1. Uncertainties in Cooling Simulations R.C. Fernow BNL Synergy Workshop FNAL 13 June 2008

2. R. Fernow - Synergy Workshop2 Cooling performance Cooling performance is characterized by final transverse emittance final longitudinal emittance total transmission yield into accelerator acceptance How confident are we about our predicted performance? Some uncertainties have begun to be addressed experimentally RF gradient limits in magnetic fields beam breakdown of gas-filled RF cavities Are there other potential sources of trouble?

3. 13 June 2008R. Fernow - Synergy Workshop3 Cooling simulations Cooling simulations depend on a lot of things magnetic field in the lattice tracking in magnetic and RF fields and matter RF cavity model mean energy loss model scattering model straggling model decay model initial beam properties collective effects

4. 13 June 2008R. Fernow - Synergy Workshop4 Decay losses determined by relativity, momentum and particle cτ δ(cτ μ ) = 2 10 -3 % and δ(cτ π ) = 2 10 -2 % dominated by uncertainty in actual momentum < 0.1% → only introduces small uncertainty in transmission

5. 13 June 2008R. Fernow - Synergy Workshop5 Mean energy loss normally assume Bethe-Bloch formula for 70-250 MeV/c muons it depends mainly on particle momentum atomic weight density effect ionization potential (logarithmic) PDG quotes ~1% accuracy → only introduces small uncertainty

6. 13 June 2008R. Fernow - Synergy Workshop6 Magnetic field in the lattice uncertainties depend on the type of lattice straight lattices coil placement δ~10 -2 % and current δ~10 -3 % → only introduces small uncertainty [TN 73, Study 2] curved lattices analytic expressions (usually overly-simplified) off-axis expansions (accuracy falls with increasing r) 3D grid (accurate, cumbersome, some interpolation error) → only introduces small uncertainty

7. 13 June 2008R. Fernow - Synergy Workshop7 Tracking in fields normally use 4 th order Runge-Kutta algorithms adaptive step size control is available equations more complicated in Icool (accelerator coordinates) can check by tracking 180 o in constant dipole field for 200 MeV/c muon in 1 T field, path ~ 2 m δx ~ 3 10 -16 m δp x ~ 5 10 -18 GeV/c for 220 MeV/c muon in same field δx < 10 -9 m δp x ~ 6 10 -11 GeV/c comparisons of single tracks Icool vs. DPGeant agreed well [TN 72] → only introduces small uncertainty

8. 13 June 2008R. Fernow - Synergy Workshop8 RF cavity model normally assume cylindrical pillbox can check by importing SuperFish field grids e.g. Study 2a [TN 323] analytic vs SF pillbox δ(μ A /p) ~ 2% SF pillbox vs SF curved windows δ(μ A /p) ~ 4% other uncertainties present for asymmetric cavities e.g. couplers, tuners can use 3D MAFIA grid if necessary → only introduces small uncertainty

9. 13 June 2008R. Fernow - Synergy Workshop9 Initial beam properties ultimately we will want an end-to-end simulation of whole front end each subsystem will have to start with the output of preceding section results will still be dependent on the initial distributions at the target typically comes from independent MARS simulation uncertainties on π production cross sections significant errors ~30%? hopefully handled by E910, HARP, MIPP mercury jet significant quadrupole distortion, cavitation effects? [TN 242] MERIT anomalies in particle rates ???

10. 13 June 2008R. Fernow - Synergy Workshop10 Scattering model MuScat experiment and Alvin’s work helped a lot good agreement of data with Fano, Tollestrup & SAMCS models [TN 336] particles in the tails can have significant cooling effects [TN 144]

11. 13 June 2008R. Fernow - Synergy Workshop11 Scattering in LiH good agreement of Tollestrup & Fano models

12. 13 June 2008R. Fernow - Synergy Workshop12 Effect of scattering Study 2a simulation using Fano vs Tollestrup δ(μ A /p) ~ 1% δ( ε TN ) ~ 8% RFOFO simulation using Fano vs. Tollestrup δ(μ A /p) ~ 0.4% δ( M 6 ) ~ 5% however RFOFO simulation with ELMS is very different δ(μ A /p) ~ +5% δ(M 6 ) ~ +49% !!! scattering and straggling distributions look similar possible that ELMS underestimates large angle scatters? large effect on M 6 is not understood

13. 13 June 2008R. Fernow - Synergy Workshop13 Scattering in strong fields MS theory assumes straight paths between scatters does bending in 20 – 50 T fields affect results? first posed by P. Lebrun in 1999 [TN 30] we are forced to use small stepsize because of field variation naturally gives strong focusing of scattered particles → probably not an issue for cooling simulations

14. 13 June 2008R. Fernow - Synergy Workshop14 Straggling model default model in Icool is Vavilov with Landau limit steps < 2 cm in hydrogen use Landau distribution recent comparisons made with S. Striganov SAMCS code previous simulations may have underestimated straggling by ~15% 200 MeV/c muon in 1 m liquid hydrogen

15. 13 June 2008R. Fernow - Synergy Workshop15 Straggling comparison significant differences in energy loss tails 172 MeV/c muon in 109 mm liquid hydrogen 500K events

16. 13 June 2008R. Fernow - Synergy Workshop16 Effects of straggling Study 2a: Landau vs SAMCS δ(ε TN ) ~ 29% δ(ε LN ) ~ 4% δ(μ A /p) ~ 33% RFOFO: Landau vs SAMCS δ(ε TN ) ~ 9% δ(ε LN ) ~ 16% δ(M 6 ) ~ 28% this is potentially a serious error are there good experimental results for benchmarking?

17. 13 June 2008R. Fernow - Synergy Workshop17 Losses good muon survival is crucial for high flux or high luminosity nagging question: do we model all potential losses accurately? e.g., some channels have particles falling out of the RF bucket

18. 13 June 2008R. Fernow - Synergy Workshop18 Particles falling out of RF bucket Study 2a (overlapped) issue for channels with no longitudinal cooling (NF) do we model this correctly? probably not important for the collider

19. 13 June 2008R. Fernow - Synergy Workshop19 Collective effects almost all cooling simulations so far track single particles some collider scenarios use intense bunches ~3 10 12 there are potential collective effects on cooling, e.g. wakefields in pillbox RF cavities [TN 117] space charge in final cooling stages need to be accurately studied in simulations first may need experimental checks?

20. 13 June 2008R. Fernow - Synergy Workshop20 Summary most aspects of the simulations are fairly well understood there are a few areas of concern π production cross section in p-Hg distortions of Hg jet effect of scattering on 6D cooling muon losses in the channel space charge in final cooling biggest uncertainty at the moment is effect of straggling