Polarized Fusion. Can Polarization Help to Increase the Energy Output of Fusion Reactors?

Since more than 60 years scientists are working on the idea to produce energy from nuclear fusion of light particles like the Hydrogen isotopes. In the meantime, the energy output of e.g. tokamak reactors was increased by five orders and modern experiments like JET are approaching the border for energy production. The international ITER collaboration is preparing the first fusion reactor that will produce about ten times more energy, compared to the energy that is needed to run the experiment. Today, the laser-induced inertial fusion reached the same level and experiments at the National Ignition Facility (NIF) in California, USA, demonstrate a ratio between produced and induced energy about one at the end of 2013. In parallel, it is discussed since 1970 to use nuclear polarized fuel to increase the total cross sections of the diff erent fusio n reactions. The energy gain of fusion reactors does not depend linearly on the total cross section. Depending on the diff erent concepts for nuclear fusion, magnetic confinement or inertial fusion, the energy gain


Introduction
Since more than 60 years scientists are working on the idea to produce energy from nuclear fusion of light particles like the Hydrogen isotopes.In the meantime, the energy output of e.g.tokamak reactors was increased by five orders and modern experiments like JET are approaching the border for energy production.The international ITER collaboration is preparing the first fusion reactor that will produce about ten times more energy, compared to the energy that is needed to run the experiment.Today, the laser-induced inertial fusion reached the same level and experiments at the National Ignition Facility (NIF) in California, USA, demonstrate a ratio between produced and induced energy about one at the end of 2013. 1 In parallel, it is discussed since 1970 to use nuclear polarized fuel to increase the total cross sections of the di fferent fusio n reactions. 2The energy gain of fusion reactors does not depend linearly on the total cross section.Depending on the different concepts for nuclear fusion, magnetic confinement or inertial fusion, the energy gain R. Engels & G. Ciullo is improved above average.M. Temporal et al. have shown, e.g., that the energy gain of laser-induced inertial fusion might be increased by a factor four, or that the necessary laser power can be reduced by 20 %, if the nuclear fuel was polarized before. 3The downsized laser power will reduce the costs of the corresponding project by a reasonable amount.In addition, the diff erential cross sections can be modified so that it will be possible to focus the ejectiles, e.g. the neutrons, on special wall areas.In a tokamak this can be used to concentrate the neutron flux to special outer parts of the blanket, where the cooling can be improved and the neutrons be used for Tritium production via the exothermic reaction 6 Li + n → 4 He+ t. 4 At the same time, less cooling is needed for the inner parts of the blanket that allows to bring the magnetic field coils closer to the fusion plasma.The increased magnetic field in the plasma will increase the energy gain additionally.Another option of polarized fuel is a new kind of plasma diagnostic inside a tokamak.In combination with modern Nuclear Magnetic Resonance technologies (NMR) anisotropies in the plasma can be measured to learn more about the diff erent plasma modes. 5

Open Questions
In contradiction to all this advantages of polarized fuel in nuclear fusion reactors it was never used up to now.Before the profit of polarization is an option for energy production a long list of questions must be answered.

The polarized differential and total cross sections
W h e naT r i t o na n daD e u t e r o nw i l lf u s ea 5 He nucleus is build for a short time, before the intermediate nucleus will decay into 4 He and a neutron.The decay is exothermic and a kinetic energy of 17.6 MeV is given to the ejectiles.This reaction is dominated by a J =3 /2 + resonance, i.e. the nuclear spin of the 5 He nucleon must be 3/2.At low energies mostly s-waves contribute (96 %) and, therefore, the spins of the Triton (S =1/2) and the Deuteron (S = 1) cannot be anti-parallel to allow the fusion process.This means that two out of six possible permutations of both spins are not contributing to the fusion process.If the spins of both projectiles are aligned right from the beginning, the total cross section is increased by a factor 1.5.In addition, the differential cross section is modified too.In the low energy regime (≤ 100 keV) of a fusion plasma the differential cross section is constant for different scattering angles.If both spins are parallel to the external magnetic field the cross sections around θ =90 ˚are increased and for 0 ˚and 180 ˚it is decreased.Other spin combinations will allow different modifications. 6For the mirror reaction 3 He+d → 4 He+p the situation is very similar.Again, the intermediate 5 Li nucleus must have a spin of 3/2.In this case, the predictions for the differential cross sections were experimentally proved with a polarized deuteron beam on a polarized 3 He target in 1970. 7Another option are the DD-reactions: d + d → 3 He + n or d + d → t + p.Even if these reactions are not used by themselves for energy production due to the smaller cross sections and the lower energy output, these reactions will run in

Polarized Fusion
Fig. 1.The different predictions for the quintet-suppression factor of the DD reactions, i.e. the ratio of the total cross sections when both deuteron spins are parallel to the quantization axis (σ 1,1 ), and the unpolarized case (σ 0 ).
parallel to the other fusion reactions.Therefore, the dependence of the cross sections on the polarization of the projectiles must be known before polarized deuterons are used for energy production.For these spin S =1o nS = 1 fusion reactions the predictions are much more complicated (see Fig. 1) and must be verified by a precise measurement with a polarized deuteron beam on a polarized Deuterium target.In this case, several spin-correlation coeffi cients can be measured for different spin combinations as a function of the beam energy and the influence on the diff erential and total cross sections can be calculated.This measurement is under construction at the Petersburg Nuclear Physics Institute in Gatchina in a collaboration with the Institute for Nuclear Physics of the research center Jülich, Germany, and the University of Ferrara, Italy.The polarized deuteron source, formerly used at the KVI in Groningen, the Netherlands, will produce a vector-or tensor-polarized beam of up to 50 µA and polarization values about 70 % of the maximum values. 8For the polarized jet target a polarized atomic beam source (ABS) is rebuilt that was used at the University of Ferrara before.The atomic flux of this source is about 6 × 10 16 atoms s −1 and the corresponding target thickness is 3 × 10 11 atoms cm −2 .The luminosity is therefore 4.5 × 10 25 cm −2 s −1 and the following count rate will be about 60 counts h −1 at a beam energy of 30 keV.This count rate is rather low, but for a stand-alone experiment without an accelerator absolutely reasonable.The polarization of the Deuterium target beam will be measured with a Lambshift polarimeter 9,10 and, in addition, the polarization of the deuteron beam will be registered with a nuclear-reaction polarimeter.

Polarisation conservation in the different types of plasma
Polarized fuel is useless, if the polarization will not survive in the fusion plasma.First calculations showed that the polarization might be preserved long enough in a magnetic confinement plasma 12 and during the interaction with the blanket of a tokamak reactor. 13Other depolarizing effects are possible, 14 but can be overcome.Nevertheless, a test under real conditions is necessary and suggested for the DIII tokamak in San Diego. 6or inertial fusion the situation seems to be relaxed due to the very short duration of the fusion process. 15For laser-induced fusion the extreme amplitudes of the oscillating magnetic field up to 10 4 T might be able to influence the polarization. 16An experiment to investigate the conservation of the polarization at these conditions is foreseen by a collaboration of the University of Düsseldorf and the Research Center Jülich in 2015 at the PHELIX-laser in Darmstadt, Germany.Laser-acceleration of 4 He 2+ ions from a 4 He gas jet up to 1 MeV was made successfully.If now polarized 3 He 2+ ions from a polarized 3 He gas jet target will be registered with a nuclearreaction polarimeter, based on the known analyzing powers of the d+ He+p reaction, it is shown that the polarization will survive in a laser-induced plasma.

How to produce and handle polarized fuel
At least for the possible energy production with polarized fuel, but even for the supposed experiments at a tokamak a reasonable amount of polarized fuel is needed.Due to "laser-pumping" macroscopic amounts of polarized 3 He gas are produced and stored in special glass bottles to be used for several applications, e.g.NMR spectroscopy of the lounge after inhaling.Laser-pumping is useful for Hydrogen atoms and, therefore, must be possible for Tritium, because the hyperfine structure of both isotopes is very similar.The polarized Tritium atoms cannot be stored for a long time, because it is a radical that attacks more or less any kind of surface.But "online" production close to a tokamak is a possible option.For Deuterium exists two methods to produce polarized nucleons: with a polarized atomic beam source 17 a large polarization up to P z =+/−0.9orPzz =+0.9/−1.8isachieved, but the intensity with less than 10 17 atoms s −1 is at least four orders to low to feed a tokamak.Frozen-spin targets of HD ice are produced at extreme magnetic fields of 15 T and temperatures below 100 mK. 6The Deuterium polarization is limited to P =0.25 and the Hydrogen atoms are an unwanted contribution for the fusion plasma.In principle, frozen DT ice is possible, but to reach the very low temperatures during the continuous decay of the tritons needs a larger amount of cooling power.One option to overcome these problems is to recombine the Deuterium atoms of an ABS into molecules and to store them.To optimize this process a collaboration was built between the University of Cologne, the Petersburg Nuclear Physics Institute and the research center Jülich.In T-shaped storage cells with a selected surface material the polarized atoms, Hydrogen or Deuterium, recombine at temperatures free path of this large ions at a cell pressure of about 10 −4 mbar is shorter than the length of the cell.Thus, all of these ions are built close to the exit of the storage cell, where the average amount of wall collisions is larger.This method should be useful for Deuterium too.In this case, the polarized D 2 molecules can be collected by freezing them at the end of the cell.If now the atomic flux of an ABS is stored for one day the amount of polarized D 2 ice will be enough to feed a tokamak for one second.

Discussion
Before polarized fuel might be useful for nuclear fusion these questions must be answered.The necessary tools we already have in hand within our community.