1. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 1 Study of Low-  p Lattice Options for a Super-PEP HER U. Wienands SLAC PEP-II

2. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 2 Context for the Super-PEP HER Would like to maintain  dipole =165 m –∆E/turn ≈ 2.2 MV at 8.5 GeV,  1/   –every arc-cell filled with a dipole in PEP-II Will likely want a smaller emittance than for PEP-II –PEP-II HER has 48 nmr nominal –For Super-B, will likely want to reduce this to 40 or even 28 nmr. Will want a low momentum-compaction factor –PEP-II: 0.00241–>0.00167 –Super-B: 0.0006…0.0001

3. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 3 How to Achieve low a p  p ≈  => high tune x –practical limit, acceptance limit –also reduces the beam emittance Modulate bending or focusing, forcing  down in dipoles –Teng & Ohnuma: ≤360° phase advance/period –Potential to reduce  p < 0 –Potentially increases beam emittance (≈ B 2 )

4. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 4 Candidate Superperiods 90° cells: –LEB-type Period: DOFO with BB00BB bending high dispersion in empty cells, low/negative in bending cells dipole packing factor is low –KAON-Factory type cell: FODO, full cells, modulate quads high packing factor large dispersion swings for low/negative  p In either of these, emittance is traded for momentum compaction.

5. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 5 HER Sextant, 90° cell  p = 0.0006  x = 50 nmr 4 periods+nsup=16 cells  dipole = 165 m

6. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 6 What about negative  p ?  p = -0.0002/period, but +0.00028/sext.  x = 68 nmr 4 periods+nsup=16 cells  dipole = 165 m

7. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 7 Can’t get negative  p easily, and  x already too large It turns out the  suppressors raise  p considerably –  p = (  p (periods)*l periods +  p (  sup )*l sup )/l arc –  p (  sup ) is large, therefore have to make these short! Shorten the dipoles in the high-  cells to lower  x –this lowers the bending radius…

8. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 8

9. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 9 Not promising! –lowest emittance achieved: 56 nmr (empty high-h cells) –sr. energy loss up by more than a factor of 2

10. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 10 Half-length Dipoles in High-  cells  p = +0.00025/sext.  x = 61 nmr 4 periods+nsup=16 cells  dipole = 139 m

11. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 11 Where to go from here? For our case, shortening the  suppressors only marginally sucessful –overall arc length has to stay due to tunnel geometry –=> dipoles get longer, or stronger => emittance  Need to look into more exotic alternatives –start with stronger focusing –108°/cell, 135°/cell, … –lower natural emittance, –less modulation needed to lower ap to desired value

12. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 12 Try 135°/cell –one period = two cells: 270° –should be able to lower  p by quad. modulation –should be able to find 180° locations for sextupoles…

13. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 13 135°/cell Period,  p =0  p = 0/cell  x = 20 nmr 7 periods+nsup=16 cells  dipole = 165 m

14. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 14 135° Lattice (cont’d) Closer inspection of this lattice reveals that –X chromaticity compensation should be easy –Y chromaticity compensation ≈ impossible high ßy locations have almost no dispersion –  Can we modify design for vertical chroma. correction –idea: raise ß y at high-dispersion location

15. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 15 135° Lattice with Doublet

16. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 16 Raise ß y /ß x at end to about 3:1 –may be sufficient in principle But: –  y now up to 7 units in ∂ /(∂p/p), – likely too high for required acceptance

17. U. Wienands, SLAC-PEP-II Super-B Hawaii Apr-05 17 Conclusion (for now) As expected, a low-  p lattice for a Super-PEP HER is not easy to find. For 90°/cell,  p ≈ 0.0006 seems to be about as low as it will go, in the PEP-II context (  x, tunnel, s.r.) –very preliminary tracking suggests chromaticity correction is feasible. For comparison, the 90° HER lattice for PEP-II will have  p ≈ 0.00167. For 135°/cell, lower  p is feasible to 1 st order, but chromaticity correction will be a major challenge.