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” 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) 20 Vertical beta β * y (mm) 0.76 Horizontal emittance  x (nm) 10 Vertical emittance  y (nm) 0.1 Bunch length σ z (mm) 10 Energy spread σ E Damping decrements d x,y 9·10 -5 Circumference C (m) 810 Number of bunches N b 380 (1350) Particles per bunch N p 7·10 10 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 , Luminosity L10 35  z 4 σ x /  σ z ·  /2 Piwinski angle: Basic relations for large Piwinski angle:

Betatron Tunes Scan Crab ON: L max =1.05·10 35 Crab OFF: L max =0.44·10 35 N p =7·10 10 N b =380 N p =3·10 10 N b =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) Crab OFF Crab ON Contour plots in the space of normalized betatron amplitudes. Scales (in sigmas): 20  100.

Crab Scan for N p =7·10 10 Contour plots in the space of normalized betatron amplitudes. Scales (in sigmas): 10  50. optimum

Summary  Luminosity of 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.