CARE-HHH-APD Mini-Workshop IR’07,

INFN, Frascati (Italy), 7-9 November 2007

M. Zobov, P. Raimondi, LNF INFN, ItalyD. N. Shatilov, BINP, Novosibirsk

K. Ohmi, KEK, Japan

Crab Waist Collision StudiesCrab Waist Collision Studiesfor e+e- Factoriesfor e+e- Factories

• Crab Waist Concept

• Crab Waist Scheme for DANE Upgrade

• 1036 cm-2s-1 in SuperB Factory

OUTLINEOUTLINE

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

2. GUINEA-PIG (D. Schulte, CERN-PS-099-014-LP) modified by P. Raimondi for storage rings

Weak-Strong Codes

Strong-Strong Codes

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

KEKB, DANE, PEP-II, BEPCII and colliders: VEPP4M, VEPP2000.

Crabbed waist is realized with a sextupole inphase with the I P in X and at / 2 in Y

2z

2x

z

x

2x/

2z*

e-e+Y

1. Large Piwinski’s angle = tg(z/x

2. Vertical beta comparable with overlap area y x/

3. Crab waist transformation y = xy’/(2)

Crab Waist in 3 Steps

1. P.Raimondi, 2° SuperB Workshop, March 20062. P.Raimondi, D.Shatilov, M.Zobov, physics/0702033

x

y 2

x

y 2

Crab Waist Scheme

x

x

yy

K

*

*

1

2

1

Sextupole (Anti)sextupole

20 2

1yxpHH

Sextupole strength Equivalent Hamiltonian

IPyx , yx ,** ,

yx

*

2* /

yyy

xs

2z

2x

z

x

x

2z*

e-e+Y

2z

2x

z

x

x

2z*

e-e+Y

1. Large Piwinski’s angle

= tg(z/x

2. Vertical beta comparable

with overlap area

y x/

3. Crabbed waist transformation

y = xy’/(2)

Crab Waist Advantages

a) Geometric luminosity gain

b) Very low horizontal tune shift

a) Geometric luminosity gain

b) Lower vertical tune shift

c) Vertical tune shift decreases with oscillation amplitude

d) Suppression of vertical synchro-betatron resonances

a) Geometric luminosity gain

b) Suppression of X-Y betatron and synchro-betatron resonances

..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

2222

2

0 12;

12;

14

1 NrNrNfnL

x

xex

xy

yey

yxb

Large Piwinski’s Angle

P.Raimondi, M.Zobov, DANE Technical Note G-58, April 2003

O. Napoly, Particle Accelerators: Vol. 40, pp. 181-203,1993

If we can increase N proportionally to :

1) L grows proportionally to ;

y remains constant;

3 x decreases as 1/;

is increased by:

a) increasing the crossing angle and increasing the bunch length z for LHC upgrade (F. Ruggiero and F. Zimmermann)

b) increasing the crossing angle and decreasing the horizontal beam size x in crabbed waist scheme

y

yyx

ye

yx

ye

y

yyyx

b

yx

b

NrNr

Nfn

NfnL

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

yL

(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

Geometric Factors

1. Minimum of y along the maximum density of the opposite beam;

2. Redistribution of y along the overlap area. The line of the minimum beta with the crab waist (red line) is longer than without it (green line).

*

2* /

yyy

xs

dxdydzdttzyxtzyxCoscfL ,,,,,,2

2 210

zx

yctzx

zx

Ntzyx

zx

yctzx

zx

Ntzyx

yzxyzx

yzxyzx

,222exp

2,,

222exp

2,,

2

2

2

2

2

2

,22/3

2,2

1,12

2

2

21

2

21

1,12/3

1,1111

22222

111111

2

22*

2

2111*

11

2

22

1

11

/1,

/1,

yyy

yyy

Tanxzzx

Tanxzzx

zz

xx

zxz

zxx

2

2

1

1

cossin

sincos

θ

2σx

2σx/ θ

e- e+

- length of the collision area

z1

x1 x2

z2

θ

Crab Waist Collisions at 1 = -, 2 =

L, %Strong-strong

Weak-strong

Geometric Luminosity Gain due to Crab Sextupoles

Normalised sextupole strength

“..crabbed waist” idea does not provide the significant luminosity enhancement. Explanation could be rather simple: the effective length of the collision area is just comparable with the vertical beta-function and any redistribution of waist position cannot improve very much the collision efficiency…” (I. A. Koop, D.B.Shwatz)

(DANE Example)

Normalised sextupole strength

Suppression of X-Y Resonances

Hor

izon

tal o

scill

atio

ns

sextupole

y

y

yy

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, DANE etc.):

1. low Piwinski angle < 1

2. y comparable with z

Crab Waist On:

1. large Piwinski angle >> 1

2. y comparable with x/

Much higher luminosity!

… and in the ideal case

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

Crab Waist:

1. Eliminates all (!) X-Y resonances

2. However, some horizontal synchrobetatron resonances appear

Here strong beam’s modulation is excluded

(100 times larger y and smaller y)

Qx

Qy

Crab Sextupoles Off

Crab Sextupoles On

Bunch Current

Tails in SuperB

DADANE Upgrade ParametersNE Upgrade ParametersDANEFINUDA

DANE Upgrade

cross/2 (mrad) 12.5 25

x (mmxmrad) 0.34 0.20

x* (cm) 170 20

x* (mm) 0.76 0.20

Piwinski 0.36 2.5

y* (cm) 1.70 0.65

y* (m) 5.4 (low current)

2.6

Coupling, % 0.5 0.5

Ibunch (mA) 13 13

Nbunch 110 110

z (mm) 22 20

L (cm-2s-1) x1032 1.6 10

Larger Piwinski angle

Lower vertical beta

Already achieved

1. With the present DANE parameters (currents, bunch length etc.) a luminosity in excess of 1033 cm-2 s-1 is predicted

2. With 2A on 2A more than 2x1033 is possible

3. Beam-beam limit is well above the reacheable currents

Weak-Strong Beam-Beam Simulation for DANE Upgrade

Luminosity vs tunes scanCrab On 0.6/ Crab Off

0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Lmax = 2.97x1033 cm-2s-1

Lmin = 2.52x1032 cm-2s-1

Lmax = 1.74x1033 cm-2s-1

Lmin = 2.78x1031 cm-2s-1

0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Beam-Beam Tails at (0.057;0.097)(Lifetrack code by D. Shatilov)

Ax = ( 0.0, 12 x); Ay = (0.0, 160 y)

c > 0

c < 0

Siddharta IR Luminosity Scan above half-integers

Lmax = 3.05 x 1033 cm-2s-1

Lmin = 3.28 x 1031 cm-2s-1

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 0.50.55

0.60.65

0.50.55

0.6

0.65

0

1 1033

2 1033

3 1033

0

1 1033

2 1033

3 1033

Strong-Strong Simulations for DANE Upgrade

Crab Waist Off

Crab Waist On

(K. Ohmi, BBSS Simulations)

Single Bunch Luminosity Single Bunch Luminosity

Crab Waist On

damping = 30.000 turns damping = 110.000 turns

x110 bunches = 1033 cm-2 s-1

Emit_x nm 0.8Emit_y nm 0.002Beta_x* mm 9.0Beta_y* mm 0.080Sigm_x* m 2.67Sigm_y* nm 12.6Sigm_z mm 6.0Sigm_e 1.0e-3Cross_angle mrad 2*25Np 1e10 2.5Nb 6000C km 3.0

s msec 10

Collision freq MHz 600Luminosity 1e36 1.0

Defined a parameters set based on ILC-like parameters:• Same DR bunch length

• Same DR bunch charges

• Same DR damping time

• Same ILC-IP betas

• Same DR emittances

• Crossing Angle and Crab Waist to minimize BB blowup

SuperB initial set of parameters

(June 2006)

0

5 1036

1 1037

1,5 1037

2 1037

2,5 1037

0 2,5 1010 5 1010 7,5 1010 1 1011 1,25 1011 1,5 1011

Luminosity [cm-2 s-1]

N0,5

1

1,5

2

2,5

3

3,5

0 3 1010 6 1010 9 1010 1,2 1011 1,5 1011

N

Vertical Emittance Blow Up

Gaussian Fit

rms

0,95

1

1,05

1,1

1,15

0 3 1010 6 1010 9 1010 1,2 1011 1,5 1011

N

Horizontal Emiittance Blow Up

Gaussian Fitrms

0,96

0,98

1

1,02

1,04

1,06

0 3 1010 6 1010 9 1010 1,2 1011 1,5 1011

N

Longitudinal Emittance Blow Up

Gaussian Fit

rms

Luminosity and blowups vs current

To achieve beam-beam limit for the initial set of parameters, Np should be increased by a factor of 2-3, that gives the luminosity exceeding 1037! Actually it means we have rather big margins to relax some critical parameters, and still get the desired luminosity L=1036. The list of parameters to optimize/relax is:

• Damping time• Crossing angle• Bunch length• Bunch current• Number of bunches• Emittances• Betatron coupling• Beta-functions

The relation y x/ must be satisfied in all optimizations!

Optimization Results• Relaxed damping time: 10msec=>16msec

• Relaxed y/x IP s: 80mm/9mm => 300mm/20mm

• Relaxed y/x IP s: 12.6nm/2.67mm => 20nm/4mm

• Relaxed crossing angle: 2*25mrad => 2*17mrad

• Possible to increase bunch length: 6mm => 7mm

• Possible increase in L by further b’s squeeze

• Possible to operate with half of the bunches and twice the bunch charge (same current), with relaxed requirements on y: 2pm => 8pm (1% coupling)

• Possible to operate with half of the bunches and twice the bunch charge (same current), with twice the emittances

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

Lmax = 1.21x1036 cm-2s-1

Lmin = 2.25x1034 cm-2s-1

Qx

Qy

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

SuperB with 2 IP (suggested by A. Variola)

1 IP 2 IP

Lmax = 1.05 x 1036 cm-2 s-1

Lmax = 6.17 x 1033 cm-2 s-1

Lmax = 1.03 x 1036 cm-2 s-1

Lmax = 7.01 x 1033 cm-2 s-1

HER LER

L=1036 cm-2 s-1

Crab=0.8Geom_Crab Crab=0.9Geom_Crab

Beam-Beam Blowup (weak-strong simulations)

Conclusions

1. We hope that now we understand how “Crab Waist” works

2. The expected luminosity increase due to “Crab Waist” is

a) at least, a factor of 6 for the DANE upgrade

b) about 2 orders of magnitude for the SuperB project

(with respect to the existing B-Factories)

3. Let us wait for the first DANE experimental results!

Thank you!