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The polarized atomic-beam target for the EDDA experiment and the time-reversal invariance test at COSY
NUCLEAR PHYSICS A ELSEVIER
Nuclear Physics A626 (1997) 117c-124c
The polarized atomic-beam target for the EDDA experiment and the time-reversal invariance test at COSY* P.D. Eversheim, M. Altmeier, and O. Felden Institut ftir Strahlen- und Kernphysik, Universitat Bonn NuBallee 14-16, 53115 Bonn, Germany
For the the EDDA experiment, which was set up to measure the ~-~ excitation function during the acceleration ramp of the cooler synchrotron COSY at JOlich, a polarized atomic-beam target was designed regarding the restrictions imposed by the geometry of the EDDA detector. Later, when the time-reversal invariance experiment is to be performed, the EDDA detector will serve as efficient internal polarimeter and the source has to deliver tensor polarized deuterons. The modular design of this polarized atomic-beam target that allows to meet these conditions will be discussed in comparison to other existing polarized atomic-beam targets.
1. INTRODUCTION Two experiments are presently planned with an atomic-beam target (ABT) at the cooler synchrotron COSY at Jtilich: The EDDA experiment and a time-reversal invariance (TRI) test. The EDDA experiment measures with high precision the proton-proton excitation function in the 0.25-2.5 GeVLab energy and 10°- 72°Lab angle range. In order to suppress systematic error contributions caused by fluctuations in the COSY-ring, data are taken during the acceleration ramp of COSY. The circular EDDA detector [1] comprises an inner and an outer layer of scintillators that allow by kinematical eoicidence and vertex reconstruction to discriminate background events from protons scattered elastically offthe target. With the unpolarized COSY-beam and an unpolarized solid state CH 2 fiber-target up to now more than 107 p-p events have been recorded. Presently the COSY-facility is set up to accelerate the polarized beam from the colliding-beams source (COSY-CBS). Once the polarized beam in COSY is available up to 2.5 GeV and the ABT is installed as shown in figure 1, the EDDA measurements can be extended to give the energy-dependence of the analyzing powers Ay, Axx, Ayy, and Axz. It has been demonstrated that due to its circular design around the beam-pipe the EDDA detector also serves as an ideal internal polarimeter. The detector continuously monitors the
*Supportedby the BMBF, Germany 0375-9474/98/$19.00 © 1998 ElsevierScience B.V. All rights reserved. Pll S0375-9474(97)00528-9
118c
P.D. Eversheim et al./Nuclear Physics A626 (1997) 1 l 7c-124c
Atomic Beam
Beam Dump
to Spinfilter
EDDA Detector
COSY Beam
--- :_~-.
IIJllJlllllJt I
iiiiiiiiiiii i i iiu
I
I[
1
Atomic Beam Source
Im
H2JD2 Figure 1. The atomic beam target for the EDDA and TRI experiment at COSY.
polarization of the beam during the acceleration ramp as well as at a fixed energy for a circularing beam in COSY. The latter property of EDDA and the ability of the ABT to provide tensor polarized deuterons allows to perform at this target station a true, clean, P-even T-odd TRI nulltest [2]. 'True' in this context stresses the fact that the interpretation of the experimental result is for instance not affected by final-state interactions or by the assumtion of special hamiltonhns. 'Clean' emphasizes that compared to the situation in complex nuclei a possible effect is not diluted by observer nucleons which do not participate in the time-reversal violating interaction. At last, the P-even T-odd null-test allows to probe with high precision a special class of TRI-
119c
I?D. Eoersheim et al./Nuclear Physics A626 (1997) 117c-124c
tests. The idea of this experiment is depicted in figure 2. In a forward scattering experiment the
~
X
a)
b)
;z
®
®
..............
~
d
d'
)
.............
d)
c)
®
®
P
) .............
Figure 2. Pictorial demonstration that a time-reversed situation is prepared by either a proton or a deuteron spin-flip, a) The basic system is shown, b) The time reversal operation is applied (momenta and spins are reversed and the particles are exchanged). In order to have a direct comparison between situation a) and b), two rotations Ry(~) or Rx(r 0 by 180 ° about the y- or x- axis are applied, leading to the situations c) and d), respectively. This is allowed, since the scattering process is invariant under rotations. (3 - Proton spin up (y-direction) ® - Proton spin down <=> - Deuteron tensor polarization time-reversal violating total analyzing power Ay,xz is measured with a normally (y) polarized proton beam, circulating in the COSY-ring, and an x-z aligned tensor polarized deuteron beam from the ABT. For this experiment the COSY-ring not only serves as an accelerator but also as an ideal forward spectrometer and detector. Whereas for the EDDA experiment and phase 1 of the TRI test the ABT has to be optimized for maximum density, phase 2 oftbe TRI test requires a target-cell for better statistics and consequently the source has to be optimized for maximum intensity. It is intended to measure in phase 2 of the TRI test the analyzing power Ay, xz with an. accuracy of 10 -7 . It can be shown [3] that the only relevant observable which can fake a TRI effect is Ay, y. For this to happen, two conditions have to come true: i) the deuteron beam from the ABT contains
12oc
FD. Eversheim et al. /Nuclear Physics A626 (1997) 117~~124~
along with the tensor polarization some vector polarization and ii) a misalignment of the atomicbeam exists from the x-z direction into the y-direction. Therefore, in order to control the polarization of the atomic-beam, the ABT beam-dump has to provide the option for a polarimeter. Since only a small fraction (1%) of the atomic-beam will be available for analysis, once a target-cell is used, the ABT beam-dump allows to make use of an off-line spin-filter polarimeter [4]. Furthermore, since the COSY-ring will probably operate best with the smallest holding field across the interaction region, all polarized beams of the ABT should be of pure state in the first place. This requirement resulted in a modular design of the ABT, with respect to the position of the second 6-pole magnet group and the order of up to three RF-transitions.
2. TEIE ATOMIC-BEAM
SOURCE
The atomic-beam of the ABT is produced in an atomic-beam source which is essentially identical to the source of the COSY-CBS as described in [5]. The Hz/D2 molecules are dissociated in an inductively coupled 350W RF-discharge. The atoms passing the aluminium nozzle channel of 20mm length and 3mm diameter are cooled to about 30K. Thus, the atoms are slowed down with the consequences that i) the first tapered 6-pole magnets have an increased solid angle of acceptance in proportion to the beam temperature, and ii) the dwell time of the atoms in the interaction region with the COSY-beam increases invers proportional to the reduced beam velocity. These beneficial effects are in part offset by gas scattering in- and outside the nozzle. In order to reduce chromatic aberrations the atomic beam transport system comprises a second 6-pole magnet, the compressor magnet. Between these magnets or behind the compressor magnet up to three Abragam-Winter RF-transition units can induce transitions between the hyperline states of hydrogen or deuterium. Differences between the atomic-beam sources of the ABT and the COSY-CBS exist in the front part of the ABT (which has to fit into the space left by the EDDA detector) and in the 6-pole magnet design. Starting from the successfbl design of the electrically driven COSY-CBS magnets, which corresponds to the magnet design of the sources of the ETH-Zurich and PSI [6], the 6-pole magnets for the ABT in COSY are now made out of permanent magnets @Id-Fe-B alloy [7 J) as shown in figure 3. 2.1.Spin preparation The nuclear spin of the atomic beam is prepared via 6-pole magnets and RF-transitions. The use of two groups of 6-pole magnets and up to three RF-transitions offers a high flexibility with respect to the preparation of the desired nuclear spin states. The 6-pole magnets defocus atoms with magnetic electron quantum number l/2 and focus states with +1/2. Therefore, the beam intensity behind the first group of 6-pole magnets is divided by two. Yet the atomic beam is unpolarized with respect to the nuclear spin. The nuclear spin is prepared by means of RF-transitions that induce a transition between a populated and an unpopulated state (those with l/2). Depending on the size of the static transversal magnetic field B, compared to critical magnetic field B, from the hyperfine term splitting AE = 2. uB*B, with the Bohr’s magnetron pB, several types of transitions are distinmJ
mJ
=
mJ
=
-
=
-
FD. Euersheim et al./Nuclear Physics A626 (1997) 117c 124c
121 c
/~d-Head AI
6-Pole Magnets
RF-Transitions
Gas Inlet
H21Dz
lOOmm
Figure 3. Details of the atomic-beam source. The hatched areas inside the 6-pole magnets show the size of the permanent magnets in contrast to the electrically driven ones from the COSYCBS.
guished: Zero Field transition (ZF, a novel transition utilized at the Bonn polarized ion source, BT ~ 0), Weak Field transition (WF, BT is within the linear Zeeman regime of the hyperfinestmcture splitting), Medium Field transition (MF, BT is just outside the linear Zeeman regime of the hyperfinestructure splitting) and Intermediate Field transition (IF, BT < Bo ). Table 1 gives the operating conditions for the various transitions. The symbols .L [Igive the orientation of the RFTable 1 Characteristics of RF-transitions Tr. No.: Type B ~ Hydrogen Frequ. [MHz] Transition(s) 1
WF
2 3 4 5
Deuterium Frequ. [MI-Iz] Transition(s)
I
7-20
143
7
14"4
IF
±
1448
244
415
24-*6
IF ZF MF
± ± I
243
314 329 20
345 2 4 6 & 3"*5 344
60
122c
PD. Eversheim et al. /Nuclear Physics A626 (1997) I1 7c-124~
magnetic field B, with respect to the atomic-beam velocity v. If B, I v, then B WI1B T Ofspecial interest are atomic-beams in a pure state, i.e. state 1 or 3 for hydrogen, 1 or 4 for deuterium, Since for these beams any magnitude of magnetic guiding field across the interaction region is sufficient to align the nuclear spin. For hydrogen the options are discussed elsewhere [8], for deuterium in view of the transitions given in table 1 all non-trivial magnet and transition combinations are given in table 2. Figure 4 gives the possible schemes for the 6-pole and RFtransition combinations.
Figure 4.Scheme of 6-pole magnet and RF-transition
(Tr.) combinations.
In table 2 the vector polarization Pa, the tensor polarization P, and the relative Intensity i, for the figures of merit are calculated according to: P, =
N+-NN++NO+N-
p
= N+-2.N”+N=
N++N“+N-
I = N++N’+Nr
3
(1)
Pure states in combionation no.: 1,6 and 7 are underlined. Favourable combinations with respect to a high figure of merit or pure vector or tensor polarization are the combinations 1/3,4/S and 617. 2.2.Modeiling the atomic beam transport The 6-pole magnet design of the ABT is derived from a modified program code [9], which calculates the beam transport through skimmers and magnets by a fast linear matrix approach. The predictive power of the code has been successllly verified by the performance of the polarized ion source of the Bonn isochronous cyclotron and the atomic-beam source of the COSY-CBS. Meanwhile the code comprises an optimization algorithm that tunes the magnet design with respect to a given figure of merit, for instance density or intensity at the interaction region. Examples of informations the program code provides at present are given in [lo]. One of the major difIiculties in modelling the beam transport is the determination of a realistic velocity and density distribution of the atomic-beam at the end of the cooled dissociator nozzle. Since inside the nozzle turbulent flow may dominate, some mm downstream the nozzle molecular flow prevails. Reliable calculations that take realistic skimmer shapes into account need CRAY computing power and are not available yet. Therefore, instead of calculated input distributions measured distributions have been used. The predictive power of the code is demonstrated by table 3, where the measured and
123c
P.D. Eoersheim et al./Nuclear Physics A626 (1997) 117c-124c
Table 2 Possible deuteron polarizations No.
Population N + N ° N-
I0 11 12 13
Polarization Pz
Pzz
Intensity
Combination
Ir
Tr. (cf. table 1)
pz2.i,
PZZ ° r
2I
1+2" "2+5*; 2 1+3 1+3"
0 0 0
2/3 4/3 8/3
1
0
1
0
1
0 0
1 2
0 0
0 0
-2 -2
2/3 1/3 2/3
2 0
1 1
0 2
2/3 -2/3
0 0
1 1
2*+3* ; 4*
4/9
0
1*
4/9
0
2+3 ; 4 1+2 ; 4+1" 3+2* 2+ 1*
1/3 1/3 2/3 2/3
1/3 1/3 2/3 2/3
1
0
0
1
1
0 2 0
0 0 0
1 0 2
-1 1 -1
1 1 1
1/3 I/3 2/3 2/3
2
0
1
1/3
1
1
2*
1/9
1
1
0
2
-1/3
1
1
I*+2"
1/9
1
3* 1"+3"
1/9 1/9
1 1
3 3+1" ; 1
1/6 1/6
1/6 1/6
1
2
0
1/3
-1
1
0
2
1
-1/3
-1
1
14
1
1
0
1/2
-1/2
15
0
1
1
-1/2
-1/2
2/3 2/3
calculated performance o f several atomic-beam sources as described in literature are compared. It is worth noting that the intensity optimized sources for the Filtex/Hermes experiment and at the Indiana Cooler operate with a threefold gas flow and at a substantially higher nozzle temperature compared to the density optimized sources like the COSY-CBS and the ABT.
3. DISCUSSION The calculated intensities and densities o f the program code exceed the measured ones by about 25%. Since no additional loss mechanisms except hitting an obstacle during the beam transport is taken into account, these 25% also give an upper limit for additional losses and nonlinearities. For instance intra-beam scattering in the vicinity o f the nozzle is discussed in this respect. On the other hand, we know from dynamic measurements of the dissociator efficiency
124c
P.D Euersheim et al./Nuclear Physics A626 (1997) 117c 124c
Table 3 Comparison of various polarized atomic-beam sources Optimized Source for:
Intensity
Density
Nozzle Temperature [K]
Gas Density Intensity Intensity Flow calculated measured [ m b a r . I / s ] [101]/cm3] [1016/s] [1016/s]
Filtex/Hermes Indiana Cooler
80 80
1.5
10.4"
11.1 *
8.1 *
1.7
5.5
7.6
6.7
COSY-CBS ABT
30 30
0.5 0.5
5.8 6.2
5.1
4.3
4.0
-
*for a nuclear polarized beam this value has to be devided by 2 by means of a quadrupole mass-spectrometer that hydrogen atoms do not necessarily recombine to 100% at ordinary stainless steel surfaces. Thus, there is an inherent danger in all intensity measurements by compression tubes that the true intensity may be underestimated. A possible consequence is that the 25% discrepancy between calculated and true intensity may be even smaller.
REFERENCES
1. EDDA Collaboration, Nucl. Instr. Meth. A 329 (1993) 151 and A371 (1996) 388. 2. P.D. Eversheim et al., Polar. Phenom in Nucl. Phys., Bloomington, USA, Alp Conf. Prec. 339 (1994) 191. 3. P.D. Eversheim, Pol. Phen. Nucl. Part. Phys., 7-10. Jan. 1992, Trieste, Italy, Prec. 2nd Adriatico Research Conf., World Scientific, (1993) 142. 4. V.P. Derenchuk, A.J. Mendez and T.B. Clegg, High Energy Spin Phys., Bloomington, USA, AlP Conf. Prec. 343 (1994) 142. 5. R. Gebel, Ph.D. Thesis, Inst. fiir Strahlen- und Kemphysik, University Bonn (1994). 6. D. Sing et al., Nucl. Instr. Meth. A306 (1991) 36. 7. P. Schiemenz, A. Ross and G. Graw, Nucl. Instr. Meth. A305 (1991) 15. 8. W. Grfiebler, Prec. Sixth Int. Symp. Polar. Phenom. in Nucl. Phys., Osaka, 1985, J. Phys. Soc. Jpn. 55 (1986) Suppl. 435. 9. C.R. Meitzler, Code STRAHL, Brookhaven National Lab. (1989). 10. P.D. Eversheim et al., Polar. Phenom. in Nucl. Phys., Bloomington, USA, AlP Conf. Prec. 339 (1994) 668.
Nuclear Physics A626 (1997) 117c-124c
The polarized atomic-beam target for the EDDA experiment and the time-reversal invariance test at COSY* P.D. Eversheim, M. Altmeier, and O. Felden Institut ftir Strahlen- und Kernphysik, Universitat Bonn NuBallee 14-16, 53115 Bonn, Germany
For the the EDDA experiment, which was set up to measure the ~-~ excitation function during the acceleration ramp of the cooler synchrotron COSY at JOlich, a polarized atomic-beam target was designed regarding the restrictions imposed by the geometry of the EDDA detector. Later, when the time-reversal invariance experiment is to be performed, the EDDA detector will serve as efficient internal polarimeter and the source has to deliver tensor polarized deuterons. The modular design of this polarized atomic-beam target that allows to meet these conditions will be discussed in comparison to other existing polarized atomic-beam targets.
1. INTRODUCTION Two experiments are presently planned with an atomic-beam target (ABT) at the cooler synchrotron COSY at Jtilich: The EDDA experiment and a time-reversal invariance (TRI) test. The EDDA experiment measures with high precision the proton-proton excitation function in the 0.25-2.5 GeVLab energy and 10°- 72°Lab angle range. In order to suppress systematic error contributions caused by fluctuations in the COSY-ring, data are taken during the acceleration ramp of COSY. The circular EDDA detector [1] comprises an inner and an outer layer of scintillators that allow by kinematical eoicidence and vertex reconstruction to discriminate background events from protons scattered elastically offthe target. With the unpolarized COSY-beam and an unpolarized solid state CH 2 fiber-target up to now more than 107 p-p events have been recorded. Presently the COSY-facility is set up to accelerate the polarized beam from the colliding-beams source (COSY-CBS). Once the polarized beam in COSY is available up to 2.5 GeV and the ABT is installed as shown in figure 1, the EDDA measurements can be extended to give the energy-dependence of the analyzing powers Ay, Axx, Ayy, and Axz. It has been demonstrated that due to its circular design around the beam-pipe the EDDA detector also serves as an ideal internal polarimeter. The detector continuously monitors the
*Supportedby the BMBF, Germany 0375-9474/98/$19.00 © 1998 ElsevierScience B.V. All rights reserved. Pll S0375-9474(97)00528-9
118c
P.D. Eversheim et al./Nuclear Physics A626 (1997) 1 l 7c-124c
Atomic Beam
Beam Dump
to Spinfilter
EDDA Detector
COSY Beam
--- :_~-.
IIJllJlllllJt I
iiiiiiiiiiii i i iiu
I
I[
1
Atomic Beam Source
Im
H2JD2 Figure 1. The atomic beam target for the EDDA and TRI experiment at COSY.
polarization of the beam during the acceleration ramp as well as at a fixed energy for a circularing beam in COSY. The latter property of EDDA and the ability of the ABT to provide tensor polarized deuterons allows to perform at this target station a true, clean, P-even T-odd TRI nulltest [2]. 'True' in this context stresses the fact that the interpretation of the experimental result is for instance not affected by final-state interactions or by the assumtion of special hamiltonhns. 'Clean' emphasizes that compared to the situation in complex nuclei a possible effect is not diluted by observer nucleons which do not participate in the time-reversal violating interaction. At last, the P-even T-odd null-test allows to probe with high precision a special class of TRI-
119c
I?D. Eoersheim et al./Nuclear Physics A626 (1997) 117c-124c
tests. The idea of this experiment is depicted in figure 2. In a forward scattering experiment the
~
X
a)
b)
;z
®
®
..............
~
d
d'
)
.............
d)
c)
®
®
P
) .............
Figure 2. Pictorial demonstration that a time-reversed situation is prepared by either a proton or a deuteron spin-flip, a) The basic system is shown, b) The time reversal operation is applied (momenta and spins are reversed and the particles are exchanged). In order to have a direct comparison between situation a) and b), two rotations Ry(~) or Rx(r 0 by 180 ° about the y- or x- axis are applied, leading to the situations c) and d), respectively. This is allowed, since the scattering process is invariant under rotations. (3 - Proton spin up (y-direction) ® - Proton spin down <=> - Deuteron tensor polarization time-reversal violating total analyzing power Ay,xz is measured with a normally (y) polarized proton beam, circulating in the COSY-ring, and an x-z aligned tensor polarized deuteron beam from the ABT. For this experiment the COSY-ring not only serves as an accelerator but also as an ideal forward spectrometer and detector. Whereas for the EDDA experiment and phase 1 of the TRI test the ABT has to be optimized for maximum density, phase 2 oftbe TRI test requires a target-cell for better statistics and consequently the source has to be optimized for maximum intensity. It is intended to measure in phase 2 of the TRI test the analyzing power Ay, xz with an. accuracy of 10 -7 . It can be shown [3] that the only relevant observable which can fake a TRI effect is Ay, y. For this to happen, two conditions have to come true: i) the deuteron beam from the ABT contains
12oc
FD. Eversheim et al. /Nuclear Physics A626 (1997) 117~~124~
along with the tensor polarization some vector polarization and ii) a misalignment of the atomicbeam exists from the x-z direction into the y-direction. Therefore, in order to control the polarization of the atomic-beam, the ABT beam-dump has to provide the option for a polarimeter. Since only a small fraction (1%) of the atomic-beam will be available for analysis, once a target-cell is used, the ABT beam-dump allows to make use of an off-line spin-filter polarimeter [4]. Furthermore, since the COSY-ring will probably operate best with the smallest holding field across the interaction region, all polarized beams of the ABT should be of pure state in the first place. This requirement resulted in a modular design of the ABT, with respect to the position of the second 6-pole magnet group and the order of up to three RF-transitions.
2. TEIE ATOMIC-BEAM
SOURCE
The atomic-beam of the ABT is produced in an atomic-beam source which is essentially identical to the source of the COSY-CBS as described in [5]. The Hz/D2 molecules are dissociated in an inductively coupled 350W RF-discharge. The atoms passing the aluminium nozzle channel of 20mm length and 3mm diameter are cooled to about 30K. Thus, the atoms are slowed down with the consequences that i) the first tapered 6-pole magnets have an increased solid angle of acceptance in proportion to the beam temperature, and ii) the dwell time of the atoms in the interaction region with the COSY-beam increases invers proportional to the reduced beam velocity. These beneficial effects are in part offset by gas scattering in- and outside the nozzle. In order to reduce chromatic aberrations the atomic beam transport system comprises a second 6-pole magnet, the compressor magnet. Between these magnets or behind the compressor magnet up to three Abragam-Winter RF-transition units can induce transitions between the hyperline states of hydrogen or deuterium. Differences between the atomic-beam sources of the ABT and the COSY-CBS exist in the front part of the ABT (which has to fit into the space left by the EDDA detector) and in the 6-pole magnet design. Starting from the successfbl design of the electrically driven COSY-CBS magnets, which corresponds to the magnet design of the sources of the ETH-Zurich and PSI [6], the 6-pole magnets for the ABT in COSY are now made out of permanent magnets @Id-Fe-B alloy [7 J) as shown in figure 3. 2.1.Spin preparation The nuclear spin of the atomic beam is prepared via 6-pole magnets and RF-transitions. The use of two groups of 6-pole magnets and up to three RF-transitions offers a high flexibility with respect to the preparation of the desired nuclear spin states. The 6-pole magnets defocus atoms with magnetic electron quantum number l/2 and focus states with +1/2. Therefore, the beam intensity behind the first group of 6-pole magnets is divided by two. Yet the atomic beam is unpolarized with respect to the nuclear spin. The nuclear spin is prepared by means of RF-transitions that induce a transition between a populated and an unpopulated state (those with l/2). Depending on the size of the static transversal magnetic field B, compared to critical magnetic field B, from the hyperfine term splitting AE = 2. uB*B, with the Bohr’s magnetron pB, several types of transitions are distinmJ
mJ
=
mJ
=
-
=
-
FD. Euersheim et al./Nuclear Physics A626 (1997) 117c 124c
121 c
/~d-Head AI
6-Pole Magnets
RF-Transitions
Gas Inlet
H21Dz
lOOmm
Figure 3. Details of the atomic-beam source. The hatched areas inside the 6-pole magnets show the size of the permanent magnets in contrast to the electrically driven ones from the COSYCBS.
guished: Zero Field transition (ZF, a novel transition utilized at the Bonn polarized ion source, BT ~ 0), Weak Field transition (WF, BT is within the linear Zeeman regime of the hyperfinestmcture splitting), Medium Field transition (MF, BT is just outside the linear Zeeman regime of the hyperfinestructure splitting) and Intermediate Field transition (IF, BT < Bo ). Table 1 gives the operating conditions for the various transitions. The symbols .L [Igive the orientation of the RFTable 1 Characteristics of RF-transitions Tr. No.: Type B ~ Hydrogen Frequ. [MHz] Transition(s) 1
WF
2 3 4 5
Deuterium Frequ. [MI-Iz] Transition(s)
I
7-20
143
7
14"4
IF
±
1448
244
415
24-*6
IF ZF MF
± ± I
243
314 329 20
345 2 4 6 & 3"*5 344
60
122c
PD. Eversheim et al. /Nuclear Physics A626 (1997) I1 7c-124~
magnetic field B, with respect to the atomic-beam velocity v. If B, I v, then B WI1B T Ofspecial interest are atomic-beams in a pure state, i.e. state 1 or 3 for hydrogen, 1 or 4 for deuterium, Since for these beams any magnitude of magnetic guiding field across the interaction region is sufficient to align the nuclear spin. For hydrogen the options are discussed elsewhere [8], for deuterium in view of the transitions given in table 1 all non-trivial magnet and transition combinations are given in table 2. Figure 4 gives the possible schemes for the 6-pole and RFtransition combinations.
Figure 4.Scheme of 6-pole magnet and RF-transition
(Tr.) combinations.
In table 2 the vector polarization Pa, the tensor polarization P, and the relative Intensity i, for the figures of merit are calculated according to: P, =
N+-NN++NO+N-
p
= N+-2.N”+N=
N++N“+N-
I = N++N’+Nr
3
(1)
Pure states in combionation no.: 1,6 and 7 are underlined. Favourable combinations with respect to a high figure of merit or pure vector or tensor polarization are the combinations 1/3,4/S and 617. 2.2.Modeiling the atomic beam transport The 6-pole magnet design of the ABT is derived from a modified program code [9], which calculates the beam transport through skimmers and magnets by a fast linear matrix approach. The predictive power of the code has been successllly verified by the performance of the polarized ion source of the Bonn isochronous cyclotron and the atomic-beam source of the COSY-CBS. Meanwhile the code comprises an optimization algorithm that tunes the magnet design with respect to a given figure of merit, for instance density or intensity at the interaction region. Examples of informations the program code provides at present are given in [lo]. One of the major difIiculties in modelling the beam transport is the determination of a realistic velocity and density distribution of the atomic-beam at the end of the cooled dissociator nozzle. Since inside the nozzle turbulent flow may dominate, some mm downstream the nozzle molecular flow prevails. Reliable calculations that take realistic skimmer shapes into account need CRAY computing power and are not available yet. Therefore, instead of calculated input distributions measured distributions have been used. The predictive power of the code is demonstrated by table 3, where the measured and
123c
P.D. Eoersheim et al./Nuclear Physics A626 (1997) 117c-124c
Table 2 Possible deuteron polarizations No.
Population N + N ° N-
I0 11 12 13
Polarization Pz
Pzz
Intensity
Combination
Ir
Tr. (cf. table 1)
pz2.i,
PZZ ° r
2I
1+2" "2+5*; 2 1+3 1+3"
0 0 0
2/3 4/3 8/3
1
0
1
0
1
0 0
1 2
0 0
0 0
-2 -2
2/3 1/3 2/3
2 0
1 1
0 2
2/3 -2/3
0 0
1 1
2*+3* ; 4*
4/9
0
1*
4/9
0
2+3 ; 4 1+2 ; 4+1" 3+2* 2+ 1*
1/3 1/3 2/3 2/3
1/3 1/3 2/3 2/3
1
0
0
1
1
0 2 0
0 0 0
1 0 2
-1 1 -1
1 1 1
1/3 I/3 2/3 2/3
2
0
1
1/3
1
1
2*
1/9
1
1
0
2
-1/3
1
1
I*+2"
1/9
1
3* 1"+3"
1/9 1/9
1 1
3 3+1" ; 1
1/6 1/6
1/6 1/6
1
2
0
1/3
-1
1
0
2
1
-1/3
-1
1
14
1
1
0
1/2
-1/2
15
0
1
1
-1/2
-1/2
2/3 2/3
calculated performance o f several atomic-beam sources as described in literature are compared. It is worth noting that the intensity optimized sources for the Filtex/Hermes experiment and at the Indiana Cooler operate with a threefold gas flow and at a substantially higher nozzle temperature compared to the density optimized sources like the COSY-CBS and the ABT.
3. DISCUSSION The calculated intensities and densities o f the program code exceed the measured ones by about 25%. Since no additional loss mechanisms except hitting an obstacle during the beam transport is taken into account, these 25% also give an upper limit for additional losses and nonlinearities. For instance intra-beam scattering in the vicinity o f the nozzle is discussed in this respect. On the other hand, we know from dynamic measurements of the dissociator efficiency
124c
P.D Euersheim et al./Nuclear Physics A626 (1997) 117c 124c
Table 3 Comparison of various polarized atomic-beam sources Optimized Source for:
Intensity
Density
Nozzle Temperature [K]
Gas Density Intensity Intensity Flow calculated measured [ m b a r . I / s ] [101]/cm3] [1016/s] [1016/s]
Filtex/Hermes Indiana Cooler
80 80
1.5
10.4"
11.1 *
8.1 *
1.7
5.5
7.6
6.7
COSY-CBS ABT
30 30
0.5 0.5
5.8 6.2
5.1
4.3
4.0
-
*for a nuclear polarized beam this value has to be devided by 2 by means of a quadrupole mass-spectrometer that hydrogen atoms do not necessarily recombine to 100% at ordinary stainless steel surfaces. Thus, there is an inherent danger in all intensity measurements by compression tubes that the true intensity may be underestimated. A possible consequence is that the 25% discrepancy between calculated and true intensity may be even smaller.
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