studies of atomic beam formation

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

PSTP2007Brookhaven National Laboratory, USA

Studies of Atomic Beam Formation

Michelle StancariUniversità degli Studi di Ferrara (Italy) and INFN

XIIth International Workshop on Polarized Sources, Targets and Polarimetry

September 10-14, 2007Brookhaven National Laboratory, USA



The last 30 years of Atomic Beams

Increase has no concrete explanation!



The last 30 years of Atomic Beams

Increase has no concrete explanation!

Predicted Intensity for RHIC source!?



ABS layout



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



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



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



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




First and extensive simulations by A. Nass (PhD thesis) at Hermes Jade Hall test stand




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



SpinLab in FerraraUnpolarized ABS (CERN)

Polarized ABS (Wisconsin)

Movable Diagnostic System (Ferrara)



Experimental SetupPressure in skimmer chamber measure of

the beam flow through the skimmer fPressure in compression volume beam

intensity after rest gas attenuation lossesVelocity distribution of beam

0.79 m



Comparison of measurements and simulations of

• Beam intensity

• Beam divergence

• Velocity distribution

And whether these quantities change with input flow



Beam Intensity through SkimmerFor 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.

in

sk

Q

Q

Special Acknowledgement for Werner Kubischta (CERN) who ran the simulations above, and many others, at 3 days of CPU per point!



Beam Intensity through SkimmerFor 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.

Simulations of the Hermes atomic beam expansion (A. Nass) predict nf=1.65.

in

sk

Q

Q

The peaking factor nf (the ratio Qsk/Qskeff)

is a way to compare two systems with different geometrical acceptance.



Experimental Confirmation

Measured skimmer chamber pressure is linear with input flow !



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!




3

sk

CV x10Q

Q

sccm) (10 Q -3CV

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?



Interpretation



Beam Velocity DistributionWe 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



Beam Velocity DistributionAnd 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

100 sccm



Pause

Beam properties do change as input flow increases

• Intensity after skimmer scales with input flow• Beam is more divergent/chaotic• Velocity distribution narrowsComing up• Compression volume intensity

measurements • Cross section tuning needed for simulations



Rest Gas AttenuationAs 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




3

sk

CV x10Q

Q

sccm) (10 Q -3CV

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?



RGA losses + divergenceSimulation 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 A2

100 K 2273 m/s 58 A2

207 K 2469 m/s 54 A2



Cross SectionFor this parameterization of the cross section,

4.0

rel

10-

2

v

m/s 2273m 4.287x10d

d

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.



Rest Gas AttenuationMethod 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.

2B

2RG

eff

RGRG

BB

v

v1

then

)v()f(v

)v()f(v

.)( )g( if

const

Simplified version

RGBeffRGA Tk

pdlexpA

RGB

BRGBeff

v-vg where

dv)dg)f(vf(v)g(g

Physical cross section

Relative velocity of collision

Hans Pauly, Atom, Molecule, and Cluster Beams 1, Springer, 2000 pp. 40-42



Measurement of for H2-H2 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



Cross Section Tuning

Relative velocity

IBS20-40 K

Expansion40-100 K

RGA200-300K

Direct measurement

Force agreement between measured and simulatedvelocity distributions to determine cross section

?

H1-H1 collisions accessible only here



Food for Thought

Hermes ANKE RHIC

Qin (mbar l/s) 1.5 1.0 1.0

0.82 0.85 0.85fg (geometrical accept.) 0.055 0.097 0.089t (magnet transmission) 0.48 0.42 0.49

calculated Qout

(A=0;n=1.750.25)14.7±2.0 17.5±2.5 15.0±2.4

meas. Qout

(1016 atoms/s)6.8 7.5 12.4

Compare three sources with very similar nozzle and skimmer geometry



Food for Thought

Hermes ANKE RHIC

Qin (mbar l/s) 1.5 1.0 1.0

0.82 0.85 0.85fg (geometrical accept.) 0.055 0.097 0.089t (magnet transmission) 0.48 0.42 0.49

calculated Qout

(A=0;n=1.750.25)14.7±2.0 17.5±2.5 15.0±2.4

meas. Qout

(1016 atoms/s)6.8 7.5 12.4

Compare three sources with very similar nozzle and skimmer geometry

HUGE attenuation losses?? (Koch estimates only 20%)



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 increasesSmall effect (except possible changes in )

• Cross sections in simulations need tuningVelocity distributions now match for moleculesAtoms 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



Future

• Cross section tuning for atoms underway

• Simulations of new nozzle and skimmer geometries also underway



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?

studies of atomic beam formation

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