Transcript Document

Luminosity of the Super-Tau-Charm Factory
with Crab Waist
D. Shatilov
BINP, 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)
 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 parameters
Horizontal beta
β*x (mm)
Vertical beta
β*y
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)
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
(mm)
20
4σx /
0.76
810
1035
σz·/

2
z
Piwinski angle:

ztg

x 
2
Basic relations for large Piwinski angle:
  
 
 
N

N

N
y
y
L

;y

;x

2
2

(
1

)

1

y
x
x
y
Betatron Tunes Scan
Luminosity contour plots in the “geographical map” colors.
Red – maximum,
Crab ON:
Np=7·1010
Blue - minimum
Lmax=1.05·1035
Nb=380
Crab OFF:
Same total
beam current
Np=3·1010
Lmax=0.44·1035
Nb=890
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): 20100.
Crab Scan for Np=7·1010
optimum
Contour plots in the space of normalized betatron amplitudes. Scales (in sigmas): 1050.
Summary
 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.