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Crab Waist Collision Studies for e+e- Factories. M. Zobov, P. Raimondi, LNF INFN, Italy D. N. Shatilov, BINP, Novosibirsk K. Ohmi, KEK, Japan. CARE-HHH-APD Mini-Workshop IR’07, INFN, Frascati (Italy), 7-9 November 2007. OUTLINE. Crab Waist Concept Crab Waist Scheme for DA F NE Upgrade - PowerPoint PPT Presentation
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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!