Design of a Polarized Atomic H Source for
a Jet Target at RHIC
T. Wise*, M. A. Chapman*, W. Haeberli*, H. Kolster†, P. A. Quin*
* Department of Physics, University of Wisconsin, Madison. WI 53706, USA
† Laboratory for Nuclear Science, MIT,Cambridbe MA 02139, USA
Abstract. As part of a project to calibrate the polarization of the RHIC proton beams we designed a
polarized atomic hydrogen beam source for use as a jet target at RHIC. The model we developed
agrees well with measured outputs from two working sources and for the system we designed
predicts 9x1016 atoms/s into a 9 mm diameter aperture 285 mm from the last focussing magnet and a
target thickness of 9x1011atoms/cm2, 316 mm from the last magnet.
MODEL DESCRIPTION
We report on the design of a polarized hydrogen jet target to be inserted into RHIC at
the 12:00 o’clock location. The jet will be used to calibrate polarimeters located
elsewhere in the ring. Our model predicts a target thickness of 9x1011 atoms/cm2 or a
factor 2.5 larger than the recently designed EDDA target at COSY.
In the early stages of this study we compared outputs from different ray tracing codes.
The comparisons revealed programming errors in the two codes we intended to use.
The corrected versions more accurately predict the output of existing sources. It is
interesting to note that both codes had previously been used as the basis for magnet
purchases. To optimize the atomic beam density we added a gradient search routine to
one of the codes and a random parameter generator to the other.
The intensity of an atomic beam source delivering a single hyperfine state of H (or D)
into an aperture can be expressed as the product of terms in Eq. 1.
I(Q,T)atoms/s =
1 
NA
  Ω  ⋅ 2 ⋅ 2 ⋅ 1.15 ⋅ A(Q,T) ⋅ α (Q,T) ⋅ t(Q,T,G)
Q

4 22.4 ⋅ 1013   2π 
(1)
Q is the flow of H2 gas into the dissociator in mbar liter/s and is followed by the
required conversion into atoms/s using Avagadro’s number. Ω is the solid angle
subtended by the aperture of the first six-pole element as seen from the nozzle of the
dissociator and A(Q,T) represents attenuation of the beam due to scattering. In our
model A(Q,T) was experimentally determined [1] by measurements with H2 gas at
various nozzle temperatures and gas flows. To allow for the significant variation in the
degree of dissociation of H2 gas as a function of gas flow and nozzle temperature, we
CP675, Spin 2002: 15th Int'l. Spin Physics Symposium and Workshop on Polarized Electron
Sources and Polarimeters, edited by Y. I. Makdisi, A. U. Luccio, and W. W. MacKay
© 2003 American Institute of Physics 0-7354-0136-5/03/$20.00
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include the term α(Q,T). We factored α into flow and temperature dependent terms:
α(Q,T) = α(Q)*α(T) with the Q and T dependence derived from experimental data in
[1] and [2] respectively.
The last term, t(Q,T,G) represents the fractional transmission of the focussing N-FeB permanent magnet 6-poles [3,4] as calculated by the ray tracing code. The value of t
depends strongly on the geometry, G, of the 6-pole magnets. The Q and T dependence
of t results from the observation that the velocity distribution of atoms at the entrance to
the focussing magnets depends on those variables. We relied on measurements of the
atomic velocity distribution leaving a dissociator of similar design reported in [5]. In
that reference the velocity distribution f(v) is expressed as
 −m

( v − v drift ) 2 


2  2 k b Tbeam
f (v) = v e
(2)
with vdrift and Tbeam measured functions of the flow Q and nozzle temperature T.
The factor 1/4 in Eq.1 arises from the fact that we calculate trajectories in one of four
hyperfine states. One of the factors 2 arises from the dissociation of H2 into 2 atoms.
The second factor 2 arises from the assumption of a simple cos(θ) angular distribution
from the nozzle which has an on-axis intensity twice that of a flat distribution. Finally,
we add the factor 1.15 based on the observation [1,2] that the angular distribution is
slightly peaked on axis compared to a simple cos(θ) distribution.
To evaluate t for a particular magnet geometry we typically calculate 2x105 individual
atom trajectories. The magnitude of the atom velocities is randomly chosen with
weighting factor f(v) from Eq. 2 and the initial direction is established by assuming a
straight line trajectory between random positions on the 2 mm diameter dissociator
nozzle and on a disc 50 mm downstream. The straight-line trajectory is extended an
additional 10 mm to the first magnet element.
To compare the relative merit of one magnet geometry over another one must
consider how the atomic beam will be used. Eq. 1 is the correct function to maximize
for a beam entering a storage cell. In our application we need to instead optimize
density of the jet along a line crossing perpendicular to the jet axis. In that case we
weight each atom which passes through the target region by the factor 1/rv as indicated
in Eq. 3. The 1/v weight accounts for the time atoms spend in the interaction region.
The factor 1/r is related to the conversion from areal density of the beam to linear
density along the RHIC beam whose cross-section is small compared to the diameter of
the atomic beam.
THICKNESS ∝ I (Q, T ) ∗ ∑ 1/rv
(3)
atoms
In practice optimization with and without the 1/rv weighting gives nearly the same
result.
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MAGNET OPTIMIZATION
The process of optimization can be thought of as a search in n dimensional parameter
space with the parameters being, for example, the length, diameter, taper, and spacing
of the various magnet elements as well as the nozzle temperature and gas flow. To treat
the problem adequately we estimate 17 parameters are needed but this results in a rather
enormous computational problem. For example if only 5 values of each parameter are
selected one has 7x1011 systems to compare. The problem is aggravated by the presence
of numerous local maxima that render a simple gradient search routine ineffective. To
begin, we reduced the problem to a more manageable 10 parameters. Systems were
generated by randomly selecting parameters within a range we deemed acceptable. For
example nozzle temperatures were selected between 30-200 K. Slopes of the magnet
bores were constrained to be flat to diverging for the first group of magnet elements and
flat to converging for the last.
L1
S1
O1
L2
GAP
L3
L4
S4
O4
S1, S2 S3
L1, L2 L3
D1
S4
L4
gap
S5
L5
D5
S6
L6
Figure 1. Simplified and complete parameterizations. The parameters S, L ,and D represent the slope,
length, and diameter of magnet elements. In the left parameterization O is the offset after projecting the
inner bore of sloped magnet elements to the nozzle and to the target aperture.
Computations continued until at least 10,000 separate magnet systems were
calculated. We noted regions of parameter space unoccupied by the top 1% systems,
constrained the range of some parameters accordingly, and calculated another 10,000
systems. The process was repeated until it became possible to apply the more general
17 parameter model. At this stage this method had already generated magnet
geometries which were predicted to yield a maximum intensity of 1.0x1017 atoms/s into
a 10 mm diameter target. Unfortunately these systems were massive and impractical to
construct. The problem of massive magnets was resolved by adding an additional filter
into the parameter selection process; only systems whose magnet volume was below a
specified threshold were calculated. The best system out of 50,000 calculated this way
was fine-tuned by applying the gradient search portion of the code. It is interesting to
note that only an additional 1% output was found by the gradient search routine. This
system is predicted to generate 9x1016 atoms/s into a 9 mm diameter aperture 285 mm
from the last magnet element. It has a total volume of approximately 1230 cm3 which is
nearly 1/2 the volume of the more massive systems we rejected. The geometry of this
system is shown in Fig. 2 followed by predictions of the beam profile at the interaction
region and velocity distributions at three locations: nozzle, the jet interaction region,
and at the location of the Breit-Rabi polarimeter detector (not shown).
936
3 16 mm
( not t o scale)
650 mm
(not t o scale)
ri
rex
L
rout
5.2
7.0
28 .5
22
7.5
9.1
35 .4
29
9.7
10.7
40.5
35.7
11 .5
11 .5
46 .0
40.3
16
14 .5
75
4 1.2
14.5
12.7
79 .0
36 .7
100mm
0
RELATIVE ATOMS/s
DENSITY (10 1 2 ATOMS/CM3 )
Figure 2. Final magnet geometry for the RHIC hydrogen jet polarimeter target. The entrance and exit
radii, overall length, and outer radius of each magnet element are indicated. The BRP magnet elements to
the right of the interaction region are not shown. All dimensions are in mm.
2
1
0
0
2
4
6
0
RADIUS, mm
1000
2000
3000
VELOCITY m/s
Figure 3. Left: calculated beam density profile at the RHIC-J ET interaction region (316 mm from the
last focussing magnet) with and without a 9 mm diameter aperture 285 mm from the last focussing
magnet. Right: calculated velocity distributions at the dissociator nozzle (open circles), at the interaction
region (squares), and at the Breit-Rabi detector, (solid circles). All plots are calculated at the predicted
optimum operating point of Tnozzle = 80K and QH2 = 2.0 mbar-liter/s.
CONCLUSION
A major concern for any simulation is to what extent the model reflects the physical
situation. To verify the reliability of our model, we entered the magnet geometry,
operating parameters, and compression tube details for two atomic beam sources [1,6]
937
1 016 ATOMS/S
whose outputs had previously been measured. The comparison between measurement
and prediction is shown in Fig. 4. An improved operating point for the COSY-ANKE
source was reported at this conference and is included in the left-hand plot of Fig. 4.
Although the code appears to slightly overestimate the optimum gas flow and nozzle
temperature it predicts the maximum output to better than 5%.
8
8
6
6
4
4
2
2
0
50
75
100
0
125
0
T nozzle, K
1
2
Q (mbar L/s)
3
Figure 4. Left: Prediction of this model (solid line) compared to measurements on the COSY-ANKE
atomic beam source as reported in [6]. The solid triangle is an improved operating point reported at this
conference. Right: prediction of this model (solid line) compared to measurements of the Wisconsin ABS
reported in [1].
ACKNOWLEDGEMENTS
This work was supported in part by United States Department of Energy under
contract number DE-FG02-88ER40438.
REFERENCES
1.
2.
3.
4.
5.
6.
T. Wise, A. D. Roberts and W. Haeberli, Nucl. Inst. Meth. A336, 410-422 (1993).
N. Koch, PHD Thesis DESY-THESIS-1999-015, (May 1999). A Study on the Production of Intense
Cold Atomic Beams for Polarized Hydrogen and Deuterium Targets
K. Halbach, Nucl. Inst. Meth. 169, 1-10 (1980)
A. Vassiliev, et al., Rev. Sci. Inst. 71, 3331-3341 (2000)
B. Lorentz, Diplomarbeit Max-Plank-Institut für Kernphysik, Heidelberg Germany (1993)
M. Mikirtychiants, et al., The Polarized Gas Target for the ANKE Spectrometer at COSY/Jülich in
Proceedings of the Ninth International Workshop on Polarized Sources and Targets edited by V. P.
Derenchuk and B. von Przewoski, World Scientific, River Edge, New Jersey 2002 pp. 47-51.
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