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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

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!

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!?

PSTP2007

Brookhaven National Laboratory, USA

Michelle Stancari


Università degli Studi di Ferrara (Italy) and INFN

ABS layout

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

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

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

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

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

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

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)

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

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


PSTP2007

Brookhaven National Laboratory, USA

Michelle Stancari


Università degli Studi di Ferrara (Italy) and INFN

Beam Intensity through Skimmer

skimmer acceptance 100 K
0.0545
0.0550
0.0555
0.0560
0.0565
0.0570
0.0575
0.0580
0.0585
0.0000
E+00
2.0000
E+19
4.0000
E+19
6.0000
E+19
8.0000
E+19
1.0000
E+20
1.2000
E+20
input flow (mole/s)
acceptance
cs1-26.9
cs2-32.2
cs3-38.6
cs3-38.6
cs7
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.

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!

PSTP2007

Brookhaven National Laboratory, USA

Michelle Stancari


Università degli Studi di Ferrara (Italy) and INFN

Beam Intensity through Skimmer

skimmer acceptance 100 K
0.0545
0.0550
0.0555
0.0560
0.0565
0.0570
0.0575
0.0580
0.0585
0.0000
E+00
2.0000
E+19
4.0000
E+19
6.0000
E+19
8.0000
E+19
1.0000
E+20
1.2000
E+20
input flow (mole/s)
acceptance
cs1-26.9
cs2-32.2
cs3-38.6
cs3-38.6
cs7
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.

in
sk
Q
Q
The peaking factor n
f

(the ratio
Q
sk
/Q
sk
eff
) is a way to compare two
systems with different geometrical
acceptance.

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 !

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!


PSTP2007

Brookhaven National Laboratory, USA

Michelle Stancari


Università degli Studi di Ferrara (Italy) and INFN

Beam Divergence after Skimmer

3
sk
CV
x10
Q
Q
sccm)

(10

Q

-3
CV
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?

PSTP2007

Brookhaven National Laboratory, USA

Michelle Stancari


Università degli Studi di Ferrara (Italy) and INFN

Interpretation

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

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
s

100 sccm

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


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

PSTP2007

Brookhaven National Laboratory, USA

Michelle Stancari


Università degli Studi di Ferrara (Italy) and INFN

Beam Divergence after Skimmer

3
sk
CV
x10
Q
Q
sccm)

(10

Q

-3
CV
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?

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.

s



40 K 2098 m/s 62 A
2

100 K 2273 m/s 58 A
2

207 K 2469 m/s 54 A
2

PSTP2007

Brookhaven National Laboratory, USA

Michelle Stancari


Università degli Studi di Ferrara (Italy) and INFN

Cross Section

For this parameterization of the cross section,



4
.
0
rel
10
-
2
v
m/s

2273
m

4.287x10
d
d











s
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.

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.

s
s


s
s
2
B
2
RG
eff
RG
RG
B
B
v
v
1
then

)
v
(
)
f(v


)
v
(
)
f(v


.)
(


)
g
(

if





const
Simplified
version












RG
B
eff
RGA
T
k
pdl
exp
A
s
RG
B
B
RG
B
eff
v
-
v
g

where


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






s
s
Physical cross section

Relative velocity of collision

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

PSTP2007

Brookhaven National Laboratory, USA

Michelle Stancari


Università degli Studi di Ferrara (Italy) and INFN

Measurement of
s

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

PSTP2007

Brookhaven National Laboratory, USA

Michelle Stancari


Università degli Studi di Ferrara (Italy) and INFN

Cross Section Tuning

Relative velocity

s

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

PSTP2007

Brookhaven National Laboratory, USA

Michelle Stancari


Università degli Studi di Ferrara (Italy) and INFN

Food for Thought

Hermes

ANKE

RHIC

Q
in
(mbar l/s)

1.5

1.0

1.0

a

0.82

0.85

0.85

f
g

(geometrical accept.)

0.055

0.097

0.089

t (magnet transmission)

0.48

0.42

0.49

calculated Q
out


(A=0;n=1.75

0.25)

14.7
±
2.0

17.5
±
2.5

15.0
±
2.4

meas. Q
out

(10
16

atoms/s)

6.8

7.5

12.4

Compare three sources with very similar nozzle and skimmer geometry

PSTP2007

Brookhaven National Laboratory, USA

Michelle Stancari


Università degli Studi di Ferrara (Italy) and INFN

Food for Thought

Hermes

ANKE

RHIC

Q
in
(mbar l/s)

1.5

1.0

1.0

a

0.82

0.85

0.85

f
g

(geometrical accept.)

0.055

0.097

0.089

t (magnet transmission)

0.48

0.42

0.49

calculated Q
out


(A=0;n=1.75

0.25)

14.7
±
2.0

17.5
±
2.5

15.0
±
2.4

meas. Q
out

(10
16

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%)

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
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


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

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?


PSTP2007

Brookhaven National Laboratory, USA

Michelle Stancari


Università degli Studi di Ferrara (Italy) and INFN