Studies of Atomic Beam Formation

1. Studies of Atomic Beam Formation Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN XIIth International Workshop on Polarized Sources, Targets and Polarimetry September 10-14, 2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

2. The last 30 years of Atomic Beams Increase has no concrete explanation! Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

3. The last 30 years of Atomic Beams Increase has no concrete explanation! Predicted Intensity for RHIC source!? Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

4. ABS layout Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

5. What is beam formation? It’s what happens here! And what determines the beam’s intensity, divergence and velocity distribution as it enters the magnet system. GOAL: put more focusable beam into the magnets Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

6. More goes in but less comes out? RHIC (from PST03) If the input flow doubles does the amount of focusable beam entering the magnets double? YES Þ difference between measured intensity and the line must be losses to attenuation. NO Þ line becomes a curve Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

7. How to attack the problem? A basic understanding of the beam formation process is missing • Transition from laminar to molecular flow which is difficult/impossible to model! Test bench studies and numerical simulations • First understand existing systems • Then explore new nozzle and skimmer geometries Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

8. Direct Simulation Monte Carlo How it works • Simulation of gas flows by following a representative set of particles through the flow and “averaging” to obtain macroscopic quantities such as density and temperature. • Executable is available as free download. There is no access to source code, but algorithms are published. (G. A. Bird) • Needs as input the scattering cross sections for H1-H1, H1-H2, and H2-H2 with their dependence on relative velocity Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

9. Direct Simulation Monte Carlo First and extensive simulations by A. Nass (PhD thesis) at Hermes Jade Hall test stand Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

10. Direct Simulation Monte Carlo New Additions (after A. Nass thesis) • Separation of beam and background • Intensity and divergence of beam after skimmer • Intensity in compression volume • Dump file at skimmer – position and velocity of each simulated atom and molecule. • Actual velocity distribution, instead of mean and rms • Before and after attenuation comparisons Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

11. SpinLab in Ferrara Unpolarized ABS (CERN) Movable Diagnostic System (Ferrara) Polarized ABS (Wisconsin) Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

12. Experimental Setup • Pressure in skimmer chamber Þ measure of the beam flow through the skimmer f • Pressure in compression volume Þ beam intensity after rest gas attenuation losses • Velocity distribution of beam 0.79 m Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

13. Comparison of measurements and simulations of • Beam intensity • Beam divergence • Velocity distribution And whether these quantities change with input flow Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

14. Beam Intensity through Skimmer For a molecular H2 beam, 4mm, 100K nozzle: Simulation predicts that 5.6% of the input flow passes through the 6 mm skimmer, but 4% expected for an effusive beam!(nf=1.40) Additionally, this fraction is essentially independent of input flow and cross section. Special Acknowledgement for Werner Kubischta (CERN) who ran the simulations above, and many others, at 3 days of CPU per point! Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

15. Beam Intensity through Skimmer For a molecular H2 beam, 4mm, 100K nozzle: Simulation predicts that 5.6% of the input flow passes through the 6 mm skimmer, but 4% expected for an effusive beam from a point-like source!(nf=1.40) Additionally, this fraction is essentially independent of input flow and cross section. The peaking factor nf (the ratio Qsk/Qskeff) is a way to compare two systems with different geometrical acceptance. Simulations of the Hermes atomic beam expansion (A. Nass)predict nf=1.65. Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

16. Experimental Confirmation Measured skimmer chamber pressure is linear with input flow ! Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

17. Beam Divergence after Skimmer If the input flow doubles, the flow through the skimmer also doubles. Is it still focusable? Difficult to measure – attenuation effects dominate. Ask the simulation: What fraction of the molecules leaving the skimmer would enter the compression volume if their direction of motion did not change? How many actually enter the volume? . . . Wait 5 slides! Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

18. Beam Divergence after Skimmer QCV is maximum intensity in compression volume if NO beam atoms are lost to collisions Beam is more divergent, and thus no-attenuation-expectations deviate from a line, but only slightly. How to confirm with test stand measurements? Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

19. Interpretation Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

20. Beam Velocity Distribution We observe that for increasing nozzle temperatures, the mean velocity of the beam increases, as does the width. for increasing input flows, the mean velocity of the beam does not change, however the width of the distribution narrows Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

21. Beam Velocity Distribution And these observations are predicted by simulations! • SIMULATED H2 molecular beam, 4mm nozzle at 100K • Final width depends on number of collisions during expansion – and thus on both input flow and s 100 sccm Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

22. Pause Beam properties do change as input flow increases • Intensity after skimmer scales with input flow • Beam is more divergent/chaotic • Velocity distribution narrows Coming up • Compression volume intensity measurements • Cross section tuning needed for simulations Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

23. Rest Gas Attenuation As input flow increases for a molecular hydrogen beam, the RGA losses vary from 2-50% because the chamber pressure increases linearly with input flow. This dominates the divergence changes. 0.79 m Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

24. Beam Divergence after Skimmer QCV is maximum intensity in compression volume if NO beam atoms are lost to collisions Beam is more divergent, and thus no-attenuation-expectations deviate from a line, but only slightly. Possible to confirm with test stand measurements? Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

25. RGA losses + divergence Simulation reproduces the measured CV intensity of a molecular hydrogen beam for a specific value of the scattering cross section. 4 mm nozzle at 100 K Nozzlerel. vel.s 40 K 2098 m/s 62 A2 100 K 2273 m/s 58 A2 207 K 2469 m/s 54 A2 no attenuation Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

26. Cross Section For this parameterization of the cross section, • The data and simulations agree for • CV intensity vs input flow (Tnoz=40, 100, 207 K) • velocity distribution widths (100 sccm, Tnoz=40, 100, 207 K) We can check the validity of this parameterization by measuring directly the cross section. Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

27. Rest Gas Attenuation Relative velocity of collision Physical cross section Hans Pauly, Atom, Molecule, and Cluster Beams 1, Springer, 2000 pp. 40-42 Method to estimate RGA losses which is independent of source operating conditions such as nozzle temperature. Only the beam’s velocity distribution and the chamber pressures are needed. Simplified version Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

28. Measurement of s for H2-H2 collisions 40 K nozzle • Experimental verification of H2-H2 cross section used in simulations! • While magnitude is correct, any fine structure in the cross section is smeared out by HUGE distribution of relative velocity for each point • Data for H1-H2 cross section exist as well. 273 K nozzle Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

29. Cross Section Tuning Force agreement between measured and simulated velocity distributions to determine cross section Direct measurement s ? IBS 20-40 K RGA 200-300K Expansion 40-100 K Relative velocity H1-H1 collisions accessible only here Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

30. Food for Thought Compare three sources with very similar nozzle and skimmer geometry Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

31. Food for Thought Compare three sources with very similar nozzle and skimmer geometry HUGE attenuation losses?? (Koch estimates only 20%) Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

32. Simulation Results • Peaking factor quantized • 1.5<nf<2.0 for HERMES (and other existing sources?) and ~1.4 for molecular beams. • Beam properties do change as input flow increases • Small effect (except possible changes in a) • Cross sections in simulations need tuning • Velocity distributions now match for molecules • Atoms will be work • Universal method for calculating RGA losses emerged • RGA losses predicted accurately • Pressure bumps due to skimmer/collimator/magnets (and their consequences) can be investigated Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

33. Future • Cross section tuning for atoms underway • Simulations of new nozzle and skimmer geometries also underway Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

34. Future • Cross section tuning for atoms underway • Simulations of new nozzle and skimmer geometries also underway • Lack of source code prevents us from adding magnetic fields or changing functional form of the cross section – rebuild from blocks? Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN

35. Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN