Luminosity of the SuperLuminosity of the Super-T-Tau-au-CCharm harm FFactory actory with with CCrab rab WWaistaist

D. ShatilovD. Shatilov

BINP, NovosibirskBINP, Novosibirsk

TAU’08 Workshop, Satellite Meeting

“On the Need for a Super-Tau-Charm Factory”

26-27 September 2008, BINP, Novosibirsk, Russia

Beam-Beam Studies (step by step)Beam-Beam Studies (step by step)

Determine the main set of parameters (emittances, beta-functions, bunch current, damping decrements, crossing angle, etc.)

Wide range scan of betatron tunes for the simplified model: linear lattice and beam-beam. Two options: with and without Crab Waist.

Select a working point, taking into account the dynamic aperture Investigations.

More detailed simulations, including beam tails (linear lattice yet). Scan for bunch current. Two options: with and without Crab Waist.

Beam-Beam simulations for the actual (nonlinear) lattice: sextupoles and octupoles included.

Set of parametersSet of parameters

Horizontal beta β*x (mm) 20

Vertical beta β*y (mm) 0.76

Horizontal emittance x (nm) 10

Vertical emittance y (nm) 0.1

Bunch length σz (mm) 10

Energy spread σE 10-3

Damping decrements dx,y 9·10-5

Circumference C (m) 810

Number of bunches Nb 380 (1350)

Particles per bunch Np 7·1010

Total beam current I (A) 1.6

Crossing angle (full) (mrad) 34

Piwinski angle 12

“Head-on” tune shifts x, y 0.79, 1.53

Actual tune shifts x, y 0.0054, 0.127

Luminosity L 1035

z

4σx /

σz·/2

2

tgx

zPiwinski angle:

)1( ;

1 ;

22

xx

yx

yy

y

y NNNL

Basic relations for large Piwinski angle:

0.5 0.55 0.6 0.65 0.7 0.75

0.5

0.55

0.6

0.65

0.7

0.75

0.5 0.55 0.6 0.65 0.7 0.75

0.5

0.55

0.6

0.65

0.7

0.75

Betatron Tunes ScanBetatron Tunes Scan

Crab ON: Lmax=1.05·1035 Crab OFF: Lmax=0.44·1035

Np=7·1010 Nb=380 Np=3·1010 Nb=890

Luminosity contour plots in the “geographical map” colors.

Red – maximum, Blue - minimum

Same total beam current

Simulations for the working point (0.533, 0.570)Simulations for the working point (0.533, 0.570)

Crab OFF

Crab ON

Contour plots in the space of normalized betatron amplitudes. Scales (in sigmas): 20100.

Crab Scan for NCrab Scan for Npp=7=7··10101010

Contour plots in the space of normalized betatron amplitudes. Scales (in sigmas): 1050.

optimum

SummarySummary

Luminosity of 1035 can be achieved with the total beam current 1.6 A and

rather small y (can be increased from 0.13 to 0.15÷0.17).

Crab Waist is a key feature, otherwise “mission impossible”.

More detailed simulations with the actual (nonlinear) lattice are required. This will be done as soon as the lattice is ready.