A Parameter Study of Time-varying Tritium Production in Solid-type Breeder Blankets

Tritium production is of critical importance to prospective DT fusion power plants. Lithium ceramic and beryllium based solid-type breeder blankets are an option for supplying the tritium required to sustain the DT plasma. This research investigates the time-varying tritium production in solid breeder blankets with different compositions. The breeder fraction was varied in conjunction with the 6Li enrichment. The parameter study considered 198 different blanket compositions for three blanket thicknesses. The cheapest configuration capable of meeting the tritium requirements were found. The cost of Li4SiO4 (including 6Li enrichment) and Be12Ti were considered. The time-varying tritium production of each blanket configuration was simulated using the interface code, FATI, that couples the radiation transport code MCNP 6 with the inventory code FISPACT-II. Economical blanket configurations capable of selfarameter lanket sufficiency were found. The cost of producing excess tritium for start-up inventories was found to be between $18,000 and $27,000 per g. Fitting functions to predict the time-averaged tritium breeding fraction and the tritium inventory at five years, were obtained for inclusion in the PROCESS systems code. PROCESS is now able to consider different breeding blanket compositions and thicknesses when assessing the engineering, physics and economic feasibility of reactor designs. © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license


Introduction
Systems codes are designed to assess the engineering, physical and economic viability of future fusion reactors. Systems codes are often designed to run quickly through several iterations to find optimal solutions. This can be achieved by accessing preprocessed results and fitted functions from more computationally intense simulations. Several systems codes exist with differing approaches and objectives. PROCESS [1] is a systems code under development at CCFE with a particular focus on minimizing a user chosen figure-of-merit (e.g. the cost of electricity). The PROCESS code has been utilized effectively in the Power Plant Conceptual Study [2] and economic studies into the feasibility of fusion energy [3]. This paper reports on a new neutronics module which links high fidelity neutronics parameters into the PRO-CESS code. Standard neutronics tools for fusion require enhancement via scripting and linking to an inventory code to allow for nuclei burn-up and transmutation when predicting tritium production. The aim of this parameter study was to provide PROCESS with a timeaveraged Tritium Breeding Ratio (TBR), the tritium inventory after 5 years of operation and material costs.
Three different blanket thicknesses have been considered as well as different lithium enrichments and lithium ceramic (Li 4 SiO 4 ) to neutron multipler ratios (Be 12 Ti).
Fitted empirical functions allow PROCESS access to this data without having to perform the full neutronics simulations. Users will now be able find the most economical blanket composition capable of tritium selfsufficiency or capable of providing a tritium surplus that could be used for subsequent reactors. Due to the small world wide reserves of tritium the rate of fusion reactor deployment will be limited by the availability of tritium [4], careful design and planning of tritium production will help alleviate this risk. The ability to minimise the cost of breeder blankets, while still achieving the required target tritium production, is of particular importance, as currently the blankets are expected to be replaced several times during the reactor's lifetime and will form a large part of the capital cost.

MCNP model
The reactor model used in this study was adapted from a tokamak DEMO model developed at KIT [5].
The model contains no blanket penetrations for heating or diagnostics and therefore overestimate global TBR as compared to a more detailed model incorporating such penetrations. Recent research [6] has suggested that each additional penetration results in a TBR reduction of 0.35% to 0.5% depending on the penetration size and the material present within the penetration. The neutron plasma source [7] utilized in the MCNP model was represented using primary plasma parameters. The model includes a first wall with a thin layer of armour, homogenized breeder modules, a rear shielding layer and a divertor with no breeding capability. Tungsten (3mm thick) was chosen for the first wall armour and Eurofer with helium coolant (3cm thick) was chosen for the first wall [8]. The breeder blanket was split radially into 5 layers and poloidally into 19 modules. The radial segmentation of the breeder zones was based on findings from a previous study which shows radial segmentation to be necessary when simulating nuclide depletion [9]. vessel and divertor (grey), toroidal field coils (green), poloidal field coils (yellow), blanket (red), blanket rear and front casing (black) and tungsten armour (blue) are included.

Materials
The homogenized breeder blanket material used was based on the HCPB design and contained fixed volumes This resulted in 198 different breeder blanket compositions for each of the 3 blanket thickness scenarios (see Table 1). In models with thin and medium scenarios blanket the additional space was filled with ho-

Calculation method
To calculate the time-averaged TBR and final tritium inventories a Monte Carlo approach was used for each blanket composition. The interface code FATI [13] was used to couple the radiation transport code MCNP 6.0 [14] with the inventory code FISPACT-II [15]. FENDL 3.0 nuclear data [16] was used preferentially for particle transport and TENDL 2014 data [17] was used when FENDL data was not avaliable for particular isotopes.
TENDL data in 315 group format was also used for isotope burn-up calculations performed by FISPACT-II. tations within the burn cells in the blanket during irradiation were assumed to be removed from the breeder zones in the purge gas flow.

Cost estimates
In order to compare breeder blanket configurations in terms of their costs it was necessary to make assumptions to quantify the cost of the variable components in each breeder blanket configuration. Other costs involved such as the cost of non blanket related parts of the reactor, the structural Eurofer, He coolant and manufacturing costs were assumed to be constant for all blanket compositions and therefore were not taken into account as a variable costs. The costs associated with increased shielding required for thinner blanket geometries were assummed to be small in comparison and were also not included in this study. The cost of Be 12 Ti was estimated to be $4,500 per kg [20], the future cost of Li 4 SiO 4 (with natural Li) was estimated to be $1000 per kg [21] and the cost of 6 Li enrichment from [22] was used. The relatively high costs of Be 12 Ti compared to Beryllium are due to additional manufacturing steps required.
The costs of the different blanket compositions (see

Theory
The breeder blanket composition affects tritium production, neutron multiplication, shielding, energy multiplication and activation. These different quantities are related, therefore changing the composition with an aim of increasing one aspect may negatively affect others.
An optimal composition would take into account the relative importance of each neutronics quantity. While early fusion reactors might be more focused on producing excess tritium, later designs could be more interested in energy multiplication to maximise electricty production. This paper assumes excess tritium production is of primary importance and aims to optimise solid-type blanket compositions accordingly.
Tritium is produced predominantly via the 6 Li(n,t) 4 He reaction but it is also produced via the 7 Li(n,n't) 4 He threshold reaction. A small amount is produced via interactions in other nuclei (e.g. 9 Be(n,t) 7 Li). Increasing the tritium production can be achieved by: 1. Increasing the number density of tritium producing isotopes.
2. Increasing the neutron population in the blanket region through neutron multiplication. 3. Decreasing the amount of parasitic neutron absorption. 4. Modifying the neutron spectra through scattering interactions so that tritium producing reactions or neutron multiplication become more likely, or so that parasitic becomes less likely.
Enriching the lithium ceramic so that it has a higher 6 Li content increases the tritium production due to the large 6 Li thermal cross section. Increasing tritium production solely by 6  to increasing the lithium content and therefore different levels of 6 Li enrichment have different optimal neutron multiplier volumes. The ratio of lithium to beryllium also varies slightly with time as 6 Li burns up more rapidly than 9 Be. For this reason it is important to take isotopic-depletion into account when choosing a blanket composition to operate for sustained time periods. The task of predicting the time-varying tritium production while accounting for nuclei burn-up is well suited to a Monte Carlo approach that accounts for these neutronic effects.

Results
The TBR of the solid-type breeder blanket was found to decrease over time as the tritium producing isotopes Tritium self-sufficiency was found to be achievable with numerous blanket configurations for all blanket thicknesses (see area within red self-sufficiency line on Figure 4). However, only blankets with high 6 Li enrichment levels and beryllium are capable of generating a useful excess of tritium, to allow for tritium losses and to fuel subsequent reactors. Figures 3 and 4 reveal that at low 6 Li enrichments the optimal tritium production is insensitive to breeder fraction while at higher 6 Li enrichments the optimal tritium production is much more sensitive to breeder fraction.   Tables 2 and 3).  It is possible to achieve the same final tritium inventory with a variety of different compositions (see Figure   4) and each blanket composition has different associated costs (see Figure 2). Figure 5 uses cost values from   the simulated values and the fit is also included.    This is comparable to production from CANDU reactors ($30,000 per g) and cheaper then proposed methods ($84,000 to $134,000 per g) of tritium production [23].
The maximum tritium production hardly varied with blanket thickness and the thicker blankets were found to generate only marginally more tritium (see Table 4).
The maximum tritium production assumed a lithium enrichment of 100% which is not practically feasible. The minimum level of 6 Li enrichment required to achieve self-sufficiency varied slightly with blanket thickness and thicker blankets were found to require marginally less 6 Li enrichment (see Table 4).   Figure 7 shows how the optimal breeder to multiplier ratio required to achieve maximum tritium production varies with lithium enrichment. During the life of the breeder blanket 6 Li is burnt-up more rapidly than 9 Be, this means the final ratio breeder fraction will be lower than the initial ratio. By modelling the blanket burn-up it is possible to compensate for this and find the optimal breeder to multiplier ratio taking into consideration uneven burn-up. Figure 7 reveals that blanket thickness makes negligible difference to the optimal breeder fraction at different enrichment levels.

Conclusion
It has been commonly assumed that the availability of tritium will be one of the limiting factors for future DT and different blanket designs (e.g. HCLL) would also be of interest to reactor designers.