.Meot,

N.Monseu, D.Tourres, C.Vescovi (LPSC, Grenoble); A.Chancé, O.Napoly (CEA Saclay);

D.P.Barber (DESY, Cockcroft Institute, Universty of Liverpool); S.Bettoni, D.Quatraro (CERN).

• Crab Waist Collision Concept

• Experimental Test at DAFNE

• Status of SuperB Accelerator Project

OUTLINE

Crab Waist Colliders (after 2006)

DAFNE, F-factory Italy Operational

SuperKEKB, B-factory Japan Partially funded

SuperB, B-factory Italy Waiting for approval

SuperC-Tau, Tau-Charm Russia Waiting for approval

BEPCII, Tau-Charm China Upgrade option studies

LHC Switzerland Upgrade option studies

1. Large Piwinski’s angle F = tg(q/2)sz/sx

2. Vertical beta comparable with overlap area by 2sx/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

x

y2

x

y2

Crabbed Waist Scheme

x

x

yy

Kb

b

bbq

*

*

1

2

1

Sextupole (Anti)sextupole

20

2

1yxpHH

q+

Sextupole strength Equivalent Hamiltonian

IP

yx bb , yx bb ,** ,yx

bb

)*

2* /

y

yyxs

b

qbb

+

2sz

2sx

q

z

x

4sx/

q

sz*q

e-e+

bY

2sz

2sx

q

z

x

4sx/

q

sz*q

e-e+

bY

1. Large Piwinski’s angle

F = tg(q/2)sz/sx

2. Vertical beta comparable

with overlap area

by 2sx/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

bs

b

ss

b

ss

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 sz for LHC

upgrade (F. Ruggiero and F. Zimmermann)

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

in crabbed waist scheme

y

yyx

ye

yx

ye

y

yyyx

b

yx

b

NrNr

Nfn

NfnL

bbs

b

ss

b

bbsss

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/by)1/2 :

2/31

y

Lb (If x allows...)

Vertical Synchro-Betatron Resonances

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

tune shift

Synchrotron amplitude in sz

Resonance suppression factor Angle = 0.00

0.0025

0.0050

0.01

Suppression of X-Y Resonances

y

y

yb

yb

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. by comparable with sz

Crab Waist On:

1. large Piwinski angle F >> 1

2. by comparable with sx/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

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)

0.931.91.8by, cm

1.700.340.44F

1.72.22.5sz, cm

502525q, mrad

0.250.820.71sx, mm

0.252.01.5bx, 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

oal

CRAB OFF CRAB ON

s+y = 398 m s+

y = 143 m

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

bx, m 1.5 2.0 0.25

by, 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. 9th 2009

L March 15th 2009

L March 13th 2009

Lum

inosity

[cm

-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 15th 2009

Lspecific

March 13th 2009

Sin

gle

Bu

nch S

pecific

Lum

inosity [c

m-2

s-1

mA

-2]

I+ * I- [A2]

Crab on/off Luminosity

vs Current Product

Crab on/off Specific

Luminosity

vs Current Product

Lifetime limit

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

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 s

y

AxAx

AyAy

Beam-Beam interaction in

DAFNE nonlinear lattice

LIFETRAC + ACCELERATICUM

CONCLUSIONS (Part I - DAFNE)

1. Crab waist works well, no doubts

2. Existing numerical codes are reliable in predicting

the luminosity with crab waist

3. Crab waist sextupoles are of great importance for

the collider luminosity increase

4. DAFNE scientific program has been approved for

the next 3 years

• Super-B aims at the construction of a very high

luminosity (1x 1036 cm-2 s−1) asymmetric e+e− flavor

factory with a possible location on or near the campuses

of the University of Rome at Tor Vergata or the INFN

Frascati National Lab.

• Goals:

– Peak luminosity >1036 cm-2s-1 at Y(4S)

– Integrated luminosity 75 ab-1

– Longitudinally polarized beam (e-) at the IP (60-85%)

– Ability to collide at the Charm threshold

– Flexible parameter choices

– High reliability

Super-B Project

Circumference 1.258 km Collider hall

66 mrad crossing

angle

Damping ring

SuperB at Frascati

e+

e-

HER arc

LER arc

HER arc

LER arc

RF

Collaboration: INFN, SLAC, IN2P3, BINP, Canada

Geological Survey

Quite same spectra with time

except for one area

PSD

Gain

[m2/H

z]

from 8h to 9h40: high increase of

amplitude in the range [3; 30]Hz

correspond exactly to traffic

Time area of

the increase

Peak observed in

the range [3; 30]Hz

7h40-8h00 no peak

8h00-8h20 low level

8h20-8h40 highest level

8h40-9h40

(step: 20 min)

decrease of level

step by step

9h40-10h00 no (same spectra as

for 7h40-8h00)Microsismic peak

(waves of ocean)

Cultural noise

(human activities)

PSD of ground motion versus time and frequency

Frequency [Hz]

Base LineLow

EmittanceHigh Current t-charm

Parameter UnitsHER

(e+)

LER

(e-)

HER

(e+)

LER

(e-)

HER

(e+)

LER

(e-)

HER

(e+)

LER

(e-)

LUMINOSITY cm-2 s-1 1.00E+36 1.00E+36 1.00E+36 1.00E+35

Energy GeV 6.7 4.18 6.7 4.18 6.7 4.18 2.58 1.61

Circumference m 1258.4 1258.4 1258.4 1258.4

X-Angle (full) mrad 66 66 66 66

bx @ IP cm 2.6 3.2 2.6 3.2 5.06 6.22 6.76 8.32

by @ IP cm 0.0253 0.0205 0.0179 0.0145 0.0292 0.0237 0.0658 0.0533

Coupling (full current) % 0.25 0.25 0.25 0.25 0.5 0.5 0.25 0.25

Emittance x (with IBS) nm 2.00 2.46 1.00 1.23 2.00 2.46 5.20 6.4

Emittance y pm 5 6.15 2.5 3.075 10 12.3 13 16

Bunch length (full current) mm 5 5 5 5 4.4 4.4 5 5

Beam current mA 1892 2447 1460 1888 3094 4000 1365 1766

RF frequency MHz 476. 476. 476. 476.

Number of bunches # 978 978 1956 1956

Tune shift x 0.0021 0.0033 0.0017 0.0025 0.0044 0.0067 0.0052 0.0080

Tune shift y 0.097 0.097 0.0891 0.0892 0.0684 0.0687 0.0909 0.0910

Total RF Wall Plug Power MW 16.38 12.37 28.83 2.81

SuperB Basic Parameters

Annecy SuperB Workshop Page 41-350

-300

-250

-200

-150

-100

-50

0

-200 -100 0 100 200

x(m)

-- straight sections

-- dipoles

-- quadrupoles

-- sextupoles

-- RF cavities

-- solenoids

IP

Rings

crossing

66 mrad

RF

LER SR

LER SR

HER

arc

LER

arc

HER

arc

LER

arc

e-

e+

C = 1258.4 m

Lattice Systems• Two Arcs

- Provide the necessary bending to close the ring.

- Optimized to generate the design horizontal emittance.

- Correct arc chromaticity and sextupole aberrations.

• Interaction Region- Provides the necessary focusing for required small beam size at IP

- Corrects FF chromaticity and sextupole aberrations.

- Provides the necessary optics conditions for Crab Waist.

• LER Spin Rotator- Includes solenoids in matched sections adjacent to the IR.

• Long Straight Section- Connects the left and right Arcs

- Contains up to 24 HER and 12 LER cavities

- Provides tune variation (tune trombones)

- Allocates collider utilities

Collider Layout

Damping Ring operates just for positrons

Main Rings injection rate: 50 Hz instead of 25

Main Linac Klystron rep. rate: 100 Hz

THERMIONIC

GUNSHB0.6 - 1 GeVPC0.95 GeV

BUNCH

COMPRESSOR5.7 GeV e+ 3.9 GeV e-

POLARIZED

SLAC GUNSHB

50 MeV

CAPTURE

SECTION

e+

e-

combinerDC dipole

0.2 GeV

50 MeV

CAPTURE

SECTION

Only 2 Transfer Lines between Linacs and D.R., instead of 4; no special dipoles

No long flat top kickers in the damping ring and transfer lines

The gun for the positron line can be thermionic, thus delivering larger current

The polarized gun for the electrons can work at a much lower current

The e- beam vertical emittance increases…. can be reduced with scrapers/collimators …

New scheme proposed recently (june 2010) …

… and under refinement

t1 t2 t2t1

e+ prod. e+ prod.

e+ Inj. e- Inj.e- Inj.

20 msec

20 msec

10 msec

TIMING

e+ Inj.

Super-B Damping Ring

compact structure (51 m) for

storing alternatively electrons

and positrons

small equilibrium emittance:

23 nm @ 1 GeV

short betatron damping time:

7.3 ms

small momentum compaction:

5.7x10-3 => short bunch length

large dynamic aperture: ± 20

mm

horizontal, ± 15 mm vertical for

-2% < ∆p/p < +2%

Parameter HER (e+) LER (e-)

Beam Energy (GeV) 6.70 4.18

Beam current (A) 1.89 2.45

b*x (mm) 26 32

b*y (mm) 0.25 0.21

Emittance X (nm-rad) 2.00 2.46

Emittance Y (pm-rad) 5.00 6.15

Crossing angle (mrad) 33

0

100

200

-100

-2000 1 2 3-1-2-3

mm

m 3-Oct-09

M. Sullivan

SB_I_ILC_R3_SR_3M

QF1QF1

HERLER

PM

Solenoids

QD0

300 mrad

200 mrad

Cryostat

PEP-II

Support tube

Interaction Region

Provides the necessary focusing for

required small beam sizes

Corrects final focus chromaticity and

sextupole abberations

Provides conditions for Crab Waist

IR Optics

Siberian Style QD0

QD0 DESIGN

On Energy Dynamic Aperture

CRAB Sextupoles is Switched On

Parameters of Crab Sexts LER HER Units

Length, L 35 35 cm

Strength, K2 ±16.67 ±16.67 m-3

Horizontal beta, βx 14.6 14.6 m

Vertical beta, βz 200 200 m

0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64

0.5

0.52

0.54

0.56

0.58

0.6

0.62

0.64

SuperB Luminosity Tune Scan

Qx

Qy

Tunes: (0.542, 0.580, 0.01)

Np = 5.74·1010; Nb = 1011

L = 1.04x1036 cm-2s-1

HER

LER

D.N.Shatilov, M. Zobov

y = 0.17

10SuperB MINI-MACII, Frascati 23-24 April 2009

Buildup in the SuperB arcs: Dipoles

Average e-cloud density for:

SEY=1.1 SEY=1.2 SEY=1.3 SEY=1.4

Snapshot of the electron (x,y) distribution

“just before” the passage of the last bunch

IBS in SuperB LER (lattice V12)

Effect is reasonably small. Nonetheless,

there are some interesting questions to

answer:

•What will be the impact of IBS during the

damping process? We have calculated the

equilibrium emittances in the presence of

IBS, but the beam is extracted before it

reaches equilibrium…

•Could IBS affect the beam distribution,

perhaps generating tails?

•What happens when vertical emittance is

very small as in SuperB?

h=2.412 nm

@N=6.5e10

v=5.812 pm

@N=6.5e10

sz=4.97 mm

@N=6.5e10

M.Boscolo, T.Demma, A.W.Chao

SuperB bunch-by-bunch feedbacks are based on identical DPU (digital

processing unit) for both longitudinal and transverse systems. The DPU

core is implemented by a single powerful FPGA (field programmable gate

array) containing >2000 DSP (digital signal processor).A. Drago

SuperB bunch-by-bunch feedbacks

More details can be found in:

159 pages

National Research Plan

Ministry’s Press Release