1. Studies on Beam Formation in an Atomic Beam Source
Why don‘t we understand the intensity output of an ABS?
Alexander Nass, Erhard Steffens
University of Erlangen-Nürnberg, Germany
Michelle Stancari
INFN, Ferrara, Italy
SPIN 2008, Charlottesville,VA,USA, Oktober 6, 2008

2. Atomic Beam Source (ABS)
Production of polarized H or D beams for polarized gas targets and polarized ion sources
H gas expands through cooled nozzle and forms of high brightness beam with skimmer and collimator
Sextupole magnets focus beam and produce electron polarization
HF - transitions  nuclear polarization
Output intensity of the sources not understood

3. Supersonic Gas Expansions
Free jet atomic or molecular beam from supersonic gas expansion from a high-p source (p0) into a low-p background (pb)
Gas accelerates during expansion and beam temperature decreases
If pb small  smooth transition to molecular flow, no shock stuctures

4. Thermodynamics
Energy equation of an ideal expanding gas without viscous and
heat conduction effects: h0 = h+v2/2
For ideal gases (dh = cp dT) and constant cp= (g / (g-1))kB/m) one
gets the maximum or terminal velocity:
For more information see D.R.Miller in: G.Scoles (Ed.), Atomic and
Molecular Beam Methods, Vol.I (Oxford Univ. Press, 1988) 14
Some properties can be calculated, but in general models are
needed to describe the beam parameters
Example: H2 (D2) expansion at
T0=100 K (g=5/3)
 v¥H2 = 1436 m/s
 v¥D2 = 1015 m/s

5. Direct Simulation Monte Carlo Method (DSMC)
Technique for computer modeling of a real gas by some thousands or millions of simulated particle trajectories
Particles are followed through representative collisions and boundary interactions in space
Key assumptions: decoupling of the motion and collisions of particles over small time steps and division of the flow field into small cells
Therefore: time steps << mean collision time
cell dimensions << local mean free path
More information on the method see: G.A.Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon Press Oxford, 1994)

6. Direct Simulation Monte Carlo Method (DSMC)
Geometry of the beam forming elements in an ABS are implemented as boundary walls with temperature T for an axially symmetric flow
Regions 1-7 are divided into small cells
The Stream Input flow is inflowing H gas and the Specified flows compensate for flow losses at the boundaries of regions 3 and 6

7. Experimental Setup Microwave dissociator with a 2,45 GHz surface wave
Beam profile monitor for intensity measurements
Fast chopper and QMS for velocity analysis
Determination of the degree of dissociation with the QMS:

8. Velocity Analysis
Velocity distribution determined with TOF-method with a fast chopper cutting out a beam package and detection with a QMS
Deconvolution of the measured distribution to remove the influence of the chopper opening function and the electronics
Resulting function is fitted to extract beam parameters
(p2=Tx, p3=vx):

9. Molecular Hydrogen Expansions
DSMC calculation of an H2 expansion with a flow of Q=1 mbarl/s and a nozzle temperature Tnozzle=100 K
vx (m/s)
Tx (K)
v¥ (m/s)
measurement
1278±8±13
19.0±1.1±0.9
DSMC (original)
1334±
33.3±
1436
DSMC (altered)
1371±2+5-15
19.0±

10. Partially Dissociated Beams
DSMC calculation of an H/H2 expansion with Q=1 mbarl/s, a=0.63 and Tnozzle=100 K H1 H2
vx (m/s)
Tx (K)
v¥ (m/s)
measurement atoms
1750±47±24
25.7±4.9±1.5
DSMC atoms
1760±
41.0±
2031
measurement molecules
1579±51±17
23.7±7.1±1.0
DSMC molecules
1590±
44.0±
1436

11. Partially Dissociated Beams
Energy and enthalpy considerations for an expanding beam with only translational degrees of freedom lead to the balance equation (see also H.Haberland et al. Rev.Sci.Instr. 56, (1985) 1712):
For T0=Tnozzle one expects:
DSMC calcu-lations show incomplete thermalization of the gas inside the nozzle

12. Density Measurements
Measurement of intensity profiles of the atomic fraction of the beam with beam profile monitor (A.Vassiliev et al., Int. Workshop on Pol.Sources and Targets, Erlangen 1999, Procs. Page 200)
2 x 16 gold plated tungsten wires of diameter dw=5mm and 2 mm spacing
Calculation of deposited power from the recombination of DSMC calculated atomic density and velocity distributions
Power calibration of the wires  the expected resistance change
Comparision with measurement

13. Partially Dissociated Beams
Density and velocity distributions from DSMC
measured

14. Partially Dissociated Beams
Calculated (circles) and measured (triangles) wire resistances
Q = 2 mbarl/s
Q = 1 mbarl/s
10 mm distance
20 mm distance
nozzle  beam profile monitor

15. The hollow carrier jet
Proposed by V.L.Varentsov et al., 7th Int. Workshop on Pol. Gas Targets and Pol. Beams, Urbana, AIP Conf. Procs. 421 (1997) 381
Supposed to increase intensity of the beam through the collimator
Cooling and confining of the atomic beam by an overexpanded hollow carrier jet
Small mixing and removal of the carrier gas with the skimmer

16. The hollow carrier jet
Measurements with D2/H2, H/H2 , D/D2 , D/He as inner / carrier gas
D2 w/o H2
D2 with H2
No intensity gain, huge amount of
carrier gas in the detector
H2 density
No cooling effect, but acceleration because of mixing of D2 and H2

17. The hollow carrier jet Measurements with Ar/N2 as inner / carrier gas
Ar w/o N2
Ar with N2
High intensity gain, no
carrier gas in the detector
N2 density
Large cooling effect, no acceleration  no mixing

18. Summary
DSMC - excellent method to describe the expansion of gases in the transition region between laminar and molecular flow
Results confirmed by several measurements of density and velocity
Origin of the discrepancies between measured and simulated temperature found and solved by modification of appropriate input parameters of the DSMC
No observation of the predicted carrier-jet effect for H and D but for heavier gases
Explanation of both experimental findings with the DSMC
Publication accepted by NIM and also available in
arXiv: [physics.atom-ph]

19. Outlook
Use of this method to design a new generation of atomic beam sources
Optimization of nozzle geometries by implementation of recombination into the calculations
Design of improved beam forming elements
Implementation of sextupole magnets into the code to finally understand the behavior of the output intensitiy of an ABS
First step – Use of the DSMC output parameters for sextupole tracking Monte Carlo simulations