Beam-Beam Collision Studies for DA  NE with Crabbed Waist Crabbed Waist Advantages Results for SIDDHARTA IR P.Raimondi, D.Shatilov (BINP), M.Zobov INFN LNF, CSI, 7 November 2006

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

Large Piwinski’s Angle P.Raimondi, M.Zobov, DA  NE Techniocal Note G-58, April 2003 O. Napoly, Particle Accelerators: Vol. 40, pp ,1993 If we can increase N proportionally to   : 1)L grows proportinally to  ;  y remains constant;  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

Low Vertical Beta Function Note that keeping  y constant by increasing the number of particles N proportionally to (1/  y ) 1/2 : (If  x allows...)

yy r yy

ξ y (z-z 0 ) Relative displacement from a bunch center z-z 0 Head-on collision. Flat beams. Tune shift increases for halo particles. Head-on collision. Round beams. ξ y =const. Crossing angle collision.Tune shift decreases for halo particles. Vertical Tune Shift

Vertical Synchro-Betatron Resonances D.Pestrikov, Nucl.Instrum.Meth.A336: ,1993

Crabbed Waist Scheme Sextupole (Anti)sextupole Sextupole strength Equivalent Hamiltonian IP

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).

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

High beta, Low density Low beta, High density yy z Beam-Beam Resonances (Example) Longitudinal Oscillations  (z)

Suppression of X-Y Resonances Horizontal oscillations sextupole 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) QxQx QyQy

Luminosity Scan for Super-PEP (crab focus on) QxQx QyQy

Parameters used in simulations Horizontal IP0.2 m (1.7 m) Vertical IP0.65 cm (1.7 cm) Horizontal tune5.057 Vertical tune5.097 Horizontal emittance0.2 mm.mrad (0.3) Coupling0.5% Bunch length20 mm Total beam current2 A Number of bunches110 Total crossing angle50 mrad (25 mrad) Horizontal beam-beam tune shift0.011 Vertical beam-beam tune shift0.080 L => 2.2 x cm -2 s -1

With the present achieved beam parameters (currents, emittances, bunchlenghts etc) a luminosity in excess of is predicted. With 2Amps/2Amps more than 2*10 33 is possible Beam-Beam limit is way above the reachable currents M. Zobov (BBC Code by Hirata)

Beam-Beam Tails at (0.057;0.097) A x = ( 0.0, 12  x ); A y = (0.0, 160  y )

Siddharta IR Luminosity Scan Crab On --> 0.6/  Crab Off L max = 2.97x10 33 cm -2 s -1 L min = 2.52x10 32 cm -2 s -1 L max = 1.74x10 33 cm -2 s -1 L min = 2.78x10 31 cm -2 s -1

Crab On: Crab Off: Lmax = 2.97 x Lmin = 2.52 x Lmax = 1.74 x Lmin = 2.78 x 10 31

Siddharta IR Luminosity Scan above half-integers L max = 3.05 x cm -2 s -1 L min = 3.28 x cm -2 s -1

for Conclusions The simulations shows that the luminosity enchancement of one order of magnitude is possible in DA  NE with the “crabbed waist” scheme; 2.Such a conclusion is rather conservative since, according to the simulations, the luminosity of 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 σ z (cm) K l (V/Q) W max (V/Q) W min (V/Q) Z / n (mΩ) P (Watts) I = 20 mA N = 110 bunches f 0 = 3.06 MHz 3D model 2D cross-section

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

mode1mode2mode3mode4 Driven mode solution Short circuit at ports F.Marcellini and D. Alesini 150 W