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### 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

The last 30 years of Atomic Beams

Increase has no concrete explanation!

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!?

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

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 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

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

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

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

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

SpinLab in Ferrara

Unpolarized ABS (CERN)

Movable Diagnostic System (Ferrara)

Polarized ABS (Wisconsin)

Michelle Stancari

Università degli Studi di Ferrara (Italy) and INFN

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

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

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

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

Experimental Confirmation

Measured skimmer chamber pressure is linear with input flow !

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!

Michelle Stancari

Università degli Studi di Ferrara (Italy) and INFN

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

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

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

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

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

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

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

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

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

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

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

Food for Thought

Compare three sources with very similar nozzle and skimmer geometry

Michelle Stancari

Università degli Studi di Ferrara (Italy) and INFN

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

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

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

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

Michelle Stancari

Università degli Studi di Ferrara (Italy) and INFN

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