1. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Alex Bogacz Dogbone configuration orbit separation simultaneous acceleration of both  +  - species 12.5 GeV Two-step-Dogbone RLA Quadrupole focusing scheme – Triplet vs FODO lattices multi-pass linac optics ‘droplette’ Arcs matching to the Arcs 5 GeV Dogbone RLA (3.5 pass) – Complete lattice design, sensitivity studies 15 GeV Dogbone RLA (6.5 pass)? Dogbone RLA – Design Choices

2. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Simultaneous acceleration of both  +   species             EE E0E0 E 0 + (n+½)  E orbit separation, energy difference between consecutive passes: 2  E

3. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. 12.5 GeV Two-step-Dogbone RLA 2 GeV to 5 GeV 5 GeV to 12.5 GeV the same energy ratio for both dogbones: 2 GeV 0.3 GeV 1 GeV/pass 5 GeV 2 GeV/pass 12.5 GeV EfEf E0E0 = 2.5

4. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. 12.5 GeV Two-step-Dogbone RLA 2 GeV to 5 GeV 5 GeV to 12.5 GeV the same energy ratio for both dogbones: 2 GeV 0.3 GeV 1 GeV/pass 5 GeV 2 GeV/pass 12.5 GeV EfEf E0E0 = 2.5

5. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Injection double-chicane      

6. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Initial beam emittance/acceptance after cooling at 273 MeV/c Study IIb  rms A = (2.5) 2  normalized emittance:  x /  y mm  rad 4.830 longitudinal emittance:  l  l   p  z /m  c) momentum spread:   p/p bunch length:  z mm 27 0.07 176 150  0.17  442

7. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Pre-accelerator  different style cryo-modules ShortMediumLong Number of periods121822 Total length of one period3 m5 m8 m Number of cavities per period 112 Number of cells per cavity122 Cavity accelerating gradient15 MV/m Real-estate gradient3.72 MV/m4.47 MV/m5.59 MV/m Aperture in cavities (2a)460 mm Aperture in solenoids (2a)460 mm Solenoid length1 m Solenoid maximum field1.5 T1.9 T3.9 T

8. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Introduction of synchrotron motion in the initial part of the linac  p/p=  0.17or  =  93 (200MHz)

9. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Linear Pre-accelerator – Longitudinal dynamics

10. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Symmetric ‘Dogbone’ RLA (3.5-pass) Scheme Main Linac (2 GeV/pass) 3 ‘droplet’ Arcs based on periodic cells (90 0 betatron phase advance per cell)    

11. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. FODO vs Triplet focusing structure FODO Triplet Advantages: much weaker quads (~3 times) shorter quads (total) easier chromaticity correction Advantages: longer straight sections smaller vertical beta-function uniform variation of betas and dispersion The same length The same phase advance per cell (  x = 90 0 =  y )

12. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Triplet - ‘flat focusing' linac profile ‘half pass’, 2-3 GeV 1-pass, 3-5 GeV mirror symmetry cond. (  out n =  in n+1,and  out n = -  in n+1, n - pass index) Initial phase adv/cell 90 deg – constant quad grarients for the entire linac phase adv. drops much faster in the horizontal plane

13. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Triplet - ‘flat focusing' linac profile 2-pass, 5-7 GeV 3-pass, 7-9 GeV mirror symmetry cond. (  out n =  in n+1,and  out n = -  in n+1, n - pass index) phase adv. drops much faster in the horizontal plane no phase adv. in the horizontal plane

14. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. FODO - ‘flat focusing' linac profile ‘half pass’, 2-3 GeV 1-pass, 3-5 GeV mirror symmetry cond. (  out n =  in n+1,and  out n = -  in n+1, n - pass index) initial phase adv/cell 90 deg – fixed gradient in all cells phase adv. drifting uniformly in both planes

15. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. FODO - ‘flat focusing' linac profile 2-pass, 5-7 GeV 3-pass, 7-9 GeV mirror symmetry cond. (  out n =  in n+1,and  out n = -  in n+1, n - pass index)

16. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. FODO - ‘flat focusing' linac profile 4-pass, 9-11 GeV 5-pass, 11-13 GeV mirror symmetry cond. (  out n =  in n+1,and  out n = -  in n+1, n - pass index)

17. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. ‘flat focusing' linac profile 6-pass, 13-15 GeV mirror symmetry cond. (  out n =  in n+1,and  out n = -  in n+1, n - pass index)

18. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Phase slippage in the linac E 0 = 2 GeV  E 0 = 2 GeV

19. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Arc 1  Layout Arc dipoles $Lb=150; => 150 cm $ang0=10.3283; => 10.328 deg $Nin=16; => 16 $Nout=2; => 2 $ang=(90+$ang0)/($Nin-2*$Nout); => 8.36 deg. # $Ang_out=$ang0+2*$Nout*$ang; => 43.77 deg. $Ang_in=2*$Nin*$ang; => 267.54 deg. $BP=$PI*$Hr*$ang/(180*$Lb); => 6.537 kGauss $Lring=227.3 m

20. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Droplet Arc – Optics ‘Building Blocks’ 90 0 phase advance/cell: inward and outward cells, missing dipole, empty cells

21. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Arc 1 – Mirror-symmetric Optics dipoles (2 per cell) $Lb=150; => 150 cm $ang0=10.3283 deg $ang=(90+$ang0)/($Nin-2*$Nout); => 8.36 deg $B=$PI*$Hr*$ang/(180*$Lb); => 6.537 kGauss quadrupoles (triplet): L[cm] G[kG/cm] 68 -0.326 125 0.328 68 -0.326 16 cells 2 cells (  out =  in,and  out = -  in, matched to the linacs) $Nout=2, need minimum of 3 triplets to match 6 Twiss parameters

22. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Straight-Arc  P eriodic transition Triplet FODO

23. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. 15 GeV Dogbone RLA (6.5 pass) energy ratio: 2 GeV 0.3 GeV EfEf E0E0 = 7.5 2 GeV/pass 15 GeV

24. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. 15 GeV Dogbone RLA (6.5 pass) energy ratio: 2 GeV 0.3 GeV EfEf E0E0 = 7.5 2 GeV/pass 15 GeV

25. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Beam Separation  Switchyard 5 GeV 9 GeV 13 GeV

26. Operated by the Jefferson Science Associates for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Dogbone RLA – Design Choices NuFact’06, UC Irvine, August 29, 2006. Summary ‘Dogbone’ RLA – preferred configuration better orbir separation for higher passes offers symmetric solution for simultaneous acceleration of  + and  - FODO lattice more favorable (compared to the triplet) to accommodate large number of passes uniform phase advance decrease in both planes smaller variation of Twiss function – easier match to the Arcs Proposed 12.5 GeV two-step-dogbone RLA (30 mm rad acceptance) 3.5 pass 5 GeV Dogbone (triplet lattices) – error sensitivity studies Magnet misalignment error analysis (DIMAD Monte Carlo on the above lattice) shows quite manageable level of orbit distortion for ~1 mm level of magnet misalignment error. Great focusing errors tolerance for the presented lattice  1% of Arc-to-Arc betatron mismatch limit sets the quadrupole field spec at 0.2% Aggressive 15 GeV dogbone RLA