1. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Studies of Atomic Beam Formation Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN XII th International Workshop on Polarized Sources, Targets and Polarimetry September 10-14, 2007 Brookhaven National Laboratory, USA

2. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN The last 30 years of Atomic Beams Increase has no concrete explanation!

3. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN The last 30 years of Atomic Beams Increase has no concrete explanation! Predicted Intensity for RHIC source!?

4. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN ABS layout

5. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN 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

6. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN 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  difference between measured intensity and the line must be losses to attenuation. NO  line becomes a curve

7. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN 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

8. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN 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 H 1 -H 1, H 1 -H 2, and H 2 -H 2 with their dependence on relative velocity

9. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Direct Simulation Monte Carlo First and extensive simulations by A. Nass (PhD thesis) at Hermes Jade Hall test stand

10. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN 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

11. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Starting Generator c) nozzle collimator Algorithm for generating tracks for ray- tracing program, used calculate t and f g Several options shown above produce differences of 5-10% in t values

12. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Starting Generator DSMC predictions compatible only with a) Preliminary measurements at X also compatible only with a) Internal note INFN/TC-06/11 available from www.lnf.infn.it/sis/preprint c) nozzle collimator b) a) c) X X Transverse Beam Density - 20 mm after skimmer

13. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN SpinLab in Ferrara Unpolarized ABS (CERN) Polarized ABS (Wisconsin) Movable Diagnostic System (Ferrara)

14. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Experimental Setup  Pressure in skimmer chamber  measure of the beam flow through the skimmer f  Pressure in compression volume  beam intensity after rest gas attenuation losses  Velocity distribution of beam 0.79 m

15. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Comparison of measurements and simulations of Beam intensity Beam divergence Velocity distribution And whether these quantities change with input flow

16. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN 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! (n f =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!

17. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN 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! (n f =1.40) Additionally, this fraction is essentially independent of input flow and cross section. Simulations of the Hermes atomic beam expansion (A. Nass) predict n f =1.65. The peaking factor n f (the ratio Q sk /Q sk eff ) is a way to compare two systems with different geometrical acceptance.

18. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Experimental Confirmation Measured skimmer chamber pressure is linear with input flow !

19. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN 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!

20. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Beam Divergence after Skimmer Q CV 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?

21. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Interpretation

22. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN 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

23. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Beam Velocity Distribution And these observations are predicted by simulations! SIMULATED H 2 molecular beam, 4mm nozzle at 100K Final width depends on number of collisions during expansion – and thus on both input flow and  100 sccm

24. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN 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

25. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN 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

26. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Beam Divergence after Skimmer Q CV 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?

27. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN 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 no attenuation Nozzle rel. vel.  40 K 2098 m/s 62 A 2 100 K 2273 m/s 58 A 2 207 K 2469 m/s 54 A 2

28. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Cross Section For this parameterization of the cross section, The data and simulations agree for CV intensity vs input flow (T noz =40, 100, 207 K) velocity distribution widths (100 sccm, T noz =40, 100, 207 K) We can check the validity of this parameterization by measuring directly the cross section.

29. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Rest Gas Attenuation Physical cross section Relative velocity of collision 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.

30. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Rest Gas Attenuation 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 Physical cross section Relative velocity of collision Hans Pauly, Atom, Molecule, and Cluster Beams 1, Springer, 2000 pp. 40-42

31. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Measurement of  for H 2 -H 2 collisions 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. 40 K nozzle 273 K nozzle

32. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN  for H 2 -H 1 collisions... data analysis still in progress. Measurements complete but

33. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Intra-Beam Scattering Transverse beam density, calculated with ray tracing program, assuming no attenuation losses and n f =1 Using the calculated beam density, the losses to IBS can be estimated with the formula below (Stancari, SPIN2004) Atomic hydrogen scattering cross section is not well known!

34. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Cross Section Tuning Relative velocity  IBS 20-40 K Expansion 40-100 K RGA 200-300K Direct measurement Force agreement between measured and simulated velocity distributions to determine cross section ? H1-H1 collisions accessible only here

35. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Food for Thought HermesANKERHIC Q in (mbar l/s) 1.51.0  0.820.85 f g (geometrical accept.) 0.0550.0970.089 t (magnet transmission) 0.480.420.49 calculated Q out (A=0;n=1.75  0.25) 14.7 ± 2.017.5 ± 2.515.0 ± 2.4 meas. Q out (10 16 atoms/s) 6.87.512.4 Compare three sources with very similar nozzle and skimmer geometry

36. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Food for Thought HermesANKERHIC Q in (mbar l/s) 1.51.0  0.820.85 f g (geometrical accept.) 0.0550.0970.089 t (magnet transmission) 0.480.420.49 calculated Q out (A=0;n=1.75  0.25) 14.7 ± 2.017.5 ± 2.515.0 ± 2.4 meas. Q out (10 16 atoms/s) 6.87.512.4 Compare three sources with very similar nozzle and skimmer geometry HUGE attenuation losses?? (Koch estimates only 20%)

37. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Simulation Results Peaking factor quantized  1.5<n f <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  ) 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

38. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN Future Cross section tuning for atoms underway Simulations of new nozzle and skimmer geometries also underway

39. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN 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?

40. PSTP2007 Brookhaven National Laboratory, USA Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN