Feasibility of a multi-purpose demonstration neutron source based on a compact superconducting spherical tokamak

Fusion Engineering and Design 88 (2013) 3312–3323

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Feasibility of a multi-purpose demonstration neutron source based on a compact superconducting spherical tokamak C. Guillemaut a,∗ , J.J.E. Herrera Velázquez a , A. Suarez b a b

Insituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, Ciudad Universitaria, 04511 Coyoacán, D.F., Mexico Laboratorio Nacional de Fusión, Asociación EURATOM-CIEMAT, 28040 Madrid, Spain

a r t i c l e

i n f o

Article history: Received 25 May 2013 Received in revised form 14 October 2013 Accepted 14 October 2013 Available online 16 November 2013 Keywords: Spherical tokamak Neutron source Superconducting Fusion–fission Transmutation Radio-isotopes

a b s t r a c t Tokamak neutron sources would allow near term applications of fusion such as fusion–fission hybrid reactors, elimination of nuclear wastes, production of radio-isotopes for nuclear medicine, material testing and tritium production. The generation of neutrons with fusion plasmas does not require energetic efficiency; thus, nowadays tokamak technologies would be sufficient for such purposes. This paper presents some key technical details of a compact (∼1.8 m3 of plasma) superconducting spherical tokamak neutron source (STNS), which aims to demonstrate the capabilities of such a device for the different possible applications already mentioned. The T-11 transport model was implemented in ASTRA for 1.5 D simulations of heat and particle transport in the STNS core plasma. According to the model predictions, total neutron production rates of the order of ∼1015 s−1 and ∼1013 s−1 can be achieved with deuterium/tritium and deuterium/deuterium respectively, with 9 MW of heating power, 1.4 T of toroidal magnetic field and 1.5 MA of plasma current. Engineering estimates indicate that such scenario could be maintained during ∼20 s and repeated every ∼5 min. The viability of most of tokamak neutron source applications could be demonstrated with a few of these cycles and around ∼100 cycles would be required in the worst cases. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Several concepts have been raised for a near term application of fusion, mainly focused on the use of deuterium/tritium (DT) plasmas in tokamaks as neutron sources. Some would like to build fusion–fission hybrid reactors where fission reactions are maintained in a sub-critical mass of fissile material by fusion neutrons, see [1–6]. Others propose to integrate tokamak neutron sources to the fission fuel cycle of the pressurized water reactors (PWRs) for the elimination of the nuclear wastes like minor actinides and long live fission products, see [7–9]. Finally, tokamak fusion sources could also be used to produce radio-isotopes for nuclear medicine [10] and in any case DT operations will require the production of tritium to be maintained, see [2,3] and [11]. Other concepts and applications (see [12–17]) have been proposed but this study is focused on the use of a tokamak neutron source for the four cases mentioned above. The generation of the adequate neutron production rate for these particular purposes does not require energy efficiency; thus, nowadays tokamak technologies would be sufficient [11]. For an industrial scale, most of these applications would require steady state fast neutron (>1 MeV) production rates up to

∗ Corresponding author. Present address: CEA, IRFM, F-13108 Saint-Paul-lezDurance, France. E-mail address: [email protected] (C. Guillemaut). 0920-3796/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fusengdes.2013.10.011

∼1020 s−1 . The 14.1 MeV neutrons from DT fusion reactions would represent an interesting option for these applications. Only the production of radio-isotopes requires lower energies which can be obtained by moderation of the fast neutrons. Although a certain number of encouraging studies have been done in this area [10,18], no tokamak has ever been dedicated to the experimental study of fusion neutron sources. A demonstration device for these applications would have to achieve repeated long discharges to generate a significant number of neutrons for the production of measurable amounts of by-products of the neutronic reactions of interest (see examples in Table 1). That is why the use of actively cooled plasma facing components (PFCs) is proposed here. Superconducting magnet systems are also considered since their limited power consumption, compared to the copper option, should decrease significantly the running cost of the machine. The possibility of reaching a higher level of commercial viability with the use of superconductors would be an important aspect to demonstrate. The neutron generation has to remain sufficiently low to avoid any particular precautions against neutron damages in the structure and the superconductors. The plasma volume and the toroidal field (TF) must also be as small as possible to limit the price of the machine and this is why the spherical tokamak option has been retained in this study. This paper presents preliminary feasibility estimates for a demonstration machine, the spherical tokamak neutron source (STNS), shown in Fig. 1. It has a major radius R = 0.51 m, a minor

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Table 1 Examples of neutron reactions of interest. Application

Reaction Te + n → I+␤ Mo + n → 99 Mo + ␥ 59 Co + n → 60 Co + ␥ 7 Li + n → 4 He + 3 H + n 6 Li + n → 4 He + 3 H 239 Pu + n → x A + y B + zn 235 U + n → x A + y B + zn 244 Cm + n → x A + y B + zn 243 Am + n → x A + y B + zn 241 Am + n → x A + y B + zn 237 Np + n → x A + y B + zn 135 Cs + n → 136 Ba + ␤+ 129 I + n → 130 Xe + ␤+ 99 Tc + n → 100 Ru + ␤+ 130

Production of radio-isotopes for nuclear medicine (examples) 3

H production

Fusion–fission

Elimination of minor actinides

Elimination of long live fission products

131

+

98

radius a = 0.32 m (aspect ratio A = 1.6), the typical plasma elongation is  ∼ 1.8, the triangularity is ı ∼ 0.5 which gives a plasma volume of ∼1.8 m3 . Even if different machines with similar geometric parameters have already been built [19,20] or proposed [6], the design options and the technologies involved in the STNS are quite different and represent interesting possibilities for such a device. The STNS would have the particularity of using the YBa2 Cu3 O7−x (YBCO) high temperature superconductor (HTS) for the central solenoid (CS) to reach magnetic fields up to 15 T and a niobium titanium (NbTi) superconductor for the TF coils. Since there is no space issue outside the central column and the vertical field is significantly smaller than the TF, the PF coils would be made of copper. More generally, the PF coils do not represent any critical issue for the STNS; thus, no study is shown on this topic in the present work. The space occupied by the PFCs, the superconductors, the metal structures and the cooling systems are estimated for the central column. The dimension of the latter is a crucial parameter since it constrains strongly the aspect ratio and the performances of the machine. All these elements must have enough space in the central column to allow repeated 20 s reference discharges with B0 = 1.4 T of central TF, Ip = 1.5 MA of plasma current (safety factor q95 ∼4.5 and normalized ˇ below the Troyon limit with ˇN ∼ 2), PNBI = 4 MW of Neutral Beam Injection (NBI) heating, PECRH = 4 MW of Electron Cyclotron Resonance Heating (ECRH) and ∼ 1 MW of ohmic heating.

Half-life

Activity (Bq kg−1 )

8.02 days 66 h 5.27 years 12.6 years

4.6 × 1018 1.75 × 1019 4.4 × 1016 3.57 × 1017

Too many by-products but very exothermal reactions (200 MeV)

Stable by-products but with characteristic gamma radiation from ␤+ /␤− annihilation

The feasibility of the parameters summarized in Fig. 1 is studied in the Sections 2–4 with a focus on the PFCs, the TF coils and the CS respectively. In Section 5, these parameters are implemented in the Automatic System of Transport Analysis (ASTRA) code [21] for the simulations of the plasma operations. In the particular case of the STNS, both DT and deuterium/deuterium (DD) reactions are considered for the production of neutrons for the different applications presented in Section 6. 2. The PFCs and their cooling system 2.1. Protection of the PFCs against magnetic forces Since the central column diameter has to be kept as small as possible, the lack of space in this part represents a challenge for the design. The values chosen for the minor and major radius of the STNS leave a diameter of 0.34 m. The central column has to accommodate the PFCs with their water cooling system, the TF and CS superconductors with their cryogenic cooling system and all the steel structures. The other surfaces of the plasma chamber are supposed to accommodate actively cooled PFCs, if required, without affecting the geometric parameters chosen for this study. For this reason, only the central column PFCs are treated here. In order not to be pulled out by the magnetic forces, the PFCs and their cooling system will be bolted on cold worked 316 L stainless steel structures (see Fig. 2) which can withstand more than ∼103 fatigue cycles of a tensile stress up to  0 ∼ 300 MPa at 473 K [22]. Beyond this temperature, it becomes weaker but the water cooling of the PFCs should prevent this from happening. Although the heat transfer from bolted PFCs is not expected to be good, it is shown in the next Section that this option is sufficient to cope with the power load on the central column. Even if spherical tokamaks seem to have a high degree of resilience to major disruptions [19,23], the very pessimistic case where the entire poloidal component Ipol of the total plasma current Itot is circulating through the central column PFCs in the poloidal direction is considered. If Ip is the toroidal plasma current fixed at 1.5 MA, then IP Itot = IP + I , pol where Ipol = q

Fig. 1. Side view of the STNS. The red rectangle represents the zone for the NBI heating power deposition in the ASTRA simulation. The blue circle is the position of the half width perimeter for the ECRH power deposition profile in the ASTRA simulation. The magnetic flux surfaces shown here are obtained with ASTRA and correspond to the equilibrium of the scenario which maximizes the neutron production rate. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

(1)

and q is the safety factor comprised between q0 = 1 in the centre and q95 = 4.5 at the edge in the case of the STNS. If an average value of q = 2.75 is taken for the plasma current, then Ipol = 0.6 MA and the TF on the high field side of the plasma chamber should be around BHFS = 4.3 T (see Section 3.1 below). During a disruption, Ipol circulating in the central column PFCs, generates a Laplace force, normal to the PFCs surface. Since the PFCs and their cooling system are bolted on a cylindrical cold worked 316 L stainless steel structure with a

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that 50% of this radiative power would be absorbed by the surfaces of the divertors and 50% would escape to be deposited uniformly on the main chamber wall. The reference scenario for neutron production requires 8 MW of auxiliary power and 1 MW of ohmic heating. Thus, on the main chamber wall, the total radiative heat flux should not exceed Prad ∼ 4.5 MW with the following average heat flux density in MW m−2 qrad ≈

Fig. 2. (a) Cross section of the STNS central column, (b) sizes of the radial extension of each element.

thickness e = 2.10−3 m (see Fig. 2), the latter will be submitted to the tensile stress ss =

Ipol BHFS 2e

,

(2)

which is ∼200 MPa here and respect the condition  ss ≤  0 for this material [22]. The PFCs material has not been decided yet and three possibilities will be considered: carbon, molybdenum or tungsten. The PFCs erosion is usually much stronger with carbon than with molybdenum or tungsten but the core plasma tolerates higher concentrations of low Z impurities than high Z impurities. The behaviour of the PFCs submitted to plasma instabilities or disruptions and the consequences on the impurity generation [24,25] also depend on the choice of material. Further studies would be required to find the most suitable material for repeated high performance discharges in the STNS. 2.2. Water cooling of the PFCs The STNS experiments would start and end with a limiter phase with a plasma leant on the central column. Since these steps should be limited in time (∼1 s) and would not have auxiliary power, it is assumed that the power deposition on the PFCs should be small in comparison with the full power phase and can be neglected for this study. For neutron production, the objective is a 20 s high performance discharge in diverted configuration. For efficient impurity removal, H-mode operations, high triangularity and high elongation plasma shapes, the STNS would use a double null configuration with an upper and a lower divertor (see Fig. 1 above). The design and study of the divertors is not the purpose of this paper and could be the object of further work. It is assumed here that the impurities would be removed efficiently enough to keep Zeff around 1 in the plasma core and that the power deposition could be handled mainly at the outer divertor targets without affecting the general geometric parameters chosen for the STNS. After the activation of the divertors, the PFCs of the central column should not receive plasma heat flux but essentially radiative heat flux. From the point of view of the central column PFCs, the highest heat flux possible would be due to the radiation of the totality of the input power in the divertors. If such extreme scenario occurs, it has been assumed

Prad . 42 Ra

(3)

In this study, the plasma elongation is fixed at  = 1.8 because it is a reasonable value achievable in present spherical tokamaks experiments (see [20,23]) allowing stability and performance. Thus, the incident radiative heat flux density on the central column PFCs should not be higher than qrad ∼ 0.4 MW m−2 . As discussed in [26], the range of reflectivities of the PFCs material can be rather large depending on the wavelength considered, the angle of incidence and the wall conditions but the case with zero reflectivity is the most pessimistic possibility for the power deposition on the surfaces facing the plasma. This simple assumption has been made here since it provides conservative engineering estimates. The PFCs and the cold worked 316 L stainless steel would be separated by a water cooling system in copper to remove the radiative heating during the discharge. The PFCs and the copper structure would have a thickness of 5 mm each (Fig. 2). The surface of the central column would be divided toroidally in 32 PFCs plus copper cooling elements and each copper structure would have six tubes of 3 mm diameter drilled inside. If the water enters at 293 K and is evacuated at 353 K, giving a Twater of 40 K, the total flow ˚water , in L s−1 , required to remove the radiative heating deposited on the central column surface Scc in m2 , is given by water =

qrad Scc . CTwater

(4)

With the water density  = 1 kg L−1 , the heat capacity C = 4185 J kg−1 K−1 and Scc ∼1 m2 , the total flow needed for the entire column is around 2.4 L s−1 , which gives an average fluid velocity of 1.7 m s−1 in each tube. In these conditions, the Reynolds number reaches Re ∼ 4000, which corresponds to a turbulent flow helping the heat transfer from copper to water. The latter can go from 500 to 10000 W m−2 K−1 , depending on the nature of the flow. The higher the Reynolds number, the higher the heat transfer coefficient is; thus, in this case, it should be closer to 10,000 than 500 W m−2 K−1 . An intermediate value of htrans ∼5000 W m−2 K−1 is taken to make a conservative estimate of the elevation of temperature Ttrans between the water and the copper. For the 192 tubes, over the height h = 1 m of the central column, the total area of transfer is Atrans = 1.8 m2 , which is used in Ttrans =

qrad Scc . htrans Atrans

(5)

This gives a temperature elevation of 44 K for the copper structure compared to the water flowing inside. Since the thermal conductivity of copper is high enough to avoid any significant gradient over the 1 mm thickness separating the water from the steel, the maximum temperature of the copper in contact with the stainless steel should be nearly ∼400 K. This gives a reasonable margin for the protection of the mechanical properties of the stainless steel. If a moderate pressure is applied on the PFCs when bolted with the copper structure on the stainless steel, a thermal contact conductance of ∼1000 W m−2 K−1 could be expected between the PFC material and the copper. According to (5), the PFCs should be ∼400 K hotter (at ∼800 K) than the copper on the side in contact with the latter for a heat transfer area of around 1 m2 . If the thermal conductivity of each possible material for the PFCs is taken

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Table 2 PFCs surface temperature compared to their melting point. Material

Carbon

Tungsten

Molybdenum

Thermal conductivity (W m−1 K−1 ) PFCs temperature T + Tcond (K) Melting point (K)

129 815 3915 (sublimation)

173 811 3695

138 814 2896

into account, the elevation of temperature of the latter between the plasma side and the side in contact with the copper is given by Tcond =

qrad Scc ln(R2 /R1 ) . 2hKT

(6)

Here, the PFCs extend radially from R1 = 0.165 m to R2 = 0.17 m in the central column (Fig. 2) and KT represents their thermal conductivity in W m−1 K−1 , Table 2 gives the Tcond for each one of them and it appears that they all stay around 800 K on the plasma side, which is still small compared to their melting point. Thus, even if the bolted connection between the PFCs and the copper does not allow a very good heat transfer, it seems to be sufficient in this case and it has the advantage of being less expensive than other options involving more efficient thermal connections. 3. The NbTi TF coils in liquid helium 3.1. The TF coils main parameters At present, the existing small tokamaks with copper TF coils are restricted in discharge duration (∼1 s) by the strong heating due to the copper finite resistivity. Even if solutions exist for the handling of this heating over longer durations, it will always represent a significant amount of power with its impact on the running cost of the machine. Like the STNS, a commercial tokamak neutron source must be capable of repeated long discharges and the use of superconducting magnets could help such machine to be more cost-effective by reducing its power consumption. This is a vital aspect for a tokamak neutron source that the STNS aims to demonstrate and that is why its TF coils would be made of NbTi superconductor to produce the 1.4 T of central TF. The NbTi would be cooled with liquid helium (LHe) at 4.2 K, allowing an operational current density J0 = 2.4 × 109 A m−2 in the cables, as will be discussed below. To limit the ripple and to have sufficient space for diagnostics, NBI lines, ECRH antennas and nuclear material compartments, the STNS will be built with 16 TF coils. The section of NbTi required in each TF coil to reach 1.4 T in the plasma centre is given by ANbTi =

2RB0 , 0 J0 NTF

(8)

With the distance from the plasma centre r = 0.37 m, BIL = 5 T. This value constrains the current density in the NbTi of each TF coil which cannot be maintained at 2.4 × 109 A m−2 when the temperature is higher than the current sharing value Tcs = 4.8 K (Fig. 3). This can be verified by Bottura’s empirical formula [27] which predicts the critical current density Jc (in A m−2 ) in the NbTi superconductors in function of the magnetic field B (in T) and the temperature T (in K): JC (B, T ) =

B





BC2 (T ) = BC20 1 −

 T 1.7  TC0

,

(10)

with BC20 = 14.5 T and TC0 = 9.2 K for NbTi. The superconductivity cannot be maintained if the temperature is higher than the critical value TC in K given by



TC (B) = TC0 1 −

BIL BC2 (T )

1/1.7

.

(11)

As shown in Fig. 3 the latter is 7.2 K with B = BIL in the TF coils of the STNS. 3.2. Stability of the NbTi superconductor

0 J0 ANbTi NTF . 2(R − r)

JC,ref CNbTi

where the following fitting parameters are characteristic of NbTi: Jc,ref = 3 × 109 A m−2 , CNbTi = 31.4 T, ˛NbTi = 0.63, ˇNbTi = 1 and NbTi = 2.3. The critical magnetic field BC2 is given by

(7)

where B0 is the central TF in T, 0 = 4␲ × 10−7 SI and NTF the number of TF coils, the section of NbTi is ANbTi = 9.3 × 10−5 m2 . The magnetic field on the NbTi of the inner leg (BIL ) of the TF coil is given by BIL =

Fig. 3. STNS TF coils operational domain in temperature and current densities given by Bottura’s formula.

B BC2 (T )

˛NbTi 

B 1− BC2 (T )

ˇNbTi 

1−



T TC0

When a quench occurs in the superconductor, the current has to circulate through the stabilizing copper strands placed around the NbTi (Fig. 4), which generates a significant heating power. The efficiency of the protection against quenches depends on the section allocated to the copper and the wetted perimeter of the cables. If both are sufficiently wide, the heating power from the copper will be absorbed fast enough by the LHe to bring the NbTi temperature back to its operational value and restore its superconducting properties.

1.7  NbTi

,

(9)

Fig. 4. Cross section of the superconducting cables of a STNS TF coil. This simple view is just meant to give an idea and allows estimates.

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Fig. 6. The TF total current (in red) and the TF field (in black) generate the Laplace force (in blue) all along the TF coils which produce tensile forces (in yellow). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Fig. 5. According to the Maddock Criterion, a STNS TF coil is stable (area a = area b) if the latter is divided in 20 cables where ␥ = 2.

The total power Q evacuated to the LHe per metre of TF coil in W m−1 is given by Q = hK (TS − Tb )

2rn , X

(12)

where hK is the Kapitza conductance [28] in W m−2 K−1 , TS and Tb are the copper and the LHe temperatures, respectively, in K (Tb = 4.2 K here), n is the number of turns in each TF coil (see Fig. 4), X is a reduction factor for the wetted area and b is the radius in m for each cable. The latter is given by

 b=

(G − Q )dT = 0.

(18)

Area a (for Q > G) = area b (for Q < G) is obtained in Fig. 5, which means that the stability criterion is verified for the parameters chosen here. In total, the NbTi superconductors plus their copper stabilizer should occupy a section of 2.79 × 10−4 m2 in each TF coil. It is assumed that if another 2.79 × 10−4 m2 section is given to the LHe cooler, hK can be maintained at the value used here.

(13)

ANbTi . ACu

(14)

Q is represented as the blue curve on Fig. 5 if each TF coil is divided in n = 20 turns with ␥ = 2, hk = 400 Ts3 and a reduced heat transfer area is considered such as X = 2 (see Fig. 4). If a perturbation rises the temperature higher than Tcs , a fraction of the current will have to be shared with the surrounding copper (see Fig. 4), rising the cable temperature even more because of its finite resistivity Cu in m approximated by Cu = 1.57×10−10 + 0.46×10−10 B.

(15)

With the magnetic field B = BIL = 5 T in this case, it gives Cu = 3.9 × 10−10 m. The current density JCu in the copper cable is given by

⎧ TS ≤ 4.8 K → JCu = 0 ⎪ ⎪ ⎪ ⎪ ⎨

4.8 < TS < 7.2 → JCu =

⎪ ⎪ ⎪ ⎪ ⎩ TS ≥ 7.2 K → JCu = J0

1 (1000TS − 4800) .

(16)



This allows the calculation of the total heat flux G dissipated by the copper per metre of TF coil in W m−1 2 G = Cu JCu ACu ,

3.3. Protection of the TF coils against magnetic forces

( + 1)ANbTi , n

with =

which is represented as the red curve in Fig. 5 for Acu = 2 × ANbTi = 1.86 × 10−4 m2 . The Maddock Criterion for stability [29] is satisfied if

(17)

At 4.2 K, the 316LN stainless steel should withstand ∼105 fatigue cycles at ∼1000 MPa before failure [30]. The possibility of using this material to build the cryostats of the STNS TF coils is considered here. It would have to contain the cables, the cryogenic fluid and should support all the mechanical constraints. The binding between the TF superconducting cables and this structure is not detailed in this paper and is assumed to be negligible in term of space consumption. The TF coils would be subject to the Laplace force due to the total current ITF = 0.223 MA circulating in each one of them and the magnetic field up to 5 T in the inner leg. In the central column, the Laplace force should push the TF coils towards the axis of the machine and is also expected to generate strong tensile forces in the superconducting cables (Fig. 6). It is assumed that outside the central column, there is enough space for any structure necessary to prevent the deformation of the TF coils without affecting the aspect ratio. However, in the central column, this can be an issue, since the lack of space does not allow big structures to strengthen the TF coils. Altogether, the stainless steel of the TF coils would form a structure which can be assimilated to a simple cylinder with a width fixed at e316LN = 13 × 10−3 m. According to (2), if I = 16ITF and B = BIL , the maximum centering stress should be around ∼220 MPa, which gives a comfortable safety margin [30]. The tensile force along the superconducting cables direction is given by TF =

ITF BIL RTF , hTF (e316LN + eNbTi )

(19)

with the TF coils average radius RTF ≈ 1 m, the TF coils poloidal width hTF = 6.1 × 10−2 m and the width occupied by the NbTi in the TF

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Table 3 Composition of a TF coil and its cryostat. Material

Fe

He

Cu

Nb

Ti

% of TF coil volume (1300 cm3 )

56.9

21.6

14.3

3.6

3.6

radiative power, Pdep in W, on the LHe cryostats of the TF coils is given by Pdep = F12 Acryo (T24 − T14 ), with F12 =

Fig. 7. The dilation of the ascending column of LHe due to the different heating processes raises its level compared to the descending column. The overflow of LHe in the ascending column generates the circulation of the fluid in the thermosiphon.

coils eNbTi = 2 × 10−3 m (Fig. 2). According to (19), the tensile stress, shared by the stainless steel and the NbTi cables, would be around ∼1000 MPa. It should be noted that the NbTi at 4.2 K has tensile stress properties comparable to the 316LN stainless steel [31]. Even, if the STNS TF coils current is ramped up and down once a day during decades, like on the French tokamak Tore Supra (also using NbTi TF coils), the fatigue should never be sufficient [30] to cause a mechanical failure. Thus, the section dedicated to the stainless steel structures would be 7.38 × 10−4 m2 which gives a total section of 1.296 × 10−3 m2 for each TF coil. In the central column, the latter would extend radially from 0.132 m to 0.155 m (Fig. 2).

3.4. Cryogenic cooling of the TF coils The evaporation rate of helium in each TF coil cryostat should be mainly due to radiative heating, heat conduction through the current leads of the coils and nuclear heating. This study is concentrated only on the current flat top phase of the STNS operation. The AC losses in the TF coils, related to the plasma current ramping and the transient events, like disruptions, are not evaluated here and would require further studies. It is considered in this article that the circulation of the cryogenic fluid happens naturally in each coil due to a thermosiphon effect, see Fig. 7. As shown in [32], this effect is already successfully applied in the superconducting Compact Muon Solenoid (CMS) detector at the CERN for the circulation of LHe and the conditions, in terms of geometry and heat leaks, are not very different in tokamaks TF coils. According to Section 2, the stainless steel cylindrical structure supporting the PFCs and their cooling system should not be hotter than 400 K during the discharges and 293 K between them. It would be separated from the surface of the TF coils cryostats by a 3 mm isolating vacuum (Fig. 2) which is assumed to be sufficiently good to avoid any heat transfer through conduction and convection. The surfaces of both sides of the vacuum would be covered with a thin film of silver which has a very low emissivity and limits the radiative heat flux coming from the side of the PFCs. The deposited

ε1 ε2 , ε2 + (1 − ε2 )ε1

(20)

where F12 represents the effective fraction of radiative power deposited on the TF cryostats, accounting for the multiple reflections between the hot and the cold surfaces on both sides of the vacuum. The total area of the cryostats facing the PFC steel support surface is Acryo ∼ 1 m2 , T1 is the cryostats temperature and T2 is the steel support temperature in K, ε1 and ε2 are the emissivities of the silver covering the cryostats and the stainless steel support surfaces, respectively (ε1 ∼ 0.005 at 4.2 K and ε2 ∼ 0.02 between 400 K and 293 K) and  = 5.67 × 10−8 SI. The predictions for the central column from (20) in these conditions are shown in the first column of Table 4. The inner side of the TF coil cryostats is stuck on the CS cryostat which is also at 4.2 K thus no heating contribution of any kind is expected from there. It is assumed that outside the central column, the radiative heating is negligible because there should be enough space for the LHe cryostats of the TF coils to be thermally shielded by liquid nitrogen screens at 77 K. The connection between the copper cables of the power supplies and the superconducting cables of the TF coils is done via some current leads at 4.2 K. Even at this temperature, the cables still conduct ∼1 W kA−1 [33] of heat to the cryostat. With 20 turns in each TF coil, it requires around 10 kA in each of the 16 current leads which gives in total a maximum conducted power of 160 W. The maximum neutron production rate considered for this study during DT operations in the STNS, reaches max = 4 × 1015 s−1 and would be maintained for 20 s in each discharge. It represents 9 kW of nuclear heating from neutrons and gamma rays (negligible with DD) and a fraction of this power is expected to reach the TF coils cryostats. In order to maintain the aspect ratio at 1.6, the central column cannot be shielded and that is why both contributions of the nuclear heating have been evaluated by the Monte Carlo N-Particle (MCNP) transport code [34] and the nuclear data libraries for fusion FENDL 2.1. Fig. 8 shows the neutron and gamma fluxes calculated and the associated nuclear heating for the different materials of the inner column, at two locations: middle of the column (close to the centre of the plasma) where the maximum nuclear heating is reached and top/bottom of the column for the minimum values. The nuclear materials compartments have been ignored in these simulations since they are not expected to affect the neutron flux and gamma flux falling on the central column. The composition of each TF coil and cryostat implemented in MCNP is presented in Table 3. The choice of material for the PFCs is not important for this study since they are too thin to have any significant shielding effect. Even without including a shielding for the TF coils outside the central column in the MCNP simulations, the neutron and gamma flux is one to two orders of magnitude smaller than in the central column. Therefore, the neutron and gamma heating in these parts of the TF coils will not exceed a few watts and since a shielding is foreseen outside the central column (see Fig. 1) it will be neglected in this study. The simulations confirm that the nuclear heating is significant only in the central column and the values are given in Table 4. According to the experience with different devices in fusion and particle physics [35] (Fig. 9), the expected Coefficient of Performance (COP) for a typical LHe cooling system in consumed power, to produce the LHe, per unit of cooling power at 4.2 K can now

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Fig. 8. MCNP simulation with a maximum neutron production rate of 4 × 1015 s−1 . (a) Neutron flux density distribution in a poloidal cross-section, (c) maximum and minimum neutron heating distribution in a slice of the central column cross-section, (b) and (d) same as (a) and (c) for the gamma flux density and heating.

Table 4 Heating power distributed over the 16 TF coils.

4. The superconducting CS

Heating power contribution

Radiative

Conductive

Neutronic

Gamma

During discharge (W) Inter discharge (W)

7 2

160 160

17 0

73 0

be kept under 250 W/W. In Globus-M [20], a spherical tokamak similar to the STNS in size and aspect ratio, a discharge can be launched every 2 to 6 min [36] depending on the wall condition. If it is assumed that the STNS would require 5 min of time interval between discharges, the duty cycle for neutron generation would reach ∼6% and the average power required for the cryogenic cooling of the entire TF system should be about ∼40 kW. If the TF coil section dedicated to the Cu/NbTi was replaced by water cooled copper, the average power loss in the central column for the 16 TF coils (according to (17)) should be around ∼100 kW.

4.1. CS main parameters and current drive The magnetic flux ˚cs in Wb generated by the CS is given by



˚cs =

 S = R2 Bcs , B.d cs

(21)

S

with Bcs , the magnetic field in the centre of the CS in T and Rcs , the average radius of the CS. In the present design of the central column (Fig. 2), the PFCs and the TF coils leave 0.132 m radius for the CS cryostat. The CS cryostat wall would be 10−3 m thick and there would be LHe at 4.2 K from 0.131 m to 0.124 m radially which means that the CS external radius cannot be larger than 0.124 m. Then, Bcs is the only parameter left to have ˚cs as high as possible to allow long discharges with a significant plasma current. The CS would be built in YBCO, a 2nd generation HTS allowing significant critical currents at high magnetic field. The YBCO tapes from SuperPower (see Table 5 for description) have begun to be used in fusion [37] and are taken as a reference for this study. They would be wound around an epoxy support (see Fig. 2) which should cope with any vertical forces with the possible help of external structures at the bottom and the top of the CS (where there is enough

Table 5 SuperPower YBCO tape section from top to bottom.

Fig. 9. COP of different LHe cooling system (blue bars) compared to the theoretical efficiency predicted by the Carnot cycle (red line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Material

Thickness

Polyimide Copper Silver YBCO Nickel substrate Copper

25 ␮m 20 ␮m 2 ␮m 1–5 ␮m 50 ␮m 20 ␮m

C. Guillemaut et al. / Fusion Engineering and Design 88 (2013) 3312–3323

3319

space) if further studies show that it is necessary. In [38], a 500 m SuperPower YBCO tape is used to build a solenoid and can tolerate, in this particular application, nearly 200 A inside a total magnetic field of 26.8 T in LHe at 4.2 K. The YBCO tape has the advantage of being already stabilized with silver and copper layers (see Table 5). The plasma current required for the reference scenario would be induced by a linear variation of the magnetic field Bcs between Bmax = 15 T and Bmin = −15 T inside the CS. This would be achieved by a linear decrease of the current in the CS tapes between Imax = 200 A and Imin = −200 A. The number of turns of YBCO tape required in the CS can be approximated by NCS ≈

Bmax Lcs . 0 Imax

(22) Fig. 10. Current density profile due to the CS from (25) along the midplane.

With the CS length Lcs = 1 m, less than 6 × 104 turns should be required. The tape section is hYBCO = 4 × 10−3 m wide, eYBCO = 1.2 × 10−4 m thick and the CS has an external radius of 0.124 m; thus, the internal radius would be 0.096 m, with Rcs = 0.11 m. Since the CS internal radius is higher than the external radius of the solenoid prototype shown in [38], the curvature should not be a problem for the YBCO tapes in the design presented here. Continuous piece lengths of more than 1000 m have been fabricated by SuperPower [38]; thus, the winding of 42 rolls would be required to build the CS of the STNS. The YBCO crystals are grown on a nickel alloy substrate to strengthen the tape and it can withstand significant tensile stress in coil applications. The integrity of the tape and its superconducting properties were not affected after 105 tensile stress cycles at 700 MPa [38]. In this case, the maximum tensile stress,  max , due to magnetic forces, can be evaluated by applying (19) with the present parameters of the problem max =

Imax Bmax Rcs , hYBCO eYBCO

(23)

and it should be less than 420 MPa; thus, no additional structures is considered for the CS. According to (21), varying Bcs between 15 T and −15 T would allow a variation of ˚cs between 0.6 Wb and −0.6 Wb which gives ˚cs ≈ −1.2 Wb. It is assumed that the plasma formation could be achieved in the STNS by merging-compression and that half of the flux would be consumed during the plasma current ramp up and FT ≈ −0.6 Wb for the current flat top, simidown (∼1 s), leaving cs larly as MAST [23]. If this variation of magnetic flux is done linearly during t ≈ 20 s, the electromotive force e in V generated in the plasma is given by e=−

FT cs . t

(24)

In this case, e = Vloop = 0.03 V during the plasma current flat top. Assuming that the plasma resistivity in the direction of the current (p in m) is the Spitzer resistivity as in [39], for an effective charge Zeff = 1, the current density profile J(r) in A m−2 along the midplane is given by J(r) =

Vloop 1 . p (r) 2(R + r)

(25)

In [37], p is essentially electron temperature (Te ) dependent; thus, the midplane Te profile corresponding to the reference scenario presented in Section 5 below has been taken to calculate the Spitzer resistivity profile p (r) and then the plasma current density profile along the midplane (see Fig. 10). The CS contribution ICS to the plasma current can be approximated by

a

ICS =

2rJ(r)dr, −a

(26)

which gives ICS ∼ 0.95 MA. Since the reference scenario requires Ip = 1.5 MA and the CS provides only ∼2/3 of it during the 20 s plasma current flat top, other contributions are needed and they would come from the current driven by the ECRH, the NBI and the bootstrap. According to Electron Cyclotron Current Drive (ECCD) experiments done on TCV [40], an efficiency of ∼0.1 MA/MW can be expected and Neutral Beam Current Drive (NBCD) experiments in DIII-D [41] demonstrated an efficiency of ∼0.03 MA/MW. Hence, the contributions IECCD and INBCD should reach respectively ∼0.4 MA and ∼0.1 MA. In [39], the bootstrap current is approximated by Ib ≈

ˇp Ip √ . 3 A

(27)

With ˇP ∼ 0.1 in the reference scenario, the bootstrap current contribution should be around Ib ∼ 0.05 MA. Thus, during the 20 s current flat top of the reference scenario, IP would be the sum of all these contributions IP = ICS + IECCD + INBCD + Ib ∼1.5 MA.

(28)

The variation of current required for such operations would raise the CS voltage VCS in V until VCS ≈

2 R2 0 NCS CS (Imax − Imin ) , LCS t

(29)

and should not exceed 3600 V with the present parameters, while the 25 ␮m thick polyimide electric insulation of the YBCO tapes withstands up to 10 kV [42]. 4.2. Cryogenic cooling of the CS As for the TF coils, the CS would also be maintained at 4.2 K with a LHe thermosiphon to keep the YBCO tapes superconducting under a maximum magnetic field of 15 T. The power leak through the electric connections, mentioned in Section 3.4 for NbTi, is constant at 1 W kA−1 at 4.2 K. Each one of the 42 rolls of YBCO tape composing the CS would have its own connection which should conduct a maximum of ∼10 W of heating to the CS cryostat. As in Section 3.4 above, the neutronic and gamma heating is also evaluated by the MCNP transport code (see Fig. 8). The composition of the CS and its cryostat is presented in Table 6. Another contribution due to the transitory regime, in current and magnetic field, inherent to the CS operation has to be accounted for. The AC losses in YBCO are widely investigated and it can be deduced from [43] that a variation of 1.3 T s−1 (15 T to −15 T in Table 6 Composition of the CS and its cryostat. Material

Fe

He

Cu

Ni

% of CS volume (36,600 cm3 )

17

31

26

26

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Table 7 Heating power in the CS. Heating power contribution

Conductive

Neutronic

Gamma

AC losses

During discharge (W) Inter discharge (W)

10 10

45 0

95 0

100 0

∼22 s of current flat top and ramps) should produce ∼100 W of heating power in the entire CS. The AC losses due to transient events like disruptions are not considered here and would require further studies. The radiative heating is negligible since the outboard side of the CS cryostat is in contact with the TF cryostat at 4.2 K and the inboard side faces an isolating vacuum (Fig. 2). The main heating contributions for the CS are summarized in Table 7. With the same power consumption for the cryogenic system and the same duty cycle as in Section 3.4, an average of 9 kW of power would be needed to liquefy the helium at the rate it is consumed in the CS. In the case of a water cooled copper CS of the same size, the average power consumption would be ∼200 kW (according to (17)). As for the TF coils, the use of superconductors for the CS should allow significant energy savings compared to the copper option. 5. Core transport modelling The parameters of the machine presented in the previous Sections (see Fig. 1) have been implemented in the ASTRA code [21], which models transport in tokamaks plasma core, to simulate the STNS plasma operations. The T-11 transport model [44] used in ASTRA, assuming anomalous transport [45] for particles and electron heat conductivity and neoclassical transport [46] for ion heat conductivity, includes also consistent convective heat loss in the heat transport equations [47]. This model was chosen because it satisfactorily predicted the core plasma parameters in different machines both in L and H-modes [47–49] including the small tight aspect ratio tokamak (START) [19] similar to the STNS in size and shape. It also described well the experiments with high convective heat loss caused by core heating from powerful NBI [50] which is expected in the STNS. The values PECRH and PNBI for the ECRH and NBI heating respectively, given in Fig. 1 correspond to the amount of power deposited in the plasma by each system. The code has been run with these parameters and the energy of the NBI has been set at 20 keV, which corresponds to the level usually used in a machine of this size [20]. The runs have been done with the following boundary conditions [47] at the separatrix: TeB = 0.1 keV, TiB = 0.2 keV and nBe = nBi = 0.3 n¯ for the electron temperature, the ion temperature and the electron and ion density respectively where n¯ is the core line averaged electron density. Since the wall material is not yet chosen, the effect of core contamination by impurities has not been studied here; thus, the effective charge has been kept at Zeff = 1 and the plasma is a 50–50% DT mix with an average atomic mass of 2.5 amu. The ASTRA results presented here correspond to steady states conditions. The plasma triangularity has been fixed at ı = 0.5, which corresponds to a demonstrated value for a spherical tokamak like START [51] and the q95 has been kept around 4.5 in all runs. The different simulation results presented in this Section have been obtained by scanning the core line averaged density from 2 × 1019 m−3 to 1.2 × 1020 m−3 in order to find the set of parameters optimizing the neutron production rate from the DT fusion reactions. The results from the simulations of plasma profiles and the predictions for the total neutron production rates are presented in Fig. 11. Transport simulations show that a maximal neutron production rate of 4 × 1015 s−1 in the STNS can be reached with DT at the line averaged density n¯ ∼5 × 1019 m−3 (Fig. 10). The latter is the reference scenario for the neutron production. The distribution of the

neutron flux obtained in this case is shown in Fig. 8 and the associated Te profile allows the current profile shown in Fig. 10 above. More generally, a wide domain of densities allows neutron production rates of the order of ∼1015 s−1 . Very similar densities and temperatures can be expected in pure deuterium plasmas with the same levels of input power and core fuelling. Since the DD reaction rate is nearly two orders of magnitude smaller than the DT reaction rate, neutron production rates of the order of ∼1013 s−1 can be expected from pure deuterium plasmas in the STNS. According to the scaling for the L–H transition power threshold for conventional tokamaks [52]: PL−H = 2.15e±0.107 n¯ 0.782±0.037 B0 0.772±0.031 a0.975±0.08 R0.999±0.101 , (30) a heating power of PL-H ∼0.3 MW should be required to switch from L to H mode in the STNS with the line average electron density n¯ = 0.5 in 1020 m−3 . Even if for tight aspect ratio tokamaks the threshold is an order of magnitude higher than the scaling predictions [52], the STNS, with 4 MW of ECRH, 4 MW of NBI heating and 1 MW of ohmic heating for the reference scenario, is expected to operate in Type-I ELMy H-mode. Most of nowadays tokamaks alternate experimental campaigns – with ∼104 s of plasma operations – and maintenance periods (∼several months). It is thus reasonable to consider that the STNS would not provide more than ∼1000 cycles in total per campaign with 20 s of discharge plus 300 s of time interval per cycle. Even with 10 DT campaigns per year, the annual fusion neutron fluence should not be higher than ∼1020 m−2 on the first wall. This would contain both the increase of the resistivity of the copper stabilizer and the decrease of the NbTi critical current to around ∼1% after 10 years of experiments [53]. With such busy schedule the tritium consumption should still be limited to a few ∼100 mg per year without taking into account the losses due to absorption in the materials, pipes, fuelling systems. . . In the case of the YBCO in the CS, according to [54], the critical current is expected to increase above the original value all along the life of the STNS. The 316 L stainless steel is the main structure material for ITER [55] and should withstand annual neutron fluences several orders of magnitude higher than in the STNS. If the disruptivity remains low (which can be expected according to [19,23]) and the TF is cycled once a day, the only limiting factor for long term operations of the STNS is the CS fatigue tensile stress limit. However, with the schedule proposed here, the CS could be operated at his limit for ∼10 years and the estimate of Section 4.1 shows that the maximum constrain in the CS should be nearly 2 times lower than the limit. 6. Measurements and demonstration To keep the TF coils as small as possible, the compartments containing the nuclear materials and, if required, the neutron moderator and multiplier (as proposed in [6]) are inserted between the TF and PF coils (see Fig. 1). However, the precise design of the nuclear materials compartments is not the topic of this article. Different techniques are available to measure the efficiency of the neutronic processes of interest (see examples in Table 1) tested in the STNS in number of event per fusion reaction. The polycrystalline chemical vapor deposited detectors used in JET [56] could also measure the neutron production rate in the STNS. The production of radio-isotopes, the transmutation of long live fission products or the fission of heavy nuclei generate different types of signature measurable with the methods explained below. The accumulation of the radio-isotopes produced by neutron capture in the nuclear materials compartments can be monitored by gamma ray spectrometry since each element of interest has a

C. Guillemaut et al. / Fusion Engineering and Design 88 (2013) 3312–3323

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Fig. 11. From right to left, top to bottom: midplane profiles for ion temperature, ion/electron density and electron temperature. The last plot shows the total neutron production rate corresponding to each scenario. The red curves and dots correspond to the reference scenario.

specific gamma emission. The population N of a given radio-isotope of half-life T1/2 (in s) is given by dN ln 2 N = D, with N = 0 at t = 0, + T1/2 dt

(31)

where is the number of radio-isotope synthesized per fusion reaction, D is the duty cycle for neutron generation (∼0.06 in the STNS)

and  is the total fusion neutron production rate in s−1 (∼1015 s−1 with DT and ∼1013 s−1 with DD). At a given time t in s, the activity AX in Bq of a population of radio-isotope X grown in the STNS is: AX (t) = D(1 − e(−t ln 2/T1/2 ) ),

(32)

and the experimental efficiency associated with the synthesis of a radio-isotope can be deduced by measuring AX .

Fig. 12. Different scenarios of evolution of the activity of some radio-isotopes (99 Mo in blue on the left and 60 Co in red on the right) in the nuclear materials compartments during STNS operations with DT. The measurement of is not possible in the grey domain. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

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For the following study, it is pessimistically assumed that AX would be diluted in ∼10 tonnes of surrounding materials, which brings the detection threshold (∼1 Bq kg−1 according to [57]) for the total activity in the nuclear materials compartments to 104 Bq. Thus, the domain of measurement of the efficiency of a given process, delimited by the grey region in Fig. 12, is constrained by the number of cycles and the detection threshold. The activity of 99 Mo (representative of most of the radioisotopes used in nuclear medicine) should already be above the detection threshold after a series of ∼20 cycles with DT even if is as low as 10−8 (Fig. 12). For a radio-isotope with lower activity like 60 Co, a series of ∼100 cycles should be required with a minimum of 10−6 (Fig. 12). With DD, these minimum values of must be two orders of magnitude higher to make possible a measurement after the same numbers of cycles. This method could also be used to monitor in real time the transmutation rate of long lived fission products through the gamma rays produced by ˇ+ /ˇ− annihilations (see Table 1). The efficiency of this process would be measurable even if it is as low as ∼ 10−11 in DT and ∼ 10−9 in DD. To demonstrate the viability of DT operations in a tokamak, the process of tritium generation must show an efficiency of > 1. As an example, if ∼ 1 event per fusion reaction, one cycle with DT would be sufficient to accumulate ∼107 Bq of tritium in total in the ∼10 tonnes of nuclear material compartments. The activity of 1 g extracted from the tritiated lithium substrate and diluted in 1 L of water for scintillation measurements should already be above the detection threshold of 1 Bq L−1 [58]. The fission reactions of uranium, plutonium or minor actinides triggered directly or indirectly by fusion neutrons should generate a significant amount of heating power. An efficiency ∼ 1 event per fusion reaction would be required for these processes to consider viable an industrial application. In this case, knowing that each fission reaction releases ∼200 MeV of energy and that the STNS neutron production rate could be up to 4 × 1015 s−1 , the generated fission power should be around ∼0.1 MW. The measurement of the elevation of temperature in the nuclear materials compartments should be sufficient to deduce the fission reaction rate with precision if it reaches viable levels. The methods proposed here for the measurement of for different neutronic processes seem to be sufficiently sensitive for the demonstration of their viability for tokamak neutron source applications. 7. Conclusions Although many simplifying assumptions have been made for the disruptions, the plasma-wall interaction, the structures outside the central column and the circulation of LHe in the superconductors, preliminary engineering estimates have been carried out in this paper for the key elements of a compact superconducting spherical tokamak, the STNS. According to this first order approach, this machine should withstand enough cycles with DT and 9 MW of heating power to demonstrate the viability of a tokamak neutron source for the following applications: (a) (b) (c) (d)

production of radio-isotopes for nuclear medicine, production of tritium for fusion research, elimination of minor actinides and long live fission products, fusion–fission hybrid concept for power generation.

According to ASTRA simulations, each DT discharge could allow a total fusion neutron production rate up to 4 × 1015 s−1 for 20 s. The small number of cycles required for most of the demonstrations (less than ∼100) would allow the testing of different materials, concepts and designs with rapid and precise results. The use of DT may

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