- Email: [email protected]
Aspects of target optimization for ADS with light ion beams at energies below 0.5 AGeV
Progress in Nuclear Energy 120 (2020) 103221
Contents lists available at ScienceDirect
Progress in Nuclear Energy journal homepage: http://www.elsevier.com/locate/pnucene
Aspects of target optimization for ADS with light ion beams at energies below 0.5 AGeV M. Paraipan a, b, *, V.M. Javadova a, S.I. Tyutyunnikov a a b
Joint Institute for Nuclear Research, Dubna, Russia Institute of Space Science, Bucharest-Magurele, Romania
A R T I C L E I N F O
A B S T R A C T
Keywords: Accelerator driven system Ion beam Energy efficiency Converter material
A comparative study about the energy efficiency of proton and light ion beams used for energy production in accelerator driven systems (ADS) is performed. The energy gain G, defined as the ratio of the energy produced to the energy spent to accelerate the beam is used as measure for the energy efficiency. The energy released in the target is obtained through simulation with the code Geant4, and the spent energy is calculated by scaling from the data about the accelerator efficiency for a reference particle. An optimal proton energy of 1.5 GeV is revealed, when the beam is accelerated in a linac. The advantage of light ion beams, especially 7Li at energies below 0.5 AGeV, which allows a reduction of the accelerator length, is substantiated. A study about the target design and the choice of the converter meant to maximize the efficiency of the energy ADS irradiated with light ion beams (7Li) with energies in the range 0.25–0.5 AGeV is presented. The influence of the fuel composition, of the geometry of the target, of the coolant and the converter materials are investigated. The most significant influence on the energy released has the material used for the converter. Cylindrical con verters from various materials, from very light (Li, Be) to very heavy (W, Pb, U) are analyzed. The influence of the dimensions of the converter on the energy released in the target is studied and the conditions which maximize the energetic efficiency and ensure a high level of burning of the actinides are determined. Solid fuel with different compositions (metal, oxide, carbide) and liquid fuel (molten salt) are considered. The advantage of a target with beryllium converter for both proton and lithium beams is underlined. The use of a Be converter with length 100–120 cm makes a beam of 7Li with the energy 0.25AGeV (in solid fuel) and 0.275 AGeV (in liquid fuel) equivalent from the point of view of the net power produced with a beam of 1.5 GeV proton, and allow the building of an accelerator 2.2–2.6 times shorter. A comparison between the evolution of the fuel composition during irradiation and its influence on the period of operation without refueling for target with LBE and Be converters is realized. The Be converter allows also to achieve a higher level of burning of the actinides and consequently a larger period between refueling.
1. Introduction The search for the solutions to the problems with which water re actors with once-through fuel cycle are confronted (low incineration rate of the nuclear fuel, insufficient nuclear safety) generated the idea to use accelerated particle beams interacting in a metal target as supple mentary source of neutrons which allows the functioning of the reactor with criticality coefficient below 0.99. A safer exploitation of nuclear plants is realized in this way, and the harder neutron spectrum obtained ensures a better incineration of the actinides. The idea appeared in the middle of last century, but as entire concept was presented in (Rubbia
et al., 1993). Since then, many programs and projects around the world are dedicated to this subject (EUROTRANS program, MYRRHA and ESS projects in European Union, OMEGA program in Japan, CIADS in China). All of them plan to use proton beams. In spite of the almost generalized opinion that the optimal beam for ADS is a proton beam with energy around 1–1.5 GeV (Oigawa et al., 2004; Zhao et al., 2014; Beller et al., 2001) we have shown in previous works that ion beams accelerated in a synchrotron or a linear accelerator have a superior energetic efficiency than protons (Paraipan et al., 2012; Baldin et al., 2017). The advantage of light ion beams, especially 7Li at energies below 0.5 AGeV is underlined in (Paraipan et al., 2017; Paraipan et al., 2019).
* Corresponding author. Joint Institute for Nuclear Research, Dubna, Russia. E-mail address: [email protected] (M. Paraipan). https://doi.org/10.1016/j.pnucene.2019.103221 Received 17 July 2019; Received in revised form 26 November 2019; Accepted 16 December 2019 Available online 24 December 2019 0149-1970/© 2019 Published by Elsevier Ltd.
M. Paraipan et al.
Progress in Nuclear Energy 120 (2020) 103221
Fig. 1. The dependence of the energy gain for protons (a) and the relative energy gain for ions (b) on the beam energy, in quasi-infinite U target enriched with 5.7% 235U.
In the present work the influence of the convertor material and di mensions on the energy released in the target is studied. The energy efficiency is calculated for the case of linear accelerator. It was shown in (Baldin et al., 2017) that the best energy efficiency would be obtained when the beam is accelerated in a synchrotron. But in a synchrotron one cannot obtain the high beam intensity necessary for ADS, so we have to limit our analysis to the situation when the beam is accelerated in a linear accelerator. In this case the values obtained for the energy effi ciency are slightly worse than in a synchrotron. The results obtained with beams of 7Li with energies in the range 0.25–0.45 AGeV are compared with those obtained with proton beam with energy 1.5 GeV. At this energy the energy efficiency of the proton beam accelerated in a linac reaches the maximum (Paraipan et al., 2018).
linear proton accelerator is realized in the technical report of the Eu ropean Spallation Source (ESS) project (ESS Technical Report, 2011). The ESS project plans to accelerate a proton beam with energy 2 GeV and beam power 5 MW with an accelerator efficiency of 0.18. For a linear accelerator Pacc depends on the accelerator length and scales as A⋅E/Z, where Z represents the atomic number of the ion, A is the mass number, and E is the energy per nucleon. In this way if Pspent0 and the accelerator efficiency η0 for a reference particle (atomic number Z0, mass number A0, final energy per nucleon E0) are known one can calculate the power spent for another particle. Assuming the same beam intensity one gets: � � � � 1 Z0 Pspent ¼ A ⋅ E⋅Ibeam 1 þ 1 (1) η0 Z
2. Method
Although such high value for the accelerator efficiency as the one estimated in (ESS Technical Report, 2011) remains to be demonstrated, we used it for the reference particle (proton) in our work. More details about the method to calculate Pspent can be found in (Paraipan et al., 2017). The power produced depends on the energy released in the target per incident projectile Edep, beam intensity Ibeam, and conversion coefficient from thermal to electrical power ηel:
The energy released in the target was calculated with the simulation toolkit Geant4 (Agostinelli et al., 2003) extended to work with elements heavier than uranium. The code Geant4 is used for modelling the par ticle interaction and transport. For the modelling of the electromagnetic interaction standard electromagnetic models were used. The inelastic interaction was modelled with cascade models (Bertini cascade for hadrons and pions, binary cascade for ions). For neutrons with energy below 20 MeV high precision neutron models, based on a detailed implementation of the experimental data from ENDF library (Chadwick et al., 2011) were used. The reliability of the predictions obtained with Geant4 was checked against experimental data about neutron yield from thin and thick metallic targets irradiated with protons and light ions (Baldin et al., 2016). The capability of Geant4 to predict the isotopes accumulation and the distribution of fission fragments was checked in (Paraipan et al., 2017; Adam et al., 2017). The conclusion was that for integral values as the neutron yield, the number of fissions or the energy released one can count on the results of the simulations in the limits of 25–30%. The energy gain G is used as measure for the energy efficiency. An often made mistake is to define the energy gain as the ratio of the power produced in the target Pprod to the power transmitted to the beam Pbeam. The correct definition of G is the ratio of the power produced in the target Pprod to the power spent to accelerate the beam Pspent. Pspent in cludes besides Pbeam the power necessary to maintain the functioning of the accelerator Pacc. Usually, Pbeam represents only a small part (below 10%) from the total power spent. Constant efforts are made in order to improve the accelerator efficiency. A rigorous estimation of Pspent for a
(2)
Pprod ¼ Edep Ibeam ηel 16
A value of 1.25⋅10 for the beam intensity and a usual value of 0.4 for ηel were used in the present work. 3. Results and discussion A first set of simulations was realized in a quasi-infinite metallic uranium target, enriched with 5.7% 235U and a criticality coefficient of 0.96. The target was a cylinder with dimensions large enough (radius 100 cm, length 20 cm) to obtain the saturation of the energy released in both radial and longitudinal directions. The cylinder was irradiated with protons with energy between 0.5 and 4 GeV, and light ions (7Li, 9Be, 11B, 12 C) with the energy from 0.25 to 1 AGeV. The dependence of the energy gain G on the proton energy is presented in Fig. 1a. One remarks that the optimal energy for proton beams is ~1.5 GeV, value at which G reaches a plateau. In the case of the investigated light ions the dependence of the relative gain (defined as the ratio of the G for ion to the G for 1.5 GeV proton) on the ion energy is shown in Fig. 1b. The most promising results are obtained with 7Li or 9Be. The curves demonstrate that one can get the same energy gain as with 1.5 GeV proton beam by accelerating 7Li or 2
M. Paraipan et al.
Progress in Nuclear Energy 120 (2020) 103221
Table 1 The energy released per projectile for different target geometries and composi tions. The explanation of the notation for the dimensions is given in the text. Dimensions cm
Composition
Edep1 MeV/p
Edep2 MeV/p
Edep3 MeV/p
L120R70r0.5d2 L150R90r0.5d2 L150R90r0.5d2 L150R90r0.5d2
U-Pu-Zr 11% Pu239 U-Pu-Zr 9.2% Pu239 U-Pu-C 11.2% Pu239 U-Pu-O 12.3% Pu239
9.584e4 9.276e4 9.276e4 1.011e5
1.437e5 1.457e5 1.457e5 1.496e5
1.342e5 1.375e5 1.375e5 1.425e5
Fig. 2. The scheme of the target.
Table 2 The energy released per projectile in U-Zr target 14.7% 235U with dimensions L140R90r1d5 irradiated with 0.35 AGeV 7Li and 1.5 GeV proton for Pb, LBE and Na coolants. Projectile
LBE
Pb
Na
Na þ enrichment 20.5% U235
Na þ layer 60 cm Pb
Li7 proton
1.212e5 1.948e5
1.179e5 1.848e5
2.728e4 4.561e4
1.229e5 1.814e5
1.173e5 1.875e5
1.5 GeV proton beams in U target cooled with Pb, LBE, and Na are given in Table 2. The ratio between the energy released realized with 7Li and proton is preserved. It should be pointed out that Pb or LBE act as better reflectors for neutrons in comparison with Na. If Na is used as coolant the energy released decreases, and the neutron leakage increases from 15% with coolant Pb or LBE to 25% with Na. If one use Na as coolant, one needs to increase the level of enrichment or to use an additional reflector layer in order to obtain the same keff. The factor that has a significant influence on the neutron spectrum and on the energy released is the material used for the converter. These aspects are analyzed in detail in the next subsection.
9
Be beams at energies 0.4–0.45 AGeV and this allows a reduction of the accelerator length with a factor of ~1.6. Another conclusion revealed from Fig. 1b is that in an accelerator with a given length it is preferable to accelerate light ions instead of proton. For example, if one accelerates 7 Li at energy 0.64 AGeV instead of protons at 1.5 GeV (needing the same accelerator length) the energy gain realized is 1.5 times higher. These first interesting results obtained with light ion beams motivate us to study in more detail the influence of the target structure and composition on the energy efficiency and to find the conditions which maximizes the energy released by light ions at low energy. Targets with different composition and structure were studied: solid fuel rods in a bath of metallic coolant (lead, sodium, lead bismuth eutectic- LBE), or liquid fuel (molten salt). For the converter various materials were checked: from low Z and density (Li, Be, C) to high Z and density (W, Pb, U). In the following subsections, the results obtained in targets with solid fuel and targets with liquid fuel are presented.
3.1.3. The converter The material and the dimensions of the converter must be chosen in such way to maximize the energy released in the target. For proton beams with energy around 1 GeV converters from heavy metals (W, Pb, LBE, U) are considered the best option (Kadi, 2007; De Paula Barros et al., 2012). Pb and LBE are preferred for the possibility to use them as converter and coolant in the same time (IAEA-TECDOC-985, 1997; Abderrahim et al., 2001). Usually, the criterion used for the choice of the converter is the neutron yield (Hashemi-Nezhad et al., 2011). In the case of low energy ion beams (below 0.5 AGeV) high Z and high density materials are not the best choice because the range of the projectile is too short and many particles are stopped without inelastic interaction. For example, a beam of protons with energy 1.5 GeV has a range of 960 mm in LBE and only 0.15% from the projectiles reach this point, but a beam of 7Li with energy 0.3 AGeV has a range of 74 mm and 54% of the ions survive until the end of the range. In the case of low energy ions better results are obtained with converters from low Z ma terials. With a beam of 0.3 AGeV 7Li 10% of the ions reach the Bragg peak in beryllium or lithium, and 20% in carbon. The use of low Z materials produces a significant increase of the range for low energy light ions. As a consequence, the probability to interact inelastically at higher energies increases, and the result is an increased yield of high energy neutrons capable to develop further inter-nuclear cascades in the target. The effect on the energy released depends on to what extend the increase of the number of high energy neutrons compensates the lowering of the inelastic cross section and of the total neutron multi plicity due to the smaller mass number of the target. In order to clarify these aspects a series of simulations with con verters from various materials was performed. The converters are cyl inders with radius 10 cm and length equal with the ion range in the given material. In the first set of simulations the neutron yield from the converter under irradiations with different beams was registered. Another set of simulations was performed with the converter placed in the center of the fuel blanket and the overall effect was measured by registering the particle fluence and the energy released in the target. A correct comparison of the energy efficiency between low energy ion beams and 1.5 GeV proton beam necessitates a length of the fuel blanket large enough to stop the proton beam inside the blanket. We used a U-Pu-Zr target with 8.9% 239Pu. The fuel blanket is an assembly of rods with diameter 0.9 cm and length 150 cm, in a bath of LBE coolant. The internal radius of the fuel blanket is 10 cm, and the external radius is
3.1. Solid fuel The analyzed aspects are: the fuel composition, the geometry of the target, the coolant used and the converter. 3.1.1. Fuel composition and target geometry The influence of the fuel composition and of the target structure on the shape of the neutron spectrum and on the energy produced was investigated. The target is described as an assembly of fuel rods immersed in a bath of coolant. The following parameters of the geom etry were varied: the radius r of the fuel rods (between 0.5 and 1 cm), the length L of the rods (between 100 and 150 cm), the distance d between rods (between 1 and 5 cm), the total radius R of the fuel assembly (be tween 70 and 90 cm). Various fuel compositions (U-Pu-Zr alloy, U-Pu oxide, U-Pu carbide) were used in the simulations. In each case the level of enrichment was properly chosen in order to implement a target with keff 0.96–0.97. The variations in target geometry or fuel composition do not change the shape of the neutron spectrum and preserve the ratio between the energy deposited obtained with proton and ion beams. As argument for this conclusion some values of the energy deposited per incident particle for beams of 7Li with energy 0.35 AGeV (Edep1) and 0.45 AGeV (Edep2), and protons with energy 1.5 GeV (Edep3) registered in targets with different structure are presented in Table 1. 3.1.2. The coolant The cooling with different metals: lead, LBE, and sodium was also analyzed. The metallic coolant does not modify the shape of the neutron spectrum either. The energy released obtained with 0.35 AGeV 7Li and 3
M. Paraipan et al.
Progress in Nuclear Energy 120 (2020) 103221
released on Etot is shown in Fig. 4. One remarks an almost linear dependence with 2 exceptions. The first is represented by the uranium converter. In this case, an important contribution to the energy deposited is given by the energy produced through fission in the converter itself. The other exception is given by the beryllium converter. With a beryllium converter one gets the maximum energy deposited in the target. One can see in Table 3 that the yield of neutrons with energy above 10 MeV and the total energy carried out by neutrons are slightly higher when a lithium converter is used instead of a beryllium converter. Still, the energy released in a target with beryllium converter is with a factor of 1.4 higher. The explanation is that Be acts also as neutron reflector and moderator. The low neutron absorption cross section and the high scattering cross section of Be make it a good neutron reflector. The use of a beryllium converter determines the apparition of a tail towards low energy in the neutron spectrum and consequently an increase of the number of fissions and of the released energy. Due to this tail in the neutron spectrum the difference between the energy released in the case when Be is used as converter and the case when the converter is the LBE coolant itself is sensitive to the level of enrichment. The dependence of the energy released on the level of enrichment in a target with beryllium converter with length 30 cm and radius 10 cm is illustrated in Table 4, for quasi-infinite cylindrical target or assembly of rods in a bath of LBE, irradiated with a beam of 7Li with the energy 0.3 AGeV. A lithium converter seems to be the second option, but the problem is that lithium at working temperature of the reactor is liquid with high corrosive action and must be contained in a thick enough steel vessel. The simulation shows that even a layer of 1 cm steel in the beam window reduces with 30% the energy deposited by a beam of 0.3 AGeV 7Li. A similar tail towards low energy as the one obtained with beryllium converter appears in the neutron spectrum when a carbon converter is used, but the effect is less pronounced than in the case of beryllium converter. In addition, in the case of a carbon converter the increase of the fission cross section produced by the change in the neutron spectrum cannot compensate the lower yield of high energy neutrons and the overall effect is an energy deposited lower even than in the case of a lithium converter.
Table 3 The neutron yield, the total energy of the escaped neutrons Etot, and the energy released Edep in the target with various converters, irradiated with a beam of 7Li with energy 0.3 AGeV. Converter material
Neutron yield total
E > 10 MeV
E > 100 MeV
Li Be C Na Al Fe W Pb LBE U
6.36 8.44 4.48 4.56 4.96 5.88 13.6 14.55 13.95 24.04
4.53 4.33 3.13 3.17 2.95 2.31 2.51 2.75 2.75 2.96
2.08 1.95 1.45 1.4 1.27 0.894 0.631 0.627 0.619 0.578
Etot, MeV
Edep, MeV
511.4 480 355.7 348.4 321.9 235.2 196.5 207.8 205.4 212.8
5.887e4 8.366e4 4.922e4 4.673e4 4.57e4 3.346e4 3.392e4 3.535e4 3.806e4 5.173e4
90 cm. The dimensions of the LBE coolant are radius 150 cm and length 270 cm. A schematic representation of the target is given in Fig. 2. The effect of the converter material is exemplified in Table 3 where the neutron yield from various converters irradiated with a beam of 7Li with energy 0.3 AGeV is presented. Besides the total neutron yield per projectile, the yield of neutrons with energy higher than 10 MeV, higher than 100 MeV, the total energy carried out by the escaped neutrons, and the energy released in the target are given, also. One can see form Table 3 that the total neutron yield is not a good criterion for the estimation of the energy released in the target. The beam interaction in heavy materials realizes the highest values of the neutron yield, but the lowest values of the energy deposited. Important is not only the number of source neutrons but also their energy. High energy neutrons are able to develop further nuclear cascades in the target, resulting a higher neutron fluence. The effect of the development of inter-nuclear cascades with further multiplication of secondary par ticles is illustrated in Fig. 3, where the neutron fluence in the fuel blanket per incident projectile is shown for converter materials Li, Be, C and LBE. A more adequate parameter is the total energy Etot carried by the neutrons which leave the converter. The dependence of the energy
Fig. 3. The neutron spectra in fuel blanket with Li, Be, C and LBE converters, irradiated with a beam of 7Li with energy 0.3 AGeV. 4
M. Paraipan et al.
Progress in Nuclear Energy 120 (2020) 103221
Fig. 4. The dependence of the energy released on the total energy carried out by the neutrons.
The increase of the radius of the beryllium converter produces an increase of the energy released, but the effect is less pronounced that in the case of the variations of the length. For a given mass of the material it is more advantageous to use a converter with lower radius and higher length. The effect of the beryllium converter on the energy efficiency of proton and 7Li beams is synthesized in Table 5. The energy released per projectile, the net power produced and the energy gain are given in the table for the case when the converter is the LBE coolant and the case when a cylinder of beryllium with length 110 m is used as converter. Due to the change in the neutron spectrum (the apparition of the low energy tail), a long beryllium converter transforms the target with criticality coefficient keff 0.94 (value corresponding to a LBE converter) in a target with keff 0.98. The net power and the energy gain presented in Table 5 were calculated assuming a beam intensity of 1.25⋅1016 p/s. In the target with LBE converter a beam of Li with energy 0.4 AGeV is equivalent from the point of view of the net power produced with a beam of 1.5 GeV protons. The use of Be converter determines an increase of the released energy with a factor of 2.3 when the target is irradiated with 1.5 GeV protons. In the case of 7Li beam the energy deposited increases 4.7 times at beam energy 0.4 AGeV and 6.3 times at beam energy 0.25 AGeV. In this way, a beam of 7Li with energy 0.25 AGeV becomes equivalent from the point of view of the net power production with a beam of 1.5 GeV protons. That means that one can produce the same net electrical power using an accelerator 2.6 times shorter. Another advantage of a Be converter is related with the period of operation without refueling and the level of the incineration of the ac tinides that can be achieved. The method used to calculate the evolution of the fuel composition during irradiation is described in the following. The target is divided in zones of almost equal fluence and energy den sity, with variation in the limit of 20% inside a zone. The neutron spectrum registered through simulation in each zone normalized to incident projectile is used to calculate the cross sections for the reactions which contribute to the isotopes accumulation rates (fission, capture, n2n, np, nd, na, nna, nnp). The fluence is considered constant during a time step. The evolution of the number of atoms of isotopes is described by a set of coupled differential equations of the form:
Table 4 The energy released per projectile in targets with and without beryllium con verter with length 30 cm and radius 10 cm, irradiated with a 0.3 AGeV 7Li beam. Target
Edep without Be converter, MeV p 1
Edep with Be converter, MeV p 1
Quasi-infinite natU Quasi-infinite 5.7% 235U Rods 8.9% 239Pu Rods 9.2% 239Pu
4.454e3 8.49e4 3.806e4 9.17e4
7.336e3 1.79e5 8.366e4 2.319e5
Fig. 5. The dependence of the energy released on the converter length in target with 8.9% Pu239, irradiated with 7Li 0.3 AGeV beam.
The dependence of the energy deposited on the length of the con verter from beryllium, lithium, and carbon is presented in Fig. 5. When lithium or carbon are used as materials for the converter the curves of the energy released exhibit a small build-up at intermediate lengths in concordance with the behavior of the neutron yield from thick targets. But in the case of beryllium one gets a continuous increase of the energy deposited with the length of the converter as result of the neutron reflector property of the beryllium.
m n n X X dNi X yij sfis;j Nj þ rik λk Nk þ sil Nl ¼ dt j¼1
5
k¼1
l¼1
k6¼i
l6¼i
ðλi þ sabs;i ÞNi
(3)
M. Paraipan et al.
Progress in Nuclear Energy 120 (2020) 103221
Table 5 The energy released per projectile, the net power produced and the energy gain in U-Pu target with keff 0.98, irradiated with proton and 7Li beams with the intensity of 1.25⋅1016 p/s. Particle
E, AGeV
Converter LBE Edep, MeV p
proton Li
7
1.5 0.25 0.3 0.35 0.4
Fig. 6. The evolution of
1
7.433e4 2.532e4 3.799e4 5.061e4 6.713e4
239
Pu (a) and
Converter Be G
Net power, MW
Edep, MeV p
3.57 2.3 2.87 3.28 3.81
42.28 11.44 19.79 28.15 39.6
1.681e5 1.606e5 1.886e5 2.501e5 3.155e5
1
G
Net power, MW
8.07 14.58 14.94 16.21 17.9
117.8 119.7 136.9 187.7 238.3
241
Pu (b) in target with converters from LBE and Be, irradiated with 7Li 0.3 AGeV beam, with intensity 1.25⋅1016 p/s.
The first term on the right side in eq. (1) represents the contribution from the fission, where sfis,j is the probability for fission of the isotope j and yij is the fission yield of the isotope i. The second term describes the contribution from the decay, where λk is the decay constant and rik is the probability of the isotope k to decay to the isotope i. The third term describes the production of the isotope i through other neutron reactions than fission. The last term describes the disappearance of the isotope i through decay and neutron absorption. The probability of a neutron reaction s is calculated as: Z Emax s ¼ Ib σ ðEÞϕðEÞdE ; (4)
build-up when the keff rises, followed by a slower decrease. Such target needs the use of the control rods during operation. With a proper adjustment of the number of control rods the keff and the energy released can be kept constant at a wanted level during operation. In our example, the target with LBE converter and initial keff 0.94 reaches the value of keff 0.98 after approximately 5 months and can be operated at this level in order to obtain the same power released as in the target with Be converter. It could rise the question why one should not operate the target in this way instead of using a Be converter. The answer is given by the difference in the periods between refueling. The neutron spectra are different in these two cases and determine a different evolution of the isotopes concentration. The evolution of 239Pu and 241Pu in targets with LBE and Be converters is illustrated in Fig. 6. The higher accumulation rate for Pu isotopes achieved in the target with Be converter ensures a longer period between refueling. If one chooses the moment when the energy released decreases with 30% from the plateau value as criterion for refueling and consider the target irradiation with a beam of 0.3 AGeV 7 Li with the intensity 1.25⋅1016 p/s the target with LBE converter must be refueled after 3370 days, but the target with Be converter can be operated until 4990 days. At the moment of refueling the initial mass of actinides is reduced with 10.2% in the case of the target with LBE converter, and with 14.8% in the target with Be converter.
Emin
where σ is the energy dependent cross section of the reaction, ϕ is the neutron fluence per incident particle, and Ib is the beam intensity. The values of the energy dependent cross section for the neutron induced reactions are taken from the ENDF database (McLane et al., 1995, Chadwick et al., 2011). The system of equation (3) is solved with the exponential matrix method, using our program written in the frame of toolkit ROOT (Brun et al., 1997). We use some simplifications. For the isotopes with lifetime below 10 min an instantaneous decay was considered. For the first isotope with lifetime higher than 10 min in each decay chain we include the contribution from precursors with shorter lifetime in the value of the fission yield. In the case of the other isotopes the values of the inde pendent fission yield are used. For a given isotope only the decay channels with probability higher than 10 3 are taken into account. The concentrations of the isotopes calculated at the end of a period are used in the simulation for the next period. The fuel composition used in the simulation includes only isotopes with concentration above 10 6. When necessary, a variable number of boron carbide control rods are inserted between the fuel rods in order to maintain constant the total energy released in the target. If one uses a target with initial level of enrichment low enough, as in our example (8.9% 239Pu) the concentration of 239Pu presents a period of
3.2. Liquid fuel In the case of the liquid target a eutectic composition 46.5LiF11.5NaF-42KF (mol %, FLiNaK) which ensure a good solubility for both UF4 and PuF3 (Degtyarev et al., 2015; Serp et al., 2014) was chosen for the carrying salt. The blanket dimensions were taken large enough to stop a proton beam with energy 1.5 GeV (length 350 cm, radius 200 cm). The enrichment of the fuel used in the following examples was 7% 239Pu. The presence of light elements (Li, Na) in the fuel composition generates a significantly softer neutron spectrum in comparison with a solid fuel target cooled with Pb or LBE. Besides that, the range of 7Li ions in molten 6
M. Paraipan et al.
Progress in Nuclear Energy 120 (2020) 103221
Fig. 7. The neutron spectra in molten salt fuel blanket irradiated with 1.5 GeV proton and 0.275 AGeV 7Li beams, without Be converter (a) and with Be converter (b).
Fig. 8. The dependence of the energy released per projectile (a), and of the net power produced (b) on the Be converter length, for molten salt target irradiated with 1.5 GeV proton and 0.25–0.3 AGeV 7Li beams.
salt is higher than in LBE and the fuel itself acts as an efficient converter for light ions, also. Сonsequently, in molten salt a beam of 7Li with lower energy that in the solid fuel produces the same net power as a beam of 1.5 GeV protons (0.325 AGeV in molten salt comparing with 0.4 AGeV in target with fuel rods). In the presence of a Be converter the neutron spectrum in a molten salt target irradiated with 7Li beam changes in the same manner as in the case of a rods target: one gets an increase of the number of high energy neutrons and of the tail of low energy neutrons, but the changings are less pronounced than in a target with solid rods. Although the difference between the range of 7Li ions in molten salt and Be is not as great as in the case of a target from heavy metals only, it is sufficient to provide an advantage. As example, for the initial energy 0.3 AGeV 35% of ions reach the end of the range in molten salt, and only 10% in Be. The change of the neutron spectrum in the presence of a Be converter is illustrated in Fig. 7 where the neutron spectra registered in a molten salt target irradiated with 1.5 GeV proton beam and 0.275 AGeV 7 Li beam are compared. The length of the Be converter was 150 cm. The energy released depends also on the length of the converter. This dependence is illustrated in Fig. 8. The dependence of the energy released per incident particle is presented for beams of protons with the energy 1.5 GeV and 7Li with the energy in the range 0.25–3 AGeV in Fig. 8a. The corresponding values of the net power produced for a beam intensity of 1.25⋅1016 p/s are given in Fig. 8b. For a beam of 1.5 GeV protons in liquid target the use of a Be con verter is not justified. Even with a converter with length 200 cm the
deposited energy increases only 1.4 times. Still, for Li ions the Be con verter is useful. The use of a Be converter with length 150 cm produces an increase of the energy released with a factor of 2.2–2.4 when the target is irradiated with Li ions. The increase is lower than in a target with solid fuel but high enough to justify its use. When a Be converter is used, a beam of 7Li with the energy 0.275 AGeV becomes equivalent with a 1.5 GeV proton beam and allows to build an accelerator 2.2 times shorter. 4. Conclusions For light ion beams at energies below 0.5 AGeV the use of converters from light materials as Li or Be increases the energy released mainly as the result of a higher ion range in low density and low Z materials. The best results are obtained with Be converters. In this case, besides the increased range one takes advantage of the neutron reflector and moderator properties of beryllium. The effect depends on the dimensions of the converter and fuel composition. The energy released is more sensitive to the variation of the converter length than of the radius. Be converters with length 100–120 cm increase the energy produced with Li beams by a factor of 4.6–6.3 in targets with solid fuel. A beam of 7Li with the energy 0.25 AGeV becomes equivalent from the point of view of the energy produced with a proton beam with energy 1.5 GeV. In this way, the length of the accelerator is reduced 2.6 times. 7
M. Paraipan et al.
Progress in Nuclear Energy 120 (2020) 103221
In molten salt fuel the energy released produced with Li ions in creases with a factor of 2.2–2.4 when a Be converter is used. A beam of 7 Li with the energy 0.275 AGeV becomes equivalent with a proton beam with energy 1.5 GeV and that allows to reduce the length of the accel erator 2.2 times.
Brun, R., et al., 1997. ROOT- an object oriented data analysis framework. Nucl. Instrum. Methods Phys. Res. A 389, 81–86. Chadwick, M.B., et al., 2011. ENDF/B-VII.1: nuclear data for science and technology: cross sections, covariances, fission product yields and decay data. Nucl. Data Sheets 112, 2887. Degtyarev, A., Myashikov, A., Ponomarev, L., 2015. Molten salt fast reactor with U-Pu fuel cycle. Prog. Nucl. Energy 82, 33–36. De Paula Barros, G., Pereira, C., Veloso, M.A.F., Costa, A.L., 2012. Study of an ADS loaded with thorium and reprocessed fuel. Sci. Technol. Nucl. Install. https://doi. org/10.1155/2012/934105. Article ID 934105. ESS Technical Design Report, April 23 2013. ESS-doc-274 Fiori F., Zhou Z., A study on the Chinese nuclear energy options and the role of ADS reactor in the Chinese nuclear expansion. Prog. Nucl. Energy 91, 159–169, 2016. Hashemi-Nezhad, S.R., Westmeier, W., Zamani-Valasiadou, M., Thomauske, B., Brandt, R., 2011. Optimal ion beam, target type and size for accelerator driven systems: implications to the associated accelerator power. Ann. Nucl. Energy 38, 1144–1155. Accelerator Driven Systems: Energy Generation and Transmutation of Nuclear Waste, Status Report, 1997. IAEA-TECDOC-985. Kadi, Y., 2007. Transmutation capabilities of the CERN energy amplifier system. Prog. Nucl. Energy 49, 606–616. McLane, V., et al., 1995. The Cross Section Evaluation Working Group, Data Formats and Procedures for the Evaluated Nuclear Data File ENDF-6, Report BNL-NCS-44945 (ENDF-102). National Nuclear Data Center, Brookhaven National Laboratory, U.S.A. Oigawa, H., et al., 2004. R&D Activities on Accelerator-Driven Transmutation System in JAERI. https://pdfs.semanticscholar.org/8831/31a7756c250df7a9ebb8caf11183 ee282ce3.pdf. Paraipan, M., Baldin, A.A., Kadykov, M.G., Tyutyunnikov, S.I., 2012. Investigation of the possibility to use ion beams for ADS through simulation in GEANT4. In: Proceedings of the 21st International Baldin Seminar on High Energy Physics Problems. JINR, Dubna, Russia. September 10–15. Paraipan, M., Baldin, A.A., Baldina, E.G., Tyutyunikov, S.I., 2018. “Light ion beams for energy production in ADS”, EPJ proceedings MMCP2017, 173. Ann. Nucl. Energy 110 (2017), 04011, 973. Paraipan, M., E and T Collaboration, 2017. Study of neutron spectra in extended U target. new experimental data. EPJ Web Conf. 138, 10005. Baldin ISHEPP XXIII. Paraipan, M., Baldin, A.A., Baldina, E.G., Tyutyunnikov, S.I., 2019. Beam and target optimization for energy production in accelerator driven systems. In: Baldin ISHEPP XXIV EPJ Web of Conferences, vol. 204. https://doi.org/10.1051/epjconf/ 201920404001, 0. Rubbia, C., et al., November 1993. An Energy Amplifier for Cleaner and Inexhaustible Nuclear Energy Production Driven by a Particle Beam Accelerator. CERN/AT/93-47. Serp, J., et al., 2014. The molten salt reactor (MSR) in generation IV: overview and perspectives. Prog. Nucl. Energy 77, 308–319. Zhao, Z., Chen, Z., Chen, H., 2014. Preliminary optimization of proton energy and target for Lead- Bismuth Eutectic target of a demonstration ADS. Prog. Nucl. Energy 71.
Authors contribution Mihaela Paraipan – conception, simulation, data analysis, writing the article. Vafa M. Javadova – simulation, data analysis. Serguey I. Tyutyunnikov – data analysis. Acknowledgments The work was partially supported by the the grant of the Plenipo tentiary Representative of the Romanian Government at JINR Dubna, JINR order 322/21.05.2018, p. 10 in the frame of E&T Collaboration. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.pnucene.2019.103221. References Abderrahim, H.A., et al., 2001. MYRRHA: a multipurpose accelerator driven system for research & development. Nucl. Instrum. Methods Phys. Res. A 463, 487–494. Adam, J., et al., 2017. Secondary particle distributions in an extended uranium target under irradiation by proton, deuteron, and carbon beams. Nucl. Instrum. Methods Phys. Res. A 872, 87–92. Agostinelli, S., et al., 2003. GEANT4 A a simulation toolkit. Nucl. Instrum. Methods A 506, 250–303. Baldin, A.A., Berlev, A.I., Kudashkin, I.V., Mogildea, G., Mogildea, M., Paraipan, M., Tyutyunnikov, S.I., 2016. Simulation of neutron production in heavy metal targets using Geant4 software. Phys. Part. Nucl. Lett. 32, 391–402. Baldin, A.A., Berlev, A.I., Paraipan, M., Tyutyunikov, S.I., 2017. Optimization of accelerated charged particle beam for ADS energy production. Phys. Part. Nucl. Lett. 14 (1), 113–119. Beller, D.E., et al., 2001. The US accelerator transmutation of waste program. Nucl. Instrum. Methods Phys. Res. A 463, 468–486.
8
Contents lists available at ScienceDirect
Progress in Nuclear Energy journal homepage: http://www.elsevier.com/locate/pnucene
Aspects of target optimization for ADS with light ion beams at energies below 0.5 AGeV M. Paraipan a, b, *, V.M. Javadova a, S.I. Tyutyunnikov a a b
Joint Institute for Nuclear Research, Dubna, Russia Institute of Space Science, Bucharest-Magurele, Romania
A R T I C L E I N F O
A B S T R A C T
Keywords: Accelerator driven system Ion beam Energy efficiency Converter material
A comparative study about the energy efficiency of proton and light ion beams used for energy production in accelerator driven systems (ADS) is performed. The energy gain G, defined as the ratio of the energy produced to the energy spent to accelerate the beam is used as measure for the energy efficiency. The energy released in the target is obtained through simulation with the code Geant4, and the spent energy is calculated by scaling from the data about the accelerator efficiency for a reference particle. An optimal proton energy of 1.5 GeV is revealed, when the beam is accelerated in a linac. The advantage of light ion beams, especially 7Li at energies below 0.5 AGeV, which allows a reduction of the accelerator length, is substantiated. A study about the target design and the choice of the converter meant to maximize the efficiency of the energy ADS irradiated with light ion beams (7Li) with energies in the range 0.25–0.5 AGeV is presented. The influence of the fuel composition, of the geometry of the target, of the coolant and the converter materials are investigated. The most significant influence on the energy released has the material used for the converter. Cylindrical con verters from various materials, from very light (Li, Be) to very heavy (W, Pb, U) are analyzed. The influence of the dimensions of the converter on the energy released in the target is studied and the conditions which maximize the energetic efficiency and ensure a high level of burning of the actinides are determined. Solid fuel with different compositions (metal, oxide, carbide) and liquid fuel (molten salt) are considered. The advantage of a target with beryllium converter for both proton and lithium beams is underlined. The use of a Be converter with length 100–120 cm makes a beam of 7Li with the energy 0.25AGeV (in solid fuel) and 0.275 AGeV (in liquid fuel) equivalent from the point of view of the net power produced with a beam of 1.5 GeV proton, and allow the building of an accelerator 2.2–2.6 times shorter. A comparison between the evolution of the fuel composition during irradiation and its influence on the period of operation without refueling for target with LBE and Be converters is realized. The Be converter allows also to achieve a higher level of burning of the actinides and consequently a larger period between refueling.
1. Introduction The search for the solutions to the problems with which water re actors with once-through fuel cycle are confronted (low incineration rate of the nuclear fuel, insufficient nuclear safety) generated the idea to use accelerated particle beams interacting in a metal target as supple mentary source of neutrons which allows the functioning of the reactor with criticality coefficient below 0.99. A safer exploitation of nuclear plants is realized in this way, and the harder neutron spectrum obtained ensures a better incineration of the actinides. The idea appeared in the middle of last century, but as entire concept was presented in (Rubbia
et al., 1993). Since then, many programs and projects around the world are dedicated to this subject (EUROTRANS program, MYRRHA and ESS projects in European Union, OMEGA program in Japan, CIADS in China). All of them plan to use proton beams. In spite of the almost generalized opinion that the optimal beam for ADS is a proton beam with energy around 1–1.5 GeV (Oigawa et al., 2004; Zhao et al., 2014; Beller et al., 2001) we have shown in previous works that ion beams accelerated in a synchrotron or a linear accelerator have a superior energetic efficiency than protons (Paraipan et al., 2012; Baldin et al., 2017). The advantage of light ion beams, especially 7Li at energies below 0.5 AGeV is underlined in (Paraipan et al., 2017; Paraipan et al., 2019).
* Corresponding author. Joint Institute for Nuclear Research, Dubna, Russia. E-mail address: [email protected] (M. Paraipan). https://doi.org/10.1016/j.pnucene.2019.103221 Received 17 July 2019; Received in revised form 26 November 2019; Accepted 16 December 2019 Available online 24 December 2019 0149-1970/© 2019 Published by Elsevier Ltd.
M. Paraipan et al.
Progress in Nuclear Energy 120 (2020) 103221
Fig. 1. The dependence of the energy gain for protons (a) and the relative energy gain for ions (b) on the beam energy, in quasi-infinite U target enriched with 5.7% 235U.
In the present work the influence of the convertor material and di mensions on the energy released in the target is studied. The energy efficiency is calculated for the case of linear accelerator. It was shown in (Baldin et al., 2017) that the best energy efficiency would be obtained when the beam is accelerated in a synchrotron. But in a synchrotron one cannot obtain the high beam intensity necessary for ADS, so we have to limit our analysis to the situation when the beam is accelerated in a linear accelerator. In this case the values obtained for the energy effi ciency are slightly worse than in a synchrotron. The results obtained with beams of 7Li with energies in the range 0.25–0.45 AGeV are compared with those obtained with proton beam with energy 1.5 GeV. At this energy the energy efficiency of the proton beam accelerated in a linac reaches the maximum (Paraipan et al., 2018).
linear proton accelerator is realized in the technical report of the Eu ropean Spallation Source (ESS) project (ESS Technical Report, 2011). The ESS project plans to accelerate a proton beam with energy 2 GeV and beam power 5 MW with an accelerator efficiency of 0.18. For a linear accelerator Pacc depends on the accelerator length and scales as A⋅E/Z, where Z represents the atomic number of the ion, A is the mass number, and E is the energy per nucleon. In this way if Pspent0 and the accelerator efficiency η0 for a reference particle (atomic number Z0, mass number A0, final energy per nucleon E0) are known one can calculate the power spent for another particle. Assuming the same beam intensity one gets: � � � � 1 Z0 Pspent ¼ A ⋅ E⋅Ibeam 1 þ 1 (1) η0 Z
2. Method
Although such high value for the accelerator efficiency as the one estimated in (ESS Technical Report, 2011) remains to be demonstrated, we used it for the reference particle (proton) in our work. More details about the method to calculate Pspent can be found in (Paraipan et al., 2017). The power produced depends on the energy released in the target per incident projectile Edep, beam intensity Ibeam, and conversion coefficient from thermal to electrical power ηel:
The energy released in the target was calculated with the simulation toolkit Geant4 (Agostinelli et al., 2003) extended to work with elements heavier than uranium. The code Geant4 is used for modelling the par ticle interaction and transport. For the modelling of the electromagnetic interaction standard electromagnetic models were used. The inelastic interaction was modelled with cascade models (Bertini cascade for hadrons and pions, binary cascade for ions). For neutrons with energy below 20 MeV high precision neutron models, based on a detailed implementation of the experimental data from ENDF library (Chadwick et al., 2011) were used. The reliability of the predictions obtained with Geant4 was checked against experimental data about neutron yield from thin and thick metallic targets irradiated with protons and light ions (Baldin et al., 2016). The capability of Geant4 to predict the isotopes accumulation and the distribution of fission fragments was checked in (Paraipan et al., 2017; Adam et al., 2017). The conclusion was that for integral values as the neutron yield, the number of fissions or the energy released one can count on the results of the simulations in the limits of 25–30%. The energy gain G is used as measure for the energy efficiency. An often made mistake is to define the energy gain as the ratio of the power produced in the target Pprod to the power transmitted to the beam Pbeam. The correct definition of G is the ratio of the power produced in the target Pprod to the power spent to accelerate the beam Pspent. Pspent in cludes besides Pbeam the power necessary to maintain the functioning of the accelerator Pacc. Usually, Pbeam represents only a small part (below 10%) from the total power spent. Constant efforts are made in order to improve the accelerator efficiency. A rigorous estimation of Pspent for a
(2)
Pprod ¼ Edep Ibeam ηel 16
A value of 1.25⋅10 for the beam intensity and a usual value of 0.4 for ηel were used in the present work. 3. Results and discussion A first set of simulations was realized in a quasi-infinite metallic uranium target, enriched with 5.7% 235U and a criticality coefficient of 0.96. The target was a cylinder with dimensions large enough (radius 100 cm, length 20 cm) to obtain the saturation of the energy released in both radial and longitudinal directions. The cylinder was irradiated with protons with energy between 0.5 and 4 GeV, and light ions (7Li, 9Be, 11B, 12 C) with the energy from 0.25 to 1 AGeV. The dependence of the energy gain G on the proton energy is presented in Fig. 1a. One remarks that the optimal energy for proton beams is ~1.5 GeV, value at which G reaches a plateau. In the case of the investigated light ions the dependence of the relative gain (defined as the ratio of the G for ion to the G for 1.5 GeV proton) on the ion energy is shown in Fig. 1b. The most promising results are obtained with 7Li or 9Be. The curves demonstrate that one can get the same energy gain as with 1.5 GeV proton beam by accelerating 7Li or 2
M. Paraipan et al.
Progress in Nuclear Energy 120 (2020) 103221
Table 1 The energy released per projectile for different target geometries and composi tions. The explanation of the notation for the dimensions is given in the text. Dimensions cm
Composition
Edep1 MeV/p
Edep2 MeV/p
Edep3 MeV/p
L120R70r0.5d2 L150R90r0.5d2 L150R90r0.5d2 L150R90r0.5d2
U-Pu-Zr 11% Pu239 U-Pu-Zr 9.2% Pu239 U-Pu-C 11.2% Pu239 U-Pu-O 12.3% Pu239
9.584e4 9.276e4 9.276e4 1.011e5
1.437e5 1.457e5 1.457e5 1.496e5
1.342e5 1.375e5 1.375e5 1.425e5
Fig. 2. The scheme of the target.
Table 2 The energy released per projectile in U-Zr target 14.7% 235U with dimensions L140R90r1d5 irradiated with 0.35 AGeV 7Li and 1.5 GeV proton for Pb, LBE and Na coolants. Projectile
LBE
Pb
Na
Na þ enrichment 20.5% U235
Na þ layer 60 cm Pb
Li7 proton
1.212e5 1.948e5
1.179e5 1.848e5
2.728e4 4.561e4
1.229e5 1.814e5
1.173e5 1.875e5
1.5 GeV proton beams in U target cooled with Pb, LBE, and Na are given in Table 2. The ratio between the energy released realized with 7Li and proton is preserved. It should be pointed out that Pb or LBE act as better reflectors for neutrons in comparison with Na. If Na is used as coolant the energy released decreases, and the neutron leakage increases from 15% with coolant Pb or LBE to 25% with Na. If one use Na as coolant, one needs to increase the level of enrichment or to use an additional reflector layer in order to obtain the same keff. The factor that has a significant influence on the neutron spectrum and on the energy released is the material used for the converter. These aspects are analyzed in detail in the next subsection.
9
Be beams at energies 0.4–0.45 AGeV and this allows a reduction of the accelerator length with a factor of ~1.6. Another conclusion revealed from Fig. 1b is that in an accelerator with a given length it is preferable to accelerate light ions instead of proton. For example, if one accelerates 7 Li at energy 0.64 AGeV instead of protons at 1.5 GeV (needing the same accelerator length) the energy gain realized is 1.5 times higher. These first interesting results obtained with light ion beams motivate us to study in more detail the influence of the target structure and composition on the energy efficiency and to find the conditions which maximizes the energy released by light ions at low energy. Targets with different composition and structure were studied: solid fuel rods in a bath of metallic coolant (lead, sodium, lead bismuth eutectic- LBE), or liquid fuel (molten salt). For the converter various materials were checked: from low Z and density (Li, Be, C) to high Z and density (W, Pb, U). In the following subsections, the results obtained in targets with solid fuel and targets with liquid fuel are presented.
3.1.3. The converter The material and the dimensions of the converter must be chosen in such way to maximize the energy released in the target. For proton beams with energy around 1 GeV converters from heavy metals (W, Pb, LBE, U) are considered the best option (Kadi, 2007; De Paula Barros et al., 2012). Pb and LBE are preferred for the possibility to use them as converter and coolant in the same time (IAEA-TECDOC-985, 1997; Abderrahim et al., 2001). Usually, the criterion used for the choice of the converter is the neutron yield (Hashemi-Nezhad et al., 2011). In the case of low energy ion beams (below 0.5 AGeV) high Z and high density materials are not the best choice because the range of the projectile is too short and many particles are stopped without inelastic interaction. For example, a beam of protons with energy 1.5 GeV has a range of 960 mm in LBE and only 0.15% from the projectiles reach this point, but a beam of 7Li with energy 0.3 AGeV has a range of 74 mm and 54% of the ions survive until the end of the range. In the case of low energy ions better results are obtained with converters from low Z ma terials. With a beam of 0.3 AGeV 7Li 10% of the ions reach the Bragg peak in beryllium or lithium, and 20% in carbon. The use of low Z materials produces a significant increase of the range for low energy light ions. As a consequence, the probability to interact inelastically at higher energies increases, and the result is an increased yield of high energy neutrons capable to develop further inter-nuclear cascades in the target. The effect on the energy released depends on to what extend the increase of the number of high energy neutrons compensates the lowering of the inelastic cross section and of the total neutron multi plicity due to the smaller mass number of the target. In order to clarify these aspects a series of simulations with con verters from various materials was performed. The converters are cyl inders with radius 10 cm and length equal with the ion range in the given material. In the first set of simulations the neutron yield from the converter under irradiations with different beams was registered. Another set of simulations was performed with the converter placed in the center of the fuel blanket and the overall effect was measured by registering the particle fluence and the energy released in the target. A correct comparison of the energy efficiency between low energy ion beams and 1.5 GeV proton beam necessitates a length of the fuel blanket large enough to stop the proton beam inside the blanket. We used a U-Pu-Zr target with 8.9% 239Pu. The fuel blanket is an assembly of rods with diameter 0.9 cm and length 150 cm, in a bath of LBE coolant. The internal radius of the fuel blanket is 10 cm, and the external radius is
3.1. Solid fuel The analyzed aspects are: the fuel composition, the geometry of the target, the coolant used and the converter. 3.1.1. Fuel composition and target geometry The influence of the fuel composition and of the target structure on the shape of the neutron spectrum and on the energy produced was investigated. The target is described as an assembly of fuel rods immersed in a bath of coolant. The following parameters of the geom etry were varied: the radius r of the fuel rods (between 0.5 and 1 cm), the length L of the rods (between 100 and 150 cm), the distance d between rods (between 1 and 5 cm), the total radius R of the fuel assembly (be tween 70 and 90 cm). Various fuel compositions (U-Pu-Zr alloy, U-Pu oxide, U-Pu carbide) were used in the simulations. In each case the level of enrichment was properly chosen in order to implement a target with keff 0.96–0.97. The variations in target geometry or fuel composition do not change the shape of the neutron spectrum and preserve the ratio between the energy deposited obtained with proton and ion beams. As argument for this conclusion some values of the energy deposited per incident particle for beams of 7Li with energy 0.35 AGeV (Edep1) and 0.45 AGeV (Edep2), and protons with energy 1.5 GeV (Edep3) registered in targets with different structure are presented in Table 1. 3.1.2. The coolant The cooling with different metals: lead, LBE, and sodium was also analyzed. The metallic coolant does not modify the shape of the neutron spectrum either. The energy released obtained with 0.35 AGeV 7Li and 3
M. Paraipan et al.
Progress in Nuclear Energy 120 (2020) 103221
released on Etot is shown in Fig. 4. One remarks an almost linear dependence with 2 exceptions. The first is represented by the uranium converter. In this case, an important contribution to the energy deposited is given by the energy produced through fission in the converter itself. The other exception is given by the beryllium converter. With a beryllium converter one gets the maximum energy deposited in the target. One can see in Table 3 that the yield of neutrons with energy above 10 MeV and the total energy carried out by neutrons are slightly higher when a lithium converter is used instead of a beryllium converter. Still, the energy released in a target with beryllium converter is with a factor of 1.4 higher. The explanation is that Be acts also as neutron reflector and moderator. The low neutron absorption cross section and the high scattering cross section of Be make it a good neutron reflector. The use of a beryllium converter determines the apparition of a tail towards low energy in the neutron spectrum and consequently an increase of the number of fissions and of the released energy. Due to this tail in the neutron spectrum the difference between the energy released in the case when Be is used as converter and the case when the converter is the LBE coolant itself is sensitive to the level of enrichment. The dependence of the energy released on the level of enrichment in a target with beryllium converter with length 30 cm and radius 10 cm is illustrated in Table 4, for quasi-infinite cylindrical target or assembly of rods in a bath of LBE, irradiated with a beam of 7Li with the energy 0.3 AGeV. A lithium converter seems to be the second option, but the problem is that lithium at working temperature of the reactor is liquid with high corrosive action and must be contained in a thick enough steel vessel. The simulation shows that even a layer of 1 cm steel in the beam window reduces with 30% the energy deposited by a beam of 0.3 AGeV 7Li. A similar tail towards low energy as the one obtained with beryllium converter appears in the neutron spectrum when a carbon converter is used, but the effect is less pronounced than in the case of beryllium converter. In addition, in the case of a carbon converter the increase of the fission cross section produced by the change in the neutron spectrum cannot compensate the lower yield of high energy neutrons and the overall effect is an energy deposited lower even than in the case of a lithium converter.
Table 3 The neutron yield, the total energy of the escaped neutrons Etot, and the energy released Edep in the target with various converters, irradiated with a beam of 7Li with energy 0.3 AGeV. Converter material
Neutron yield total
E > 10 MeV
E > 100 MeV
Li Be C Na Al Fe W Pb LBE U
6.36 8.44 4.48 4.56 4.96 5.88 13.6 14.55 13.95 24.04
4.53 4.33 3.13 3.17 2.95 2.31 2.51 2.75 2.75 2.96
2.08 1.95 1.45 1.4 1.27 0.894 0.631 0.627 0.619 0.578
Etot, MeV
Edep, MeV
511.4 480 355.7 348.4 321.9 235.2 196.5 207.8 205.4 212.8
5.887e4 8.366e4 4.922e4 4.673e4 4.57e4 3.346e4 3.392e4 3.535e4 3.806e4 5.173e4
90 cm. The dimensions of the LBE coolant are radius 150 cm and length 270 cm. A schematic representation of the target is given in Fig. 2. The effect of the converter material is exemplified in Table 3 where the neutron yield from various converters irradiated with a beam of 7Li with energy 0.3 AGeV is presented. Besides the total neutron yield per projectile, the yield of neutrons with energy higher than 10 MeV, higher than 100 MeV, the total energy carried out by the escaped neutrons, and the energy released in the target are given, also. One can see form Table 3 that the total neutron yield is not a good criterion for the estimation of the energy released in the target. The beam interaction in heavy materials realizes the highest values of the neutron yield, but the lowest values of the energy deposited. Important is not only the number of source neutrons but also their energy. High energy neutrons are able to develop further nuclear cascades in the target, resulting a higher neutron fluence. The effect of the development of inter-nuclear cascades with further multiplication of secondary par ticles is illustrated in Fig. 3, where the neutron fluence in the fuel blanket per incident projectile is shown for converter materials Li, Be, C and LBE. A more adequate parameter is the total energy Etot carried by the neutrons which leave the converter. The dependence of the energy
Fig. 3. The neutron spectra in fuel blanket with Li, Be, C and LBE converters, irradiated with a beam of 7Li with energy 0.3 AGeV. 4
M. Paraipan et al.
Progress in Nuclear Energy 120 (2020) 103221
Fig. 4. The dependence of the energy released on the total energy carried out by the neutrons.
The increase of the radius of the beryllium converter produces an increase of the energy released, but the effect is less pronounced that in the case of the variations of the length. For a given mass of the material it is more advantageous to use a converter with lower radius and higher length. The effect of the beryllium converter on the energy efficiency of proton and 7Li beams is synthesized in Table 5. The energy released per projectile, the net power produced and the energy gain are given in the table for the case when the converter is the LBE coolant and the case when a cylinder of beryllium with length 110 m is used as converter. Due to the change in the neutron spectrum (the apparition of the low energy tail), a long beryllium converter transforms the target with criticality coefficient keff 0.94 (value corresponding to a LBE converter) in a target with keff 0.98. The net power and the energy gain presented in Table 5 were calculated assuming a beam intensity of 1.25⋅1016 p/s. In the target with LBE converter a beam of Li with energy 0.4 AGeV is equivalent from the point of view of the net power produced with a beam of 1.5 GeV protons. The use of Be converter determines an increase of the released energy with a factor of 2.3 when the target is irradiated with 1.5 GeV protons. In the case of 7Li beam the energy deposited increases 4.7 times at beam energy 0.4 AGeV and 6.3 times at beam energy 0.25 AGeV. In this way, a beam of 7Li with energy 0.25 AGeV becomes equivalent from the point of view of the net power production with a beam of 1.5 GeV protons. That means that one can produce the same net electrical power using an accelerator 2.6 times shorter. Another advantage of a Be converter is related with the period of operation without refueling and the level of the incineration of the ac tinides that can be achieved. The method used to calculate the evolution of the fuel composition during irradiation is described in the following. The target is divided in zones of almost equal fluence and energy den sity, with variation in the limit of 20% inside a zone. The neutron spectrum registered through simulation in each zone normalized to incident projectile is used to calculate the cross sections for the reactions which contribute to the isotopes accumulation rates (fission, capture, n2n, np, nd, na, nna, nnp). The fluence is considered constant during a time step. The evolution of the number of atoms of isotopes is described by a set of coupled differential equations of the form:
Table 4 The energy released per projectile in targets with and without beryllium con verter with length 30 cm and radius 10 cm, irradiated with a 0.3 AGeV 7Li beam. Target
Edep without Be converter, MeV p 1
Edep with Be converter, MeV p 1
Quasi-infinite natU Quasi-infinite 5.7% 235U Rods 8.9% 239Pu Rods 9.2% 239Pu
4.454e3 8.49e4 3.806e4 9.17e4
7.336e3 1.79e5 8.366e4 2.319e5
Fig. 5. The dependence of the energy released on the converter length in target with 8.9% Pu239, irradiated with 7Li 0.3 AGeV beam.
The dependence of the energy deposited on the length of the con verter from beryllium, lithium, and carbon is presented in Fig. 5. When lithium or carbon are used as materials for the converter the curves of the energy released exhibit a small build-up at intermediate lengths in concordance with the behavior of the neutron yield from thick targets. But in the case of beryllium one gets a continuous increase of the energy deposited with the length of the converter as result of the neutron reflector property of the beryllium.
m n n X X dNi X yij sfis;j Nj þ rik λk Nk þ sil Nl ¼ dt j¼1
5
k¼1
l¼1
k6¼i
l6¼i
ðλi þ sabs;i ÞNi
(3)
M. Paraipan et al.
Progress in Nuclear Energy 120 (2020) 103221
Table 5 The energy released per projectile, the net power produced and the energy gain in U-Pu target with keff 0.98, irradiated with proton and 7Li beams with the intensity of 1.25⋅1016 p/s. Particle
E, AGeV
Converter LBE Edep, MeV p
proton Li
7
1.5 0.25 0.3 0.35 0.4
Fig. 6. The evolution of
1
7.433e4 2.532e4 3.799e4 5.061e4 6.713e4
239
Pu (a) and
Converter Be G
Net power, MW
Edep, MeV p
3.57 2.3 2.87 3.28 3.81
42.28 11.44 19.79 28.15 39.6
1.681e5 1.606e5 1.886e5 2.501e5 3.155e5
1
G
Net power, MW
8.07 14.58 14.94 16.21 17.9
117.8 119.7 136.9 187.7 238.3
241
Pu (b) in target with converters from LBE and Be, irradiated with 7Li 0.3 AGeV beam, with intensity 1.25⋅1016 p/s.
The first term on the right side in eq. (1) represents the contribution from the fission, where sfis,j is the probability for fission of the isotope j and yij is the fission yield of the isotope i. The second term describes the contribution from the decay, where λk is the decay constant and rik is the probability of the isotope k to decay to the isotope i. The third term describes the production of the isotope i through other neutron reactions than fission. The last term describes the disappearance of the isotope i through decay and neutron absorption. The probability of a neutron reaction s is calculated as: Z Emax s ¼ Ib σ ðEÞϕðEÞdE ; (4)
build-up when the keff rises, followed by a slower decrease. Such target needs the use of the control rods during operation. With a proper adjustment of the number of control rods the keff and the energy released can be kept constant at a wanted level during operation. In our example, the target with LBE converter and initial keff 0.94 reaches the value of keff 0.98 after approximately 5 months and can be operated at this level in order to obtain the same power released as in the target with Be converter. It could rise the question why one should not operate the target in this way instead of using a Be converter. The answer is given by the difference in the periods between refueling. The neutron spectra are different in these two cases and determine a different evolution of the isotopes concentration. The evolution of 239Pu and 241Pu in targets with LBE and Be converters is illustrated in Fig. 6. The higher accumulation rate for Pu isotopes achieved in the target with Be converter ensures a longer period between refueling. If one chooses the moment when the energy released decreases with 30% from the plateau value as criterion for refueling and consider the target irradiation with a beam of 0.3 AGeV 7 Li with the intensity 1.25⋅1016 p/s the target with LBE converter must be refueled after 3370 days, but the target with Be converter can be operated until 4990 days. At the moment of refueling the initial mass of actinides is reduced with 10.2% in the case of the target with LBE converter, and with 14.8% in the target with Be converter.
Emin
where σ is the energy dependent cross section of the reaction, ϕ is the neutron fluence per incident particle, and Ib is the beam intensity. The values of the energy dependent cross section for the neutron induced reactions are taken from the ENDF database (McLane et al., 1995, Chadwick et al., 2011). The system of equation (3) is solved with the exponential matrix method, using our program written in the frame of toolkit ROOT (Brun et al., 1997). We use some simplifications. For the isotopes with lifetime below 10 min an instantaneous decay was considered. For the first isotope with lifetime higher than 10 min in each decay chain we include the contribution from precursors with shorter lifetime in the value of the fission yield. In the case of the other isotopes the values of the inde pendent fission yield are used. For a given isotope only the decay channels with probability higher than 10 3 are taken into account. The concentrations of the isotopes calculated at the end of a period are used in the simulation for the next period. The fuel composition used in the simulation includes only isotopes with concentration above 10 6. When necessary, a variable number of boron carbide control rods are inserted between the fuel rods in order to maintain constant the total energy released in the target. If one uses a target with initial level of enrichment low enough, as in our example (8.9% 239Pu) the concentration of 239Pu presents a period of
3.2. Liquid fuel In the case of the liquid target a eutectic composition 46.5LiF11.5NaF-42KF (mol %, FLiNaK) which ensure a good solubility for both UF4 and PuF3 (Degtyarev et al., 2015; Serp et al., 2014) was chosen for the carrying salt. The blanket dimensions were taken large enough to stop a proton beam with energy 1.5 GeV (length 350 cm, radius 200 cm). The enrichment of the fuel used in the following examples was 7% 239Pu. The presence of light elements (Li, Na) in the fuel composition generates a significantly softer neutron spectrum in comparison with a solid fuel target cooled with Pb or LBE. Besides that, the range of 7Li ions in molten 6
M. Paraipan et al.
Progress in Nuclear Energy 120 (2020) 103221
Fig. 7. The neutron spectra in molten salt fuel blanket irradiated with 1.5 GeV proton and 0.275 AGeV 7Li beams, without Be converter (a) and with Be converter (b).
Fig. 8. The dependence of the energy released per projectile (a), and of the net power produced (b) on the Be converter length, for molten salt target irradiated with 1.5 GeV proton and 0.25–0.3 AGeV 7Li beams.
salt is higher than in LBE and the fuel itself acts as an efficient converter for light ions, also. Сonsequently, in molten salt a beam of 7Li with lower energy that in the solid fuel produces the same net power as a beam of 1.5 GeV protons (0.325 AGeV in molten salt comparing with 0.4 AGeV in target with fuel rods). In the presence of a Be converter the neutron spectrum in a molten salt target irradiated with 7Li beam changes in the same manner as in the case of a rods target: one gets an increase of the number of high energy neutrons and of the tail of low energy neutrons, but the changings are less pronounced than in a target with solid rods. Although the difference between the range of 7Li ions in molten salt and Be is not as great as in the case of a target from heavy metals only, it is sufficient to provide an advantage. As example, for the initial energy 0.3 AGeV 35% of ions reach the end of the range in molten salt, and only 10% in Be. The change of the neutron spectrum in the presence of a Be converter is illustrated in Fig. 7 where the neutron spectra registered in a molten salt target irradiated with 1.5 GeV proton beam and 0.275 AGeV 7 Li beam are compared. The length of the Be converter was 150 cm. The energy released depends also on the length of the converter. This dependence is illustrated in Fig. 8. The dependence of the energy released per incident particle is presented for beams of protons with the energy 1.5 GeV and 7Li with the energy in the range 0.25–3 AGeV in Fig. 8a. The corresponding values of the net power produced for a beam intensity of 1.25⋅1016 p/s are given in Fig. 8b. For a beam of 1.5 GeV protons in liquid target the use of a Be con verter is not justified. Even with a converter with length 200 cm the
deposited energy increases only 1.4 times. Still, for Li ions the Be con verter is useful. The use of a Be converter with length 150 cm produces an increase of the energy released with a factor of 2.2–2.4 when the target is irradiated with Li ions. The increase is lower than in a target with solid fuel but high enough to justify its use. When a Be converter is used, a beam of 7Li with the energy 0.275 AGeV becomes equivalent with a 1.5 GeV proton beam and allows to build an accelerator 2.2 times shorter. 4. Conclusions For light ion beams at energies below 0.5 AGeV the use of converters from light materials as Li or Be increases the energy released mainly as the result of a higher ion range in low density and low Z materials. The best results are obtained with Be converters. In this case, besides the increased range one takes advantage of the neutron reflector and moderator properties of beryllium. The effect depends on the dimensions of the converter and fuel composition. The energy released is more sensitive to the variation of the converter length than of the radius. Be converters with length 100–120 cm increase the energy produced with Li beams by a factor of 4.6–6.3 in targets with solid fuel. A beam of 7Li with the energy 0.25 AGeV becomes equivalent from the point of view of the energy produced with a proton beam with energy 1.5 GeV. In this way, the length of the accelerator is reduced 2.6 times. 7
M. Paraipan et al.
Progress in Nuclear Energy 120 (2020) 103221
In molten salt fuel the energy released produced with Li ions in creases with a factor of 2.2–2.4 when a Be converter is used. A beam of 7 Li with the energy 0.275 AGeV becomes equivalent with a proton beam with energy 1.5 GeV and that allows to reduce the length of the accel erator 2.2 times.
Brun, R., et al., 1997. ROOT- an object oriented data analysis framework. Nucl. Instrum. Methods Phys. Res. A 389, 81–86. Chadwick, M.B., et al., 2011. ENDF/B-VII.1: nuclear data for science and technology: cross sections, covariances, fission product yields and decay data. Nucl. Data Sheets 112, 2887. Degtyarev, A., Myashikov, A., Ponomarev, L., 2015. Molten salt fast reactor with U-Pu fuel cycle. Prog. Nucl. Energy 82, 33–36. De Paula Barros, G., Pereira, C., Veloso, M.A.F., Costa, A.L., 2012. Study of an ADS loaded with thorium and reprocessed fuel. Sci. Technol. Nucl. Install. https://doi. org/10.1155/2012/934105. Article ID 934105. ESS Technical Design Report, April 23 2013. ESS-doc-274 Fiori F., Zhou Z., A study on the Chinese nuclear energy options and the role of ADS reactor in the Chinese nuclear expansion. Prog. Nucl. Energy 91, 159–169, 2016. Hashemi-Nezhad, S.R., Westmeier, W., Zamani-Valasiadou, M., Thomauske, B., Brandt, R., 2011. Optimal ion beam, target type and size for accelerator driven systems: implications to the associated accelerator power. Ann. Nucl. Energy 38, 1144–1155. Accelerator Driven Systems: Energy Generation and Transmutation of Nuclear Waste, Status Report, 1997. IAEA-TECDOC-985. Kadi, Y., 2007. Transmutation capabilities of the CERN energy amplifier system. Prog. Nucl. Energy 49, 606–616. McLane, V., et al., 1995. The Cross Section Evaluation Working Group, Data Formats and Procedures for the Evaluated Nuclear Data File ENDF-6, Report BNL-NCS-44945 (ENDF-102). National Nuclear Data Center, Brookhaven National Laboratory, U.S.A. Oigawa, H., et al., 2004. R&D Activities on Accelerator-Driven Transmutation System in JAERI. https://pdfs.semanticscholar.org/8831/31a7756c250df7a9ebb8caf11183 ee282ce3.pdf. Paraipan, M., Baldin, A.A., Kadykov, M.G., Tyutyunnikov, S.I., 2012. Investigation of the possibility to use ion beams for ADS through simulation in GEANT4. In: Proceedings of the 21st International Baldin Seminar on High Energy Physics Problems. JINR, Dubna, Russia. September 10–15. Paraipan, M., Baldin, A.A., Baldina, E.G., Tyutyunikov, S.I., 2018. “Light ion beams for energy production in ADS”, EPJ proceedings MMCP2017, 173. Ann. Nucl. Energy 110 (2017), 04011, 973. Paraipan, M., E and T Collaboration, 2017. Study of neutron spectra in extended U target. new experimental data. EPJ Web Conf. 138, 10005. Baldin ISHEPP XXIII. Paraipan, M., Baldin, A.A., Baldina, E.G., Tyutyunnikov, S.I., 2019. Beam and target optimization for energy production in accelerator driven systems. In: Baldin ISHEPP XXIV EPJ Web of Conferences, vol. 204. https://doi.org/10.1051/epjconf/ 201920404001, 0. Rubbia, C., et al., November 1993. An Energy Amplifier for Cleaner and Inexhaustible Nuclear Energy Production Driven by a Particle Beam Accelerator. CERN/AT/93-47. Serp, J., et al., 2014. The molten salt reactor (MSR) in generation IV: overview and perspectives. Prog. Nucl. Energy 77, 308–319. Zhao, Z., Chen, Z., Chen, H., 2014. Preliminary optimization of proton energy and target for Lead- Bismuth Eutectic target of a demonstration ADS. Prog. Nucl. Energy 71.
Authors contribution Mihaela Paraipan – conception, simulation, data analysis, writing the article. Vafa M. Javadova – simulation, data analysis. Serguey I. Tyutyunnikov – data analysis. Acknowledgments The work was partially supported by the the grant of the Plenipo tentiary Representative of the Romanian Government at JINR Dubna, JINR order 322/21.05.2018, p. 10 in the frame of E&T Collaboration. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.pnucene.2019.103221. References Abderrahim, H.A., et al., 2001. MYRRHA: a multipurpose accelerator driven system for research & development. Nucl. Instrum. Methods Phys. Res. A 463, 487–494. Adam, J., et al., 2017. Secondary particle distributions in an extended uranium target under irradiation by proton, deuteron, and carbon beams. Nucl. Instrum. Methods Phys. Res. A 872, 87–92. Agostinelli, S., et al., 2003. GEANT4 A a simulation toolkit. Nucl. Instrum. Methods A 506, 250–303. Baldin, A.A., Berlev, A.I., Kudashkin, I.V., Mogildea, G., Mogildea, M., Paraipan, M., Tyutyunnikov, S.I., 2016. Simulation of neutron production in heavy metal targets using Geant4 software. Phys. Part. Nucl. Lett. 32, 391–402. Baldin, A.A., Berlev, A.I., Paraipan, M., Tyutyunikov, S.I., 2017. Optimization of accelerated charged particle beam for ADS energy production. Phys. Part. Nucl. Lett. 14 (1), 113–119. Beller, D.E., et al., 2001. The US accelerator transmutation of waste program. Nucl. Instrum. Methods Phys. Res. A 463, 468–486.
8