PNPI participants: N. Chernov, K. Grigoryev, I. Ivanov, E. Komarov, L. Kotchenda, P. Kravtsov,
M. Mikirtychyants, S. Sherman, S. Terekhin, V. Trofimov, A. Vasilyev, M. Vznuzdaev
1. Introduction
A double-polarized dd-fusion experiment is under preparation at PNPI, Gatchina. The experimental
program includes measurements of the asymmetry in the differential cross sections for the reactions d + d →
He + n and d + d → t + p. The total cross-section modification for polarized dd-fusion will also be
investigated. An increase by a factor of 1.5 was already established for the d + 3He and d + t reactions. The
spin-correlation coefficients Cz,z and Czz,zz will be measured for both reactions to determine the quintet-state
suppression factor, which has quite different theoretical predictions and is very important for building a
neutron-lean fusion reactor. In addition, more spin-correlation coefficients can be measured at different
energies with this experimental set-up in order to get more information about the dd-fusion process. The
screening effect due to atomic electrons which shows up in the astrophysical S-factor may also be
investigated in this experiment for different spin combinations of the electron and the nucleus.
The principal aspects of the thermonuclear fusion problem include understanding of the nuclear
processes of the fundamental fusion reactions at low energies, confinement of the hot and dense plasma, and
energy extraction from the plasma. Standard candidates for the fusion fuel include the hydrogen isotopes
(deuterium and tritium) and the light helium isotope – 3He. For the practical use of fusion reactors one needs
to know the nuclear cross sections for nuclear interactions of light nuclei. These cross sections were
extensively studied, but not all of them are well known. This is also true for the spin sector, where spin
effects in few-body reactions are very large.
One of the classical examples is the bound state in the nucleon-nucleon system. It exists only in the spintriplet channel, the spin-singlet scattering length being about four times larger than the spin-triplet one and
having an opposite sign. The second example is the broad 0+ resonance in the 4He nucleus. It causes a
gigantic cross section for n-3He scattering in the spin-singlet channel, which leads to an almost 100% spin
filtering of neutrons with an excellent transmission rate of 50% in the polarized 3He target [1]. This
technique is used to generate intense polarized neutron beams [2]. The fact that the amplitudes of important
fusion reactions
d + 3H → n + 4He and
d + 3He → p + 4He
are dominated by an S-wave J = 3/2+ resonance, significantly simplifies handling of the double-polarization
effects. Simple counting of the spin states implies that only 2/3 of nuclei can undergo fusion in unpolarized
plasma. Alternatively, the full polarization of the deuteron and 3He would enhance the fusion cross section
by 50% [3].
Based on the available experimental data on the deuteron-deuteron interactions, Ad'yasevich and
Fomenko suggested in 1969 a possibility of polarization enhancement of the dd-fusion rate by a factor of two
[4]. The first experimental proposal to study the polarization coefficients in the double-polarized fusion [5]
was not realized because the polarized atomic and ion beam technique at that time did not allow to produce
beams of enough intensity.
A substantial step forward was made in 1982 in a theoretical study of depolarization of nuclei in
magnetically confined plasma [6]. The main conclusion was that the depolarization time significantly
exceeds that of the fusion reaction. Presently, it is considered feasible to confine 3He with the nuclear
polarization reaching 55%, and to inject neutral deuterium with the nuclear polarization of about 55%. The
experiment is planned at the DIII-D Tokamak at San Diego [7]. The estimated enhancement of the fusion
should be around 15%. If the retention of the deuterium polarization is confirmed, these measurements will
be continued with tritium.
An alternative approach to confirm experimentally the persistence of the nuclear polarization in a fusion
process in the plasma generated by a petawatt laser hitting a polarized frozen HD target was suggested at
Orsay [8]. Detecting the final state gamma quanta and neutrons, one would have an experimental access to
both reactions p + d → 3He + γ and d + d → 3He + n.
T-matrix an. Lemaitre 1993 (p)
T-matrix an. Lemaitre 1993 (n)
R-matrix an. Hale and Doolen 1984 (p)
R-matrix an. Hale and Doolen 1984 (n)
RRGM Hofmann and Fick 1984/
R-matrix and Hale et al. 1983 (p)
DWBA Zhang et al. 1999 (n)
part-wave an. Zhang et al. 1999 (p)
4-body Faddeev, Uzu et al. 2002 (p)
4-body Faddeev, Uzu et al. 1999(p)
Deltuva and Fonseca,
Phys. Rev. C 81 (2010)
D(d,p) H
Quintet suppression factor 1,1/0
D(d,n) He
Lab. energy (keV)
Fig. 1. Theoretical predictions of the quintet suppression factor
2. Measurements of the cross sections for polarized fusion reactions
 
The reactions d  t and d  3 He with the initially polarized particles have been already investigated
 
[3]. As for the basic fusion reaction d  d in the energy range of 10–100 keV, the spin-correlation
components of this reaction have not been measured yet. For the practical use of the polarized fuel in a
fusion reactor, only two spin combinations are of importance, when the deuteron spins are parallel or antiparallel to each other. Theoretical predictions for a change of the reaction cross section are shown in Fig. 1.
Here, the quintet state suppression factor (QSF) is defined as the ratio of the reaction cross section for
parallel spins of the initial particles to the total unpolarized reaction cross section. The value of the QSF = 1
means that the polarization of the initial particles does not affect the total reaction cross section. Large
discrepancy in predictions illustrates a great demand for direct measurements of this observable to check
theoretical models. The experimental plan includes measurements of the asymmetry of the differential cross
sections, determination of the total cross-section change for polarized initial particles, and measurements of
the spin-correlation factors Cz,z and Czz,zz for investigation of the quintet suppression factor.
3. Investigations of methods for increasing the intensity of polarized sources
Polarized deuterium is produced at present mainly with the help of atomic beam sources (ABS). These
sources are used at accelerator injectors (with subsequent ionization of atoms) or for the internal targets at
storage rings of accelerators [9]. Building of a polarized atomic beam source is possible only in the
framework of high-expenditure accelerator experiments due to high cost of the ABS equipment. The
intensity of the world-best polarized sources do not exceed 1017 at/s. At the same time, the feeding flux of
polarized deuterons for 100 MW full fledged polarized thermonuclear reactors should be 1021–1022 at/s.
An intensity increase by 4–5 orders of magnitude is not feasible with atomic beam sources. Thus, it is
necessary to search for a new source of polarized deuterons. One of possible directions in this search is to
use nuclear polarized molecular deuterium.
4. Experiment
We propose to investigate at various energies (between 10 and 100 keV) the angular distributions of the
products of the reactions
d  d  t  p and
d  d  3 He  n.
The energy of the initial particles is very low, and the penetrating depth is exceedingly small. The solid
target experiments would have large uncertainties in the results because of an unknown surface polarization
and influence of the multiple scattering on the energy of the reaction products. To reduce these uncertainties,
one can investigate direct interaction of a polarized deuteron beam with polarized neutral deuterium atoms in
vacuum (Fig. 2).
The ABS for this experiment is constructed on the basis of the Cologne University source which was
used in the SAPIS project [10]. It produces a beam of neutral polarized atoms with the given vector or tensor
polarization. Polarized atoms in the beam have thermal velocities with the energy of about 0.1 eV. The beam
intensity of 1015 at/s achieved at the Cologne University is not sufficient for measurements, and there are
plans to upgrade the ABS and to increase the beam intensity up to 1016 at/s.
Using neutral atoms for the target allows to increase significantly the target density (there is no space
charge restriction), but it requires to take into account an impact of the atomic electron on the reaction rate,
which does not exist in the ionized plasma of thermonuclear reactors. An electron screening effect (the socalled astrophysical S-factor) is well known and measured experimentally [11]. This effect has a
considerable influence on the reaction rate at the energies below 10 keV, but is not important at higher
energies. Reversing the arguments, direct experimental investigations of this effect with allowance for
polarization of both the incident nucleus and the target atomic electron would be very interesting on its own.
No experimental data exist, and no theoretical calculations in this field have been performed so far.
He (0.8 MeV),
3 +
H (1.0 MeV)
d 0 (0.1 eV)
or LSP
d0d 
Polarized Atomic Beam Source
I ~ 1 ∙ 1016 a/s
Target density ~ 10 a/cm
Vector polarization: ± 0.7
He 2  n  e
H  pe
d  (1-32 keV)
Polarized Ion Source
Ion beam: I ≤ 20 μ A
(1.3 ∙ 1014 d/s)
Ebeam ≤ 32 keV
Vector polarization: ± 0.7
d 0 (0.1 eV)
n (2.4 MeV),
p (3.0 MeV)
Lamb-Shift Polarimeter
Fig. 2. Layout of the experiment
Neutral atoms of the target will be bombarded by positive deuterium ions (deuterons), which are
produced by a polarized ion source (POLIS). This source was utilized as an injector of the cyclotron
accelerator at the KVI institute, Groningen, Netherland. The source is producing an ion beam of 20 μA and
energies up to 35 keV [12]. A substantial upgrade of this source to increase the beam energy up to 100 keV
is required. At this energy one can cross-check the experimental results with the existing data (available for
the energies higher than 100 keV). It is planned to use a linear ion accelerator to increase the ion energy from
35 keV up to the desired range of 35-100 keV. This upgrade will change the constant beam into a bunched
one with certain intensity losses.
The production and use of polarized ion and atomic beams require accurate measurements of the
polarization. It is planned to use three polarimeters in the experiment: two Lamb-shift polarimeters (LSP) for
initial tuning of the beams and a nuclear reaction polarimeter for constant monitoring of the ion beam
polarization during the production runs.
The LSP has a substantially better precision, and allows measurements of more spin states of the beam,
but its operation is more complicated compared to the nuclear reaction polarimeter. Therefore, this
polarimeter will be used only for tuning of the beam sources and periodic checking of the polarization. The
nuclear reaction polarimeter makes use of the asymmetry of the nuclear fusion reaction products, which can
be detected with semiconductor detectors.
One of the main tasks of the experiment is to detect the fusion reaction products – protons, tritium and
He ions (neutrons cannot be detected in this experiment). The estimated count rate at the energy of 20 keV
is about 13 events per hour. Therefore, the detector system should have low background and noise to
distinguish these rare events. Problems of the cosmic radiation and the natural radioactivity of the
construction materials should be carefully investigated.
Fig. 3. Initial prototype of the detector system
5. Detector set-up
The main goal of the experiment is to perform direct measurements of the angular distributions of the
reaction products. Therefore, the detector system should cover the maximum solid angle around the
interaction point (the ideal case – 4-π solid angle), with typical angular resolution of 10–15°. The prototype
of the detector system will consist of two Elementary Detector Cells (EDC) located at 180° to each other,
which can be rotated by two step motors in a gimbal suspension (see Fig. 3). This set-up will be used to
measure the energy resolution of the detectors, preliminary angular distributions with small statistics, and
also to determine the necessary angular resolution for the final detector system. The prototype will also help
to investigate technical questions to the detectors: the degradation time of the semiconductors in the vacuum
with some traces of atomic deuterium, which is quite an active substance, the lifetime of the detector in the
experimental conditions, etc. The final detector system should cover 4-π solid angle. It is supposed to be
built in a cubic shape construction with 80% covering of the area around the interaction point (Fig. 4).
The detector system will be surrounded with Helmholtz coils to provide constant magnetic field in the
interaction region and rotation of the atomic polarization. The Elementary Detector Cell will contain 16
surface barrier silicon detectors with the total size of 32×32 mm2.
The readout electronics for the detector system is under development, including electronic signal
conditioning and processing with a dedicated software. All information from the detector system will be
acquired, accumulated and analysed off-line to determine the differential cross sections.
Fig. 4. Detector set-up
6. Conclusion
This experiment to measure the cross sections for the polarized deuterium fusion reaction will provide
for the first time direct measurements of the spin-correlation coefficients in the energy range of 10–100 keV,
and finally will give a systematic ground for the practical use of polarized deuterons in the thermo-nuclear
fusion with estimation of possible benefits from the polarization.
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 
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