Download - 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
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
The last 30 years of Atomic Beams
Increase has no concrete explanation!
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
PSTP2007Brookhaven National Laboratory, USA
ABS layout
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
PSTP2007Brookhaven National Laboratory, USA
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
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
PSTP2007Brookhaven National Laboratory, USA
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
PSTP2007Brookhaven National Laboratory, USA
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
PSTP2007Brookhaven National Laboratory, USA
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
PSTP2007Brookhaven National Laboratory, USA
SpinLab in FerraraUnpolarized ABS (CERN)
Polarized ABS (Wisconsin)
Movable Diagnostic System (Ferrara)
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
PSTP2007Brookhaven National Laboratory, USA
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!
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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.
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
Experimental Confirmation
Measured skimmer chamber pressure is linear with input flow !
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
PSTP2007Brookhaven National Laboratory, USA
Beam Divergence after Skimmer
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?
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
Interpretation
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
Beam Divergence after Skimmer
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?
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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.
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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%)
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
Michelle Stancari Università degli Studi di Ferrara (Italy) and INFN
PSTP2007Brookhaven National Laboratory, USA
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
PSTP2007Brookhaven National Laboratory, USA
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
PSTP2007Brookhaven National Laboratory, USA