Post-merge Guggenheim stage 12

R.C. FernowBNL

AAG Thursday Meeting

27 December 2012

2

Introduction

• we have been working on post-merge Guggenheim channel ring simulationscurved lattice cellsdipole fields from tipping the solenoidsgenerate Icool field maps in cylindrical coordinatesemittance exchange by tracking thru wedgesuses RF Be windows scaled from Study 2

• we have working files for all the (11) flip stages• now looking at first non-flip stage

3

Small ring

• first tried small ring (ρ = 1.53 m), similar to last flip lattice• could not find a reasonable closed orbit• tried varying starting parameters for orbit finder by hand• computed 2D beta functions were not reasonable• transmission thru cooling cell was very small

4

Larger ring

• looked at larger ring with ρ = 5.47 m•found a good closed orbit solution•2D beta functions still bad ( β ~ 2 mm, should be ~5.9 cm)•dispersion was small D = 3.3 cm•for 120o wedge

met reference emittance goals for this stageεTN = 0.432 mm, εLN = 2.37 mm after 12 cells

•but transmission was very poor ~0.476

5

Still larger ring

• looked at even larger ring with ρ = 10.95 m•found a good closed orbit•beta functions were still bad ( β ~ 2 mm)•dispersion was very small D = 1.7 cm•for 120o wedge

not able to meet both reference emittance goals for this stageεTN = 0.452 mm, εLN = 2.68 mm after 39 cellstransmission increased, but was still poor ~0.707

•tried wedge angles up to 140o

but was unable to reach the longitudinal emittance goal

6

Eigenvalue analysis

ρ [m] mag phase mag phase

5.47 1.000000 ±170.93 0.999999 ±5.83

10.95 1.000000 ±170.93 0.999999 ±5.83

∞ 1.000011 ±169.45 0.999989 ±6.08

• for ∞ case, both eigenvalues must be the same• possible trouble with

intrinsic design of the lattice ?errors or bad approximations in the simulation ?methods used in the analysis program ?

• currently looking with Scott at eigenvalues of the one-cell transport matrix• trying to find evidence for the source of poor performance