BeamBeam Collision Studies for DAFNE with Crabbed Waist

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Beam-Beam Collision Studiesfor DAFNE with
Crabbed Waist

• Crabbed Waist Advantages
• Results for SIDDHARTA IR

P.Raimondi, D.Shatilov (BINP), M.Zobov INFN LNF,
CSI, 7 November 2006
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Crabbed Waist in 3 Steps

• Large Piwinskis angle F tg(q)sz/sx
• Vertical beta comparable with overlap area by
  sx/q
• Crabbed waist transformation y xy/(2q)

P. Raimondi, November 2005
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Crabbed Waist Advantages

• Geometric luminosity gain
• Very low horizontal tune shift

• Large Piwinskis angle
• F tg(q)sz/sx
• 2. Vertical beta comparable
• with overlap area
• by sx/q
• 3. Crabbed waist transformation
• y xy/(2q)

• Geometric luminosity gain
• Lower vertical tune shift
• Vertical tune shift decreases with oscillation
  amplitude
• Suppression of vertical synchro-betatron
  resonances

• Geometric luminosity gain
• Suppression of X-Y betatron and synchro-betatron
  resonances

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..and besides,

• There is no need to increase excessively beam
  current and to decrease the bunch length
• Beam instabilities are less severe
• Manageable HOM heating
• No coherent synchrotron radiation of short
  bunches
• No excessive power consumption
• The problem of parasitic collisions is
  automatically solved due to higher crossing angle
  and smaller horizontal beam size

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Large Piwinskis Angle
P.Raimondi, M.Zobov, DAFNE Techniocal Note G-58,
April 2003
O. Napoly, Particle Accelerators Vol. 40, pp.
181-203,1993

• If we can increase N proportionally to F
• L grows proportinally to F
• xy remains constant
• xx decreases as 1/F

• F is increased by
• increasing the crossing angle q and increasing
  the bunch length sz for LHC upgrade (F. Ruggiero
  and F.Zimmermann)
• increasing the crossing angle q and decreasing
  the horizontal beam size sx in crabbed waist
  scheme

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Low Vertical Beta Function
Note that keeping xy constant by increasing the
number of particles N proportionally to (1/by)1/2

(If xx allows...)
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by
by
r
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Vertical Tune Shift
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Vertical Synchro-Betatron Resonances
D.Pestrikov, Nucl.Instrum.Meth.A336427-437,1993
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Crabbed Waist Scheme
Sextupole
(Anti)sextupole
IP
Sextupole strength
Equivalent Hamiltonian
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Geometric Factors

• Minimum of by along the maximum density of the
  opposite beam
• Redistribution of by along the overlap area. The
  line of the minimum beta with the crabbed waist
  (red line) is longer than without it (green line).

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Geometric Factors (2)
Geom. gain
Geom. gain
..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)
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Beam-Beam Resonances (Example)
by
High beta, Low density
Low beta, High density
r(z)
z
Longitudinal Oscillations
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Suppression of X-Y Resonances
Horizontal oscillations
sextupole

• Performing horizontal oscillations
• Particles see the same density and the same
  (minimum) vertical beta function
• The vertical phase advance between the sextupole
  and the collision point remains the same (p/2)

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Luminosity Scan for Super-PEP (crab focus off)
Qy
Qx
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Luminosity Scan for Super-PEP (crab focus on)
Qy
Qx
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Parameters used in simulations
L gt 2.2 x 1033 cm-2 s-1
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M. Zobov
(BBC Code by Hirata)
With the present achieved beam parameters
(currents, emittances, bunchlenghts etc) a
luminosity in excess of 1033 is predicted. With
2Amps/2Amps more than 21033 is
possible Beam-Beam limit is way above the
reachable currents
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Beam-Beam Tails at (0.0570.097)
Ax ( 0.0, 12 sx) Ay (0.0, 160 sy)
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Siddharta IR Luminosity Scan
Crab On --gt 0.6/q
Crab Off
Lmax 2.97x1033 cm-2s-1 Lmin 2.52x1032 cm-2s-1
Lmax 1.74x1033 cm-2s-1 Lmin 2.78x1031 cm-2s-1
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Crab On
Lmax 2.97x1033 Lmin 2.52x1032
Crab Off
Lmax 1.74x1033 Lmin 2.78x1031
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Siddharta IR Luminosity Scan above half-integers
Lmax 3.05 x 1033 cm-2s-1 Lmin 3.28 x 1031
cm-2s-1
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for Conclusions.....

• The simulations shows that the luminosity
  enchancement of one order of magnitude is
  possible in DAFNE with the crabbed waist
  scheme
• 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.

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S.Tomassini, 27/09/2006
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B.Spataro and M.Zobov, 04/10/2006
MAFIA Time Domain Simulations
I 20 mA N 110 bunches f0 3.06 MHz
3D model
2D cross-section
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B.Spataro and M.Zobov, 13/10/2006
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Driven mode solution Short circuit at ports
150 W
F.Marcellini and D. Alesini
mode1
mode2
mode3
mode4