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**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

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**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

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**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

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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

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**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)

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**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

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**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:

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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):

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**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±

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**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

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**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

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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

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**Partially Dissociated Beams**

Density and velocity distributions from DSMC measured

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**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

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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

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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

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**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

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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]

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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

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