Introduction

Controlled nuclear fusion has a great potential to serve inexhaustible energy source for humankind due to the fact that fusion fuels are abundantly available in the nature. In addition a fusion energy system has attributes of an attractive product with respect to safety and environmental advantages. For this reason, there have been many research and development studies conducted especially on both inertial and magnetic fusion energy reactors during the last 40 years. Nevertheless, the market penetration of a fusion reactor will probably be in far future, probably later than 2050 even towards 2100.

One of the major fusion reactor design concepts is ARIES-RS, a magnetic fusion energy reactor. Several neutronic and design studies on pure ARIES-RS fusion reactor were made [1–5]. It is a design of commercial 1000 MWel power plant based on a reversed shear tokamak, deuterium–tritium (DT) burning plasma [1]. The pure ARIES-RS fusion reactor, using a vanadium alloy structure cooled by lithium, has a fusion power of 2170 MW [2]. It has an energy multiplication ratio (M) of 1.2 [4] producing a total power of ∼2600 MW. In order to enhance the neutronic performance of the ARIES-RS fusion reactor, its hybrid version was proposed in previous works [6–8]. It was shown that rich neutronic economy of ARIES-RS could have been used to produce fissile fuel and increase energy multiplication factor by inserting a fissile fuel zone of 10 cm thickness in the inner lithium zone [6–8]. A 10 cm fission zone at the inner blanket with ThC fuel leaded to a blanket multiplication of M = 1.946 or M = 3.03 with UC fuel and increased the fusion power from 2170 to 4200 MW or to 6500 MW, respectively [6]. In addition to fusion power amplification, substantial fissile fuel namely, 4410 kg 233U/year or 6500 kg 239Pu/year could be produced at start-up conditions under a full fusion power of 2170 MW by providing sufficient tritium for the (DT) driver [6]. The similar improvements with respect to energy multiplication and fissile fuel breeding in the ARIES-RS fusion reactor using various dispersed uranium and thorium fuels were also observed in other two studies [7, 8]. Although substantial neutronic improvements can be reached by inserting a 10 cm fissile zone in the ARIES-RS fusion reactor, this would bring the structural changes in the design of the ARIES-RS reactor which is not easy. Instead of inserting a new fissile zone to the reactor, a coolant bearing nuclear fuels can also be used to improve the neutronic performance of this reactor. This would only need a chemical separation unit to extract fissile fuel to be used in either fission reactors using enriched fuel or breeder reactors.

This study investigates the neutronic analysis of the ARIES-RS fusion reactor with various heavy metal molten salts containing Li2BeF4 (Flibe) + UF4 or ThF4 with different molecular fractions.

The ARIES-RS Blanket Geometry

The pure ARIES-RS fusion reactor uses the blanket containing a vanadium alloy (V-4Cr-4Ti) structure cooled by natural lithium. Figure 1 shows the vertical cross-sectional view of the fusion reactor [1] and the one-dimensional blanket model used in this study for calculations is illustrated in Fig. 2 [4]. In this blanket the V-4Cr-4Ti is used as the first wall structure. And then, fuel breeding zone (FBZ) follows immediately the first wall. In this zone, the heavy metal molten salts consisting of Flibe + UF4 or ThF4 were considered as a coolant to breed both fusile and fissile fuel and increase energy multiplication (Table 1). The molecular fraction of the heavy metal fluoride content in the molten salts was gradually increased from 2% up to 12% by a step of 2%. The inner blanket is a cylindrical shell where a replaceable shield, called structural ring surrounds the inner FBZ. High and low temperature shields follow thereafter. On the other hand, the outer blanket has a torus shape in which a reflector zone surrounds the outer FBZ. Then, high and low temperature shields follow the reflector zone. The heavy metal molten salt as a coolant was also used in the zones of reflector, replaceable shield and high temperature shields. Table 1 gives the blanket zones and their components.

Fig. 1
figure 1

Vertical cross-section of the ARIES-RS reactor

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Fig. 2
figure 2

One-dimensional blanket model of the ARIES-RS fusion reactor [4]. VV, vacuum vessel; LTS, low temperature shield; HTS, high temperature shield; RS, replaceable shield; FBZ, fuel breeding zone; FW, first wall; RF, reflector (dimensions are given in cm, not in scale)

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Table 1 The blanket zones and their components [4]
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Calculation Method

One-dimensional S N calculations were carried out for a cylindrical geometry with the aid of the SCALE 4.3 System using the 238 groups library, derived from ENDF/B-V [9]. The neutron transport calculations were carried out by solving the Boltzmann transport equation with transport code XSDRNPM [10] in S 8–P 3 approximation by using Gaussian quadratures [11]. The numerical output of XSDRNPM was evaluated with XSCALC [12] to get the main reactor parameters. The resonance calculations in the fissionable fuel element cell were made with

  • BONAMI [13] for unresolved resonances and

  • NITAWL-II [14] for resolved resonances.

CSAS control module [15] was utilized to extract the resonance self-shielded weighted cross-sections for XSDRNPM.

Results and Discussion

Neutron Spectrum

The neutron spectrum at various locations for the inner blanket using the coolant of 96% Flibe + 4% UF4 is depicted in Fig. 3. It can be seen that the neutron spectrum softening takes place by deeper penetration through the blanket. While the primary fusion neutrons coming from fusion plasma dominate at the right side of the FBZ, the secondary neutrons generating from fission and collisions become dominant in the FBZ. Neutron attenuation through the inner blanket is 5–6 orders of magnitude at intermediate and high neutron energies.

Fig. 3
figure 3

Neutron spectrum at different locations of the inner blanket using 96% Flibe + 4% UF4: (1) on the right side of the heavy molten salt zone, (2) in the middle of the heavy molten salt zone, (3) on the left side of the heavy molten salt zone, (4) on the left side of the shielding zone, (5) on the left side of the HT zone, (6) leakage spectrum

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Figure 4 represents the neutron spectrum at different locations of the outer blanket containing the same coolant. Again, the neutron spectrum softening through this blanket can be observed clearly due to the same reason explained above. Higher neutron attenuation through the outer blanket reaching 5–10 orders of magnitude at intermediate and high neutron energies can be seen.

Fig. 4
figure 4

Neutron spectrum at different locations of the outer blanket with 96% Flibe + 4% UF4: (1) on the left side of the heavy molten salt zone, (2) in the middle of the heavy molten salt zone, (3) on the right side of the heavy molten salt zone, (4) on the right side of the shielding zone, (5) on the right side of the HT zone, (6) leakage spectrum

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Tritium Breeding

A commercial (DT) driven fusion power plant must produce its own tritium. Tritium is an artificial fuel used in the (DT) fusion plasmas. It can be produced from the breeding reactions of 6Li and 7Li isotopes in the blanket as given below:

$$ ^6 {\text{Li}} + {\text{n}} \to \alpha + T + 4.784\,{\text{MeV}} $$
(1)
$$ ^7 {\text{Li}} + {\text{n}} \to \alpha + T + {\text{n}} - 2.467\;{\text{MeV}} $$
(2)

Tritium breeding ratio (TBR) should be ≥1.05 to maintain tritium self-sufficiency of the (DT) fusion driver of the reactor. It can be achieved in the blanket containing lithium bearing coolants and/or materials.

TBR can be defined as follows:

$$ {\text{TBR = }}T_{\text{6}} {\text{ + }}T_{\text{7}} $$
(3)

where, \( T_6 = \iint {\Phi \bullet \Sigma _{({\text{n}},\alpha ){\text{T}}} }{\text{d}}E\,{\text{d}}V \) on 6Li, and \( T_7 = \iint {\Phi \bullet \Sigma _{({\text{n}},{\text{n}^\prime}\alpha ){\text{T}}} }{\text{d}}E\,{\text{d}}V \) on 7Li.

Figure 5 shows the change in the TBR per incident fusion neutron for the blanket using two different molten salts with different mole fractions of heavy metals. One can observe that TBR decreases gradually with increasing heavy metal content of both molten salts. Higher TBR values can be reached for the molten salt with UF4 than that with ThF4 due to the fact that uranium increases neutron economy by making more fission compared to thorium (Fig. 6). Tritium self-sufficiency is maintained in the blanket only for the coolants; 98% Flibe + 2% UF4, 96% Flibe + 4% UF4 and 98% Flibe + 2% ThF4. The major part of tritium is bred by 6Li (Table 2), whereas, almost all of it is produced in the FBZ of the blanket. The contribution of other zones (reflector, replaceable shield and high temperature) to TBR is very low.

Fig. 5
figure 5

TBR variation with respect to the molten salt composition for the blanket with: (1) Flibe + UF4, (2) Flibe + ThF4

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Fig. 6
figure 6

Energy multiplication versus heavy metal content with (1) Flibe + UF4, (2) Flibe + ThF4 and integral fission versus heavy metal content with (3) Flibe + UF4, (4) Flibe + ThF4 (per incident fusion neutron)

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Table 2 Contribution of 6Li (T6) and 7Li (T7) on TBR in the blanket with various coolants
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Energy Multiplication

Incident fusion energy can be amplified in the blanket by exothermic nuclear energy reactions, namely neutron capture in 6Li and fission by heavy metal in the molten salt in addition to the kinetic energy transfer of the fusion source neutrons. Although the fission is in a relatively modest level for the investigated blanket (Fig. 6), energy release per fission is considerably higher than per fusion event. Hence, there can be an important contribution of the fission energy release to total plant power production depending on heavy metal content in the coolant so that electricity generation can be increased remarkably. M can be defined as follows:

$$ M = \frac{{200 * \langle \Phi \bullet \Sigma _{\text{f}} \rangle + 4.784 * T_6 - 2.467 * T_7 + 14.1}} {{17.6}} $$
(4)

where, \( \langle \Phi \bullet \Sigma _{\text{f}} \rangle = \iint {\Phi \bullet \Sigma _{\text{f}} }{\text{d}}E\,{\text{d}}V = {\text{Total}}\,{\text{integral}}\,{\text{fission}}\,{\text{rate}}{\text{.}} \)

One can see from Fig. 6 that the M increases gradually with respect to UF4 content reaches 1.53 for the coolant 88% Flibe + 12% UF4. However, it slightly changes with respect to ThF4 content and remains almost constant at relatively low levels. It is due to the fact that the integral fission rate in uranium is much more than thorium.

Use of heavy metal in the Flibe causes the production of gaseous fission products. However, the fission rate in the coolant remains modest and the flowing coolant is removed and circulated continuously out of the reactor chamber to extract fissile fuel. A very short residence time for gaseous fission products in the chamber would take place.

Fissile Fuel Production

In addition to fission, fissile fuel breeding occurs in the heavy metal molten salt by converting the 238U to 239Pu, and 232Th to 233U via neutron capture reactions depending on the composition of the molten salt. One of the most important benefits gained from the heavy metal molten salt is the fissile fuel production to be used in conventional nuclear fission reactors. Fresh fissile fuel can be separated from the circulating molten salt in the blanket by a chemical process continuously. This would eliminate the partial burning of the new fissile isotopes in the blanket under energetic fusion neutrons.

Figure 7 shows the total fissile fuel breeding rate and the annual fissile fuel production with respect to the heavy metal content in the salt. It is clear that both of them increases linearly with increasing heavy metal. Although, the fissile fuel production is ∼400 kg 239Pu/year with the molten salt 98% Flibe + 2% UF4, it reaches ∼2400 kg 239Pu/year for the molten salt 88% Flibe + 12% UF4. The similar amount of fissile fuel breeding is available for the molten salt with thorium.

Fig. 7
figure 7

Total fissile fuel breeding rate (1) 238U(n,γ)239Pu, (2) 232Th(n,γ)233U and annual fissile fuel production (3) 239Pu, (4) 233U with respect to the heavy metal content

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Use of the molten salt Flibe + UF4 leads to the production of a precious nuclear fuel, 239Pu with a market value of 80,000 $/kg. The revenue from the fissile fuel breeding by the molten salt, Flibe + UF4, can become 32 and 192 M$/a for 2% UF4 and 12% UF4, respectively. In the case of Flibe + ThF4 and for a market value of 300,000 $/kg for 233U, the revenue becomes 140 M$/a for 2% ThF4 and can increase up to 750 M$/a for 12% ThF4. This would greatly reduce total electricity cost per kWh.

Conclusions

Among the investigated salts, only the Flibe with 2% UF4 or ThF4 and 4% UF4 supplied sufficient tritium breeding. Addition of higher heavy metal salts degraded tritium production and decreased below 1.05. Therefore, the molecular percentage of ThF4 and UF4 in the molten salt mixture should not exceed 3 and 4, respectively. Although, the energy multiplication was at low levels and practically not affected by the Flibe with ThF4, it gradually increased with UF4 content for the Flibe + UF4. Substantial amount of fissile fuel was produced by using heavy metal molten salt in the blanket. This would have a significant positive impact on decreasing the cost of electricity generated.