Beam-Beam Collision Studiesfor DANE with Crabbed Waist

• Crabbed Waist Advantages• Results for SIDDHARTA IR

P.Raimondi, D.Shatilov (BINP), M.Zobov

INFN LNF, CSI, 7 November 2006

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. Crabbed waist transformation y = xy’/(2)

Crabbed Waist in 3 Steps

P. Raimondi, November 2005

1. Large Piwinski’s angle

= tg(z/x

2. Vertical beta comparable

with overlap area

y x/

3. Crabbed waist transformation

y = xy’/(2)

Crabbed 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 Techniocal 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 proportinally to ;

2 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...)

y

ryy

y

rE

1

ξy(z-z0)

Relative displacementfrom a bunch center

z-z0

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

Head-on collision.Round beams. ξy=const.

Crossing angle collision.Tune shiftdecreases for halo particles.

Vertical Tune Shift

Vertical Synchro-Betatron Resonances

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

x

y 2

x

y 2

Crabbed 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

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 crabbed waist (red line) is longer than without it (green line).

*

2* /

yyy

xs

0

5 1035

1 1036

1,5 1036

2 1036

2,5 1036

0 100 200 300 400 500

crab, simulationsgeometric factorsno crab, simulations

y [m]

Luminosity [cm-2 s-1]

Geometric Factors (2)

..”crabbed waist” idea does not provide the significant luminosity enchancement. 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 and D.B.Shwartz (BINP)

Geom. gain

Geom. gain

High beta, Low densityLow beta, High density

y

z

Beam-Beam Resonances (Example)

Longitudinal Oscillations

(z)

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)

Luminosity Scan for Super-PEP (crab focus off)

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

Qx

Qy

Luminosity Scan for Super-PEP (crab focus on)

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

Qx

Qy

Parameters used in simulationsHorizontal beta @ IP 0.2 m (1.7 m)

Vertical beta @ IP 0.65 cm (1.7 cm)

Horizontal tune 5.057

Vertical tune 5.097

Horizontal emittance 0.2 mm.mrad (0.3)

Coupling 0.5%

Bunch length 20 mm

Total beam current 2 A

Number of bunches 110

Total crossing angle 50 mrad (25 mrad)

Horizontal beam-beam tune shift 0.011

Vertical beam-beam tune shift 0.080

L => 2.2 x 1033 cm-2 s-1

0

2

4

6

8

10

12

14

0 10 20 30 40 50

200um,20mm200um,15mm100um,15mm

I [mA]

L [10^33]

With the present achieved beam parameters (currents, emittances, bunchlenghts etc) a luminosity in excess of 1033 is predicted.With 2Amps/2Amps more than 2*1033 is possibleBeam-Beam limit is way above the reachable currents

M. Zobov(BBC Code by Hirata)

Beam-Beam Tails at (0.057;0.097)

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

Siddharta IR Luminosity Scan

Crab 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

Crab On:

Crab Off:

Lmax = 2.97x1033

Lmin = 2.52x1032

Lmax = 1.74x1033

Lmin = 2.78x1031

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

for Conclusions.....

1. The simulations shows that the luminosity enchancement of one order of magnitude is possible in DANE with the “crabbed waist” scheme;

2. Such a conclusion is rather conservative since, according to the simulations, the luminosity of 1033 cm-2 s-1 can be obtained even without the “crabbing” sextupoles.

S.Tomassini, 27/09/2006

MAFIA Time Domain Simulations

B.Spataro and M.Zobov, 04/10/2006

σz

(cm)

Kl

(V/Q)

Wmax

(V/Q)

Wmin

(V/Q)

Z / n(mΩ)

P (Watts)

1 3.589 1010 1.382 1011 -9.577 1010 12.2 516

1.5 1.260 1010 4.152 1010 -4.717 1010 8.24 181

2. 5.766 109 2.699 1010 -2.777 1010 9.52 83

2.5 2.609 109 2.101 1010 -1.833 1010 11.58 38

3.0 1.104 109 1.602 1010 -1.300 1010 12.71 16

I = 20 mA

N = 110 bunches

f0 = 3.06 MHz

3D model 2D cross-section

-5

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6

Re[

Z](

)

Freq[GHz]

-10

0

10

20

30

40

0 1 2 3 4 5 6

Im[Z

](

)

Freq[GHz]

-1

-0.5

0

0.5

1

1.5

0 1 2 3 4 5 6

scal

ed w

ake

pot

enti

al

distance from bunch head (m)

B.Spataro and M.Zobov, 13/10/2006

mode1 mode2 mode3 mode4

Driven mode solutionShort circuit at ports

F.Marcellini and D. Alesini

150 W