Half Flip 6D Lattice R. B. Palmer, Rick Fernow (BNL) Thursday - - PowerPoint PPT Presentation

Half Flip 6D Lattice

• R. B. Palmer, Rick Fernow

(BNL) Thursday 2/14/13

• Introduction
• lattice types
• Parameters of Half-Flip lattices
• ICOOL simulation using matrices
• Conclusion

1

Cooling Scheme Emit trans (micron) Emit long (mm) Initial Final

150 240

10.0 102 103 104 6 8 2 4 6 8 1.0 2 4 6 8 10.0 2 4 102 Phase Rotation 6D before merge 6D Merge 6D after merge Advanced 3D Cooling Baseline 4D Final Advanced 4D Final

• 2

RFOFO Flip

Radii (cm) Axial Fields (T) Length (cm) 25 50 75 100 125

• 20

20 184 154

• 154
• 184

Bo 11.66 max Bs 15.04 11.49 maxRBJs 260.8 310.0 Brf 10.0

• ◦

3

Non-Flip

Rick: this has no stable orbits, unless very little bending

4

Half Flip

Radii (cm) Axial Field (T) Length (cm) 25 50 75 100 125

• 20

20 114 114

• 114 -114 -114 -114

114 114 beta (cm) Momentum (MeV/c) 150 175 200 225 250 2 4 2π/ 4π 1.5π/ 3π 1π/ 2π no tilt/ tilt

• Without bending all cells have identical focusing (∝ B2)
• With bending (Guggenheim), or coil tilting (Balbakov) the symmetry is broken

and a resonance exists in the center of the pass band

• But the coil tilts are very small and this resonance may not be too bad

5

Coil dimensions

file β cell L dL R dR j cm cm cm cm cm cm A/mm2 70 5.2 68.75 3.000 28.000 18.000 15.000 117.26 71 4.6 68.75 0.000 29.000 18.000 15.000 105.77 72 3.9 68.75 0.000 13.000 12.000 15.000 96.80 13.000 16.000 18.000 15.000 96.85 74 2.9 58 4.218 8.436 5.905 21.091 158.14 12.655 6.327 19.404 7.593 134.22 76 2.1 58 1.687 10.967 4.218 16.873 153.79 77 1.6 58 0.000 10.967 4.218 16.873 158.75

• locations and dimensions are symmetric left-right in each cell
• currents are reversed left-right in each cell
• when there are two lines for one file, there are two coils per half cell

6

j vs B for required 3 cm betas

B on coil (T) j (a/mm2) RFOFO flip magenta Half flip lattices red shorter blue longer Non-flip black 10 20 30 6 7 8 9 2 3 4 102 42 3

• ◦
• 3
• 3
• ◦
• 3

60% YBCO good direction 50% BSCCO cable ≈ YBCO bad direction 25% NbTi 1.9 25% NbSn 1.9

• Half flip design uses less fields on coils than Non-flip but its cells are longer
• They are now ok for both Nb3Sn and YBCO in the bas direction
• In addition, the field lines are more axial than in the flip lattice

7

j vs B extended to lower betas

B on coil (T) j (a/mm2) RFOFO flip magenta Half flip lattices red shorter blue longer Non-flip black 1.8 10 20 30 6 7 8 9 2 3 4 102 42 3

• ◦
• 1.6
• 3◦
• 1.6
• 3
• ◦
• 3
• 60% YBCO good direction

50% BSCCO cable ≈ YBCO bad direction 25% NbTi 1.9 25% NbSn 1.9

• Half flip solution probably ok to 1.6 cm with longer cells
• This should cool to 150 µm for the enhanced performance goal

8

ICOOL using matrices for half-flip with longer cells

200 400 600 0.1 1.0 10.0 102 103 freq 805 45 222324252627282930 31 70 71 72 74 76 77 length (m) 0.24 46.25 1.98 0.15 ǫ ⊥ mm 31.59 Transm % 1.91 ǫ mm

• Performance should be a little better with shorter cells
• And this has not been optimized yet

9

Conclusion

ǫ⊥=240 µm ǫ⊥=150 µm case files Len ǫ

• Trnsm. % Len

ǫ

• Trnsm. %

1 tap16a0 RFOFO 470 2.1 47.3 3 tap16a5v Non-flips 375 2.1 53.7 471 2.15 46.2 3 tap16a5x Half flips 410 1.98 46.2 510 1.91 31.6

• Half-Flip lattice meets current density requirements
• And meets minimum cooling requirements (240 µm)

– More losses than Non-Flip – But about the same as original RFOFO Flip lattices

• Even meets extended cooling requirement (150 µm)

– But with more losses than Non-Flip

• But may have additional losses from resonance in center of acceptance if

bending one way

• Rick:

Simple coil tilts did not give enough dispersion – Perhaps the Valeri Balbakov version would allow more flexibility in the generation of dispersion

• Needs real simulation with/without Balbakov modification

10