Computed Pion Yields from a Tantalum Rod Target

1. m Computed Pion Yields from a Tantalum Rod Target Comparing MARS15 and GEANT4 across proton energies Stephen Brooks, Kenny Walaron NuFact’05

2. Contents • Benchmark problem • Physics models and energy ranges • MARS15 model • GEANT4 “use cases” • Effects on raw pion yield and angular spread • Probability map “cuts” from tracking • Used to estimate muon yields for two different front-ends, using both codes, at all energies Stephen Brooks, Kenny Walaron NuFact’05

3. Benchmark Problem Pions • Pions counted at rod surface • B-field ignored within rod (negligible effect) • Proton beam assumed parallel • Circular parabolic distribution, rod radius Protons 1cm Solid Tantalum 20cm Stephen Brooks, Kenny Walaron NuFact’05

4. Possible Proton Energies Stephen Brooks, Kenny Walaron NuFact’05

5. Total Yield of p+ and p− Normalised to unit beam power NB: Logarithmic scale! Stephen Brooks, Kenny Walaron NuFact’05

6. Angular Distribution: MARS15 What causes the strange kink in the graph between 3GeV and 5GeV? Stephen Brooks, Kenny Walaron NuFact’05

7. MARS15 Uses Two Models • The “Cascade-Exciton Model” CEM2003 for E<5GeV • “Inclusive” hadron production for E>3GeV • Nikolai Mokhov says: A mix-and-match algorithm is used between 3 and 5 GeV to provide a continuity between the two domains. The high-energy model is used at 5 GeV and above. Certainly, characteristics of interactions are somewhat different in the two models at the same energy. Your results look quite reasonable, although there is still something to improve in the LANL's low-energy model, especially for pion production. The work is in progress on that. A LAQGSM option coming soon, will give you an alternative possibility to study this intermediate energy region in a different somewhat more consistent way. Stephen Brooks, Kenny Walaron NuFact’05

8. Angular Distribution: +GEANT4 GEANT4 appears to have its own ‘kink’ between 15GeV and 30GeV Stephen Brooks, Kenny Walaron NuFact’05

9. GEANT4 Hadronic “Use Cases” Stephen Brooks, Kenny Walaron NuFact’05

10. Total Yield of p+ and p−: +GEANT4 Stephen Brooks, Kenny Walaron NuFact’05

11. Raw Pion Yield Summary • It appears that an 8-30GeV proton beam: • Produces roughly twice the pion yield… • …and in a more focussed angular cone ...than the lowest energies. • Unless you believe the BIC model! • Also: the useful yield is crucially dependent on the capture system. Stephen Brooks, Kenny Walaron NuFact’05

12. Tracking through Two Designs • Both start with a solenoidal channel • Possible non-cooling front end: • Uses a magnetic chicane for bunching, followed by a muon linac to 400±100MeV • RF phase-rotation system: • Line with cavities reduces energy spread to 180±23MeV for injecting into a cooling system Stephen Brooks, Kenny Walaron NuFact’05

13. Fate Plots • Pions from one of the MARS datasets were tracked through the two front-ends and plotted by (pL,pT) • Coloured according to how they are lost… • …or white if they make it through • This is not entirely deterministic due to pion  muon decays and finite source Stephen Brooks, Kenny Walaron NuFact’05

14. Fate Plot for Chicane/Linac (Pion distribution used here is from a 2.2GeV proton beam) Stephen Brooks, Kenny Walaron NuFact’05

15. Fate Plot for Phase Rotation Stephen Brooks, Kenny Walaron NuFact’05

16. Probability Grids • Can bin the plots into 30MeV/c squares and work out the transmission probability within each Chicane/Linac Phase Rotation Stephen Brooks, Kenny Walaron NuFact’05

17. Probability Grids • Can bin the plots into 30MeV/c squares and work out the transmission probability within each • These can be used to estimate the transmission quickly for each MARS or GEANT output dataset for each front-end Stephen Brooks, Kenny Walaron NuFact’05

18. Chicane/Linac Transmission (MARS15) Energy dependency is much flatter now we are selecting pions by energy range Stephen Brooks, Kenny Walaron NuFact’05

19. Phase Rotator Transmission (MARS15) Stephen Brooks, Kenny Walaron NuFact’05

20. Chicane/Linac Transmission (GEANT4) Stephen Brooks, Kenny Walaron NuFact’05

21. Phase Rotator Transmission (GEANT4) Stephen Brooks, Kenny Walaron NuFact’05

22. Conclusions (energy choice) • While 30GeV may be excellent in terms of raw pion yields, the pions produced at higher energies are increasingly lost due to their large energy spread • Optimal ranges appear to be: Stephen Brooks, Kenny Walaron NuFact’05

23. Conclusions (codes, data) • GEANT4 ‘focusses’ pions in the forward direction a lot more than MARS15 • Hence double the yields in the front-ends • Binary cascade model needs to be reconciled with everything else • Other models say generally the same thing, but variance is large • Need HARP data in the range of interest! Stephen Brooks, Kenny Walaron NuFact’05

24. References • S.J. Brooks, Talk on Target Pion Production Studies at Muon Week, CERN, March 2005; http://stephenbrooks.org/ral/report/ • K.A. Walaron, UKNF Note 30: Simulations of Pion Production in a Tantalum Rod Target using GEANT4 with comparison to MARS; http://hepunx.rl.ac.uk/uknf/wp3/uknfnote_30.pdf Stephen Brooks, Kenny Walaron NuFact’05

25. Stephen Brooks, Kenny Walaron NuFact’05

26. Energy Deposition in Rod (heat) • Scaled for 5MW total beam power; the rest is kinetic energy of secondaries Stephen Brooks, Kenny Walaron NuFact’05

27. Total Yield of p+ and p− From a purely target point of view, ‘optimum’ moves to 10-15GeV • Normalised to unit rod heating (p.GeV = 1.6×10-10 J) Stephen Brooks, Kenny Walaron NuFact’05

28. Angular Distribution 2.2GeV 6GeV Backwards p+ 18% p− 33% 8% 12% 15GeV 120GeV 8% 11% 7% 10% Stephen Brooks, Kenny Walaron NuFact’05

29. Possible Remedies • Ideally, we would want HARP data to fill in this “gap” between the two models • K. Walaron at RAL is also working on benchmarking these calculations against a GEANT4-based simulation • Activating LAQGSM is another option • We shall treat the results as ‘roughly correct’ for now, though the kink may not be as sharp as MARS shows Stephen Brooks, Kenny Walaron NuFact’05

30. Simple Cuts • It turns out geometric angle is a badly-normalised measure of beam divergence • Transverse momentum and the magnetic field dictate the Larmor radius in the solenoidal decay channel: Stephen Brooks, Kenny Walaron NuFact’05

31. Simple Cuts • Acceptance of the decay channel in (pL,pT)-space should look roughly like this: pT Larmor radius = ½ aperture limit pTmax Pions in this region transmitted qmax pL Angular limit (eliminate backwards/sideways pions) Stephen Brooks, Kenny Walaron NuFact’05

32. Simple Cuts • So, does it? • Pions from one of the MARS datasets were tracked through an example decay channel and plotted by (pL,pT) • Coloured green if they got the end • Red otherwise • This is not entirely deterministic due to pion  muon decays and finite source Stephen Brooks, Kenny Walaron NuFact’05

33. Simple Cuts • So, does it? Stephen Brooks, Kenny Walaron NuFact’05

34. Simple Cuts • So, does it? Roughly. Stephen Brooks, Kenny Walaron NuFact’05

35. Simple Cuts • So, does it? Roughly. • If we choose: • qmax = 45° • pTmax = 250 MeV/c • Now we can re-draw the pion yield graphs for this subset of the pions Stephen Brooks, Kenny Walaron NuFact’05

36. Cut Yield of p+ and p− • Normalised to unit beam power (p.GeV) High energy yield now appears a factor of 2 over low energy, but how much of that kink is real? Stephen Brooks, Kenny Walaron NuFact’05

37. Cut Yield of p+ and p− This cut seems to have moved this optimum down slightly, to 8-10GeV • Normalised to unit rod heating Stephen Brooks, Kenny Walaron NuFact’05

38. Chicane/Linac Transmission 6-10GeV now looks good enough if we are limited by target heating • Normalised to unit rod heating Stephen Brooks, Kenny Walaron NuFact’05

39. Phase Rotator Transmission • Normalised to unit rod heating Stephen Brooks, Kenny Walaron NuFact’05

40. Stephen Brooks, Kenny Walaron NuFact’05

41. Rod with a Hole • Idea: hole still leaves 1-(rh/r)2 of the rod available for pion production but could decrease the path length for reabsorption Rod cross-section r rh Stephen Brooks, Kenny Walaron NuFact’05

42. Rod with a Hole • Idea: hole still leaves 1-(rh/r)2 of the rod available for pion production but could decrease the path length for reabsorption • Used a uniform beam instead of the parabolic distribution, so the per-area efficiency could be calculated easily • r = 1cm • rh = 2mm, 4mm, 6mm, 8mm Stephen Brooks, Kenny Walaron NuFact’05

43. Yield Decreases with Hole 30 GeV 2.2 GeV Stephen Brooks, Kenny Walaron NuFact’05

44. Yield per Rod Area with Hole 30 GeV 2.2 GeV This actually decreases at the largest hole size! Stephen Brooks, Kenny Walaron NuFact’05

45. Rod with a Hole Summary • Clearly boring a hole is not helping, but: • The relatively flat area-efficiencies suggest reabsorption is not a major factor • So what if we increase rod radius? • The efficiency decrease for a hollow rod suggests that for thin (<2mm) target cross-sectional shapes, multiple scattering of protons in the tantalum is noticeable Stephen Brooks, Kenny Walaron NuFact’05

46. Variation of Rod Radius • We will change the incoming beam size with the rod size and observe the yields Stephen Brooks, Kenny Walaron NuFact’05

47. Variation of Rod Radius • We will change the incoming beam size with the rod size and observe the yields • This is not physical for the smallest rods as a beta focus could not be maintained Stephen Brooks, Kenny Walaron NuFact’05

48. Variation of Rod Radius • We will change the incoming beam size with the rod size and observe the yields • For larger rods, the increase in transverse emittance may be a problem downstream • Effective beam-size adds in quadrature to the Larmor radius: Stephen Brooks, Kenny Walaron NuFact’05

49. Total Yield with Rod Radius Stephen Brooks, Kenny Walaron NuFact’05

50. Cut Yield with Rod Radius Rod heating per unit volume and hence shock amplitude decreases as 1/r2 ! Multiple scattering decreases yield at r = 5mm and below Fall-off due to reabsorption is fairly shallow with radius Stephen Brooks, Kenny Walaron NuFact’05