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Simplified methods for estimations of 3T production in boronized shielding materials and Li burn up in breeder blankets
Fusion Engineering and Design 23 (1993) 1-16 North-Holland
Simplified methods for estimations of 3T production in boronized shielding materials and Li burn up in breeder blankets Sergei Zimin Department Naka-gun,
of ITER Ibaraki-ken,
Project, Japan
Naka
Fusion
Research
Establishment,
Japan
Atomic
Energy
Research
Institute,
Naka-machi
Submitted 6 November 1992, revised version 22 January 1993; accepted 19 April 1993 Handling Editor: M. Ohta
The systems of integral equations are developed to evaluate tritium generation in boronized shields and lithium burn-up in blankets of thermonuclear reactors. These systems of integral equations are solved analytically with reasonable simplifications. By so doing, relatively simple methods to evaluate both the tritium generation in a boronized shield and the lithium depletion in blankets are developed and proposed for future work under thermonuclear reactor projects. The method obtaining ‘T production in boronized shielding materials is checked for various blanket designs of ITER CDA, namely ceramic breeder concepts and a Pb-Li breeder concept. The amount of tritium generated in the inboard boronized shielding blanket of ITER/OTR and lithium depletion in the outboard LisO-bearing blanket of ITER/FER are evaluated by the proposed methods to demonstrate practical usefulness of these evaluation procedures.
1. Introduction Neutrons originating from fusion reactions in the plasma region of thermonuclear reactors interact in the blanket and shielding regions that surround the plasma. The interactions of the neutrons in the blanket have to provide some useful functions, e.g. the deposition of the fusion neutrons kinetic energy plus the release of additional nuclear energy from exothermic reactions, the production of tritium in the 6Li and ‘Li isotopes in the lithium-bearing blankets of thermonuclear reactors, etc. However, the neutron interactions in thermonuclear reactors have also many negative side effects, e.g., radiation damage effects, induced radioactivity and radiation doses, some transmutations etc. In addition to these factors, 3T (tritium) production in the region out of the breeder blanket becomes a serious factor. An employment of boronized shields is considered in a number of projects of thermonuclear reactors, e.g. ITER CDA [l] and ITER/OTR [2]. However, if the boronized shield is to be used in thermonuclear reactor designs, 3T can be generated in the shield region [3] due to tritium production reactions in i”B and llB. The amount of 3T produced depends on both the level of boronization and the total volume of boronized shield. The production of 3T in a shield negatively affects the reactor safety by creating undesirable 3T leakages from the shield region to other reactor zones. These 3T leakages have to be taken into account during maintenance and decommissioning of shield modules. The bum-up of 6Li and ‘Li in blankets depletes lithium density and may lead to a decrease of the tritium breeding ratio (TBR) with operating time. The depletion depends on both the level of lithium enrichment and the method used to confine the breeder. Only in a few studies [4-71 has the problem of lithium depletion been addressed. Ref. [5] shows, for example, that the maximum and average 6Li depletion in Li,O-bearing blanket can reach for 1 MW a/m2 about 1% and OS%, respectively. The TBR decrease for 3 MW a/m2 is estimated to be about 1% [61. 0920-3796/93/$06.00
0 1993 - Elsevier Science Publishers B.V. All rights reserved
2
S. Zimin / Estimations of 3Tproduction
By imposing thermal-hydraulic, economic and structural-mechanic constraints, the total amount of lithium in the blanket, lithium enrichment, and the number and thickness of lithium zones can be substantially restricted and do not necessarily follow the optimized configuration determined by neutronits requirement. Numerous penetrations in a vacuum chamber decrease a total TBR as well. Thus, usually the total TBR of an experimental thermonuclear reactor ranges from 0.6 to 0.9. For instance, in ref. [8] for all blankets proposed for ITER CDA, the total TBR was estimated to be less than 0.9. Therefore, just 1% of TBR decreasing is to be considered as a serious problem for the blanket design. These processes are to be taken into account in the design of current experimental thermonuclear reactors like ITER EDA [9] whose total operating time is expected to be about 1 MW a/m*. For the next generations of a thermonuclear reactor like DEMO and future commercial thermonuclear power plants, the above-mentioned processes are expected to be much more important because of relatively large operating time, namely more than 10 and 25 MW a/m*, respectively. The present work attempts to provide simplified methods for estimations of above-mentioned nuclear processes by creating and solving analytical equations of neutron balance for each of the above-mentioned processes separately. Major nuclear reactions on both lithium and boron isotopes are surveyed for this purpose. Two main parts of this paper are dedicated to the tritium generation in l”B and “B of the boronized shield and the depletion of 6Li and ‘Li in breeder blankets. 2. Tritium
generation in boronized shields
2.1. Tritium generation in “B Utilization of boron is studied in many thermonuclear reactor projects, e.g. ITER [l], ITER/OTR [2], etc. This material is very effective for the neutron absorption. Therefore, it helps to suppress the neutron absorption in Fe (the neutron absorption in Fe is a negative nuclear process from the view point of shielding because it leads to a high energy photon flux in the shield). However, tritium can be generated in the boronized shield by the reaction: 24He. “B+n 3T + *Be The cross-section of this reaction [lo] versus neutron energy is shown in Fig. 1. In addition, 7Li is generated by the reaction: “B+n 4He+7Li+y Therefore, the reaction:
(2.1.1)
(E=0.478MeV).
(2.1.2)
7Li+n n’ +4He +3T (2.1.3) can be the additional source of 3T generation. Let p”(r, t) be the density of “B, p7(r, t) be the density of 7Li and pT(r, t) be the density of 3T. Let a,“(r, E) be the absorption cross-section of “B, c$.(r, E) be the cross-section of the (2.1.1) reaction and o&(r, E) be the cross-section of the (2.1.3) reaction. The decay of 3T is not taken into account for simplification. In that case the system of integral equations could be written for densities of “B, 7Li and 3T as follows: dp”(r,
t)/dt
= -p”(r,
r)/$‘(r,
E) *4(r,
E, t) dE,
i
I
dp7(r, t)/dt=p”(r,
(dpT(r,
t)/dt=P7(r,
r)/o,1’(r,
E) *4(r,
E, t) dE,
t)/+(r,
E) *4(r,
E, t) dE+p”(r,
(2.1.4) t)/+(r,
E)*4(r,
E> t) dE,
S. Zimin / Estimations of ‘Tproduction IO'
IO0 is g ,o-' .-s 5 " 1g2 z v IO-:
IO-;
I
0
I
10.0 Neutron Energy ( MeV1
20.0
Fig. 1. JENDL-3 cross-sections of neutron reactions in “B versus neutron energy.
where &, E, t) is the neutron flux spectrum at a position r, and a time t which contains neutron energy information. The major boron depletion is expected by the (2.1.2) reaction [3]. Therefore, in the first equation of (2.1.4) we can neglect the reaction (2.1.1). This assumption will be justified in Section 2.3 where neutron spectra in the region of interest are discussed. In the second equation of (2.1.4) we neglect the depletion of ‘Li, reaction (2.1.31, for simplification as well. Therefore, the equations for average densities after integrating (2.1.4) by the zone volume can be written as follows:
I
dp”( t)/dr = -pl’( t) *J,“(t), dp’(t)l/dt =p”(t) *J;‘(t), dp=(t)/dt
=P’@) ‘&(t>
+P”(t)
(2.1.5) ‘.$r(f),
where
V = the total volume. If the neutron flux does not depend on time (this is validated by the fact that 3T is generated mostly in ‘Li by fast neutrons, where the neutron spectrum is not changed with l”B burning down), the equations
S. Zimin
/ Estimations
of
3Tproductiotl
Fig. 2. The nuclear densities of “B, ‘Li and T versus reactor operating time without taking into account T decay.
(2.15) can be solved analytically. Let pk” be the density of “B at the moment t = 0. The solution can be written as follows: p?(t)
.I
= pA” exp( -JJ”t ),
p’(t)
=pkO(l,-
exp( -JJOf)),
p’(t)
=p~“[(J,7,T/J,‘o)(1-exp(-J,‘o~))
(2.1.6) +./i,Tt]
+p~“(l-ew(-J,‘!+)).
Figure 2 shows the densities of “B, ‘Li and 3T versus the operation time of ITER/OTR thermonuclear reactor. The equations (2.1.6) are used for obtaining these curves. The neutron flux is calculated for the inboard ITER/OTR configuration [3] with the ANISN code. After 5 full time years CITY) operation with an average neutron wall load of 1 MW/m2, the densities of “B, ‘Li and 3T are obtained as follows: pl” = 0.99pk” = 2.97 p'= 3.0
1021 cmm3,
1019 cmm3,
X
p* = 1.28
X
X
10” cme3.
Therefore, about 60 g of 3T is expected to be generated after 5 FTY in all volume of the inboard shielding blanket which consist of 98 v/o of SS/H,O and 2 v/o of B (enriched with 90% loBI. The total amount of 3T generated in “B for the same conditions is estimated to be less than 3 g as described in Section 2.2. Obviously llB plays a minor role in comparison with “B. However, in the case of natural boron (80% of llB and 20% of “B) the underestimation of 3T generation could be rather large. This problem is discussed in the next section. The main. error of the proposed simplified method, in which 3T generation has been estimated for both l”B and “B isotopes, is expected to be connected with the neglection of the 3T decay. For instance, neglecting 3T decay for 3 MW a/m2 and 5 MW a/m2 operation times can lead to more than 10% and 15% decrease of 3T, respectively. Therefore, the error depends on the operation time. For an experimental thermonuclear reactor like ITER whose operation time is expected to be 1 MW a/m2, the total error of the proposed method is expected to be less than 5%. On the contrary, in the case of
S. Zirnin
/
Eslimations
of 3Tproduction
5
Neutron Energy ( MeV1 Fig. 3. JENDL-3 cross-sections of neutron reactions in “B versus neutron energy.
DEMO reactors whose operation time is expected to be more that 10 MW a/m2, a correction connected with 3T decay will have to be made. 2.2. Tritium generation in “B The (n, T) and (n, n’T) reactions are possible in “B as well [lO,ll] (see Fig. 3). However, the cross sections of these reactions in the 14-MeV energy region are less than the cross section of the (2.2.1) reaction (n, T2a) in i”B by about 4 and 50 times, respectively. On the other hand, the thresholds of these reactions are closed to 11 MeV and 13 MeV, respectively. However, the threshold of (n, T2a) reaction in l”B is less than 1 MeV. Thus, the (n, l’2a) reaction in l”B will play a main role in the generation of 3T in the boronized shield, if B is enriched with “B. As it is mentioned above, the utilization of an enriched boron is studied in many thermonuclear reactor projects, e.g. ITER and ITER/OTR. Therefore, the (n, T) and (n, n’T) reactions is ilB are not considered in Section 2.1 for simplification. The underestimation of 3T generation in the extreme case of natural boron (80% of “B and 20% of “B) is expected to be less than 20-30%. In the case of 50% and 90% enrichment, the underestimation of tritium production is expected to be 8-16% and 4-8%, respectively. However, if necessary, the tritium generation in “B can be evaluated separately. Let pll(r, t) and pT(r, t) be the densities of “B and 3T, respectively. If we do not take into account for simplification of the decay of 3T, the equations could be written for densities of “B and 3T as follows: dp”(r,
t)/dt=
-+(c
t)/[a,‘,\(r,
E) +q&q+,
E)]4(r,
E, c) dE, (2.2.1)
L where +(r, E, t) is the neutron flux spectrum at position r, and time t which contains the neutron energy information, and a,‘;r(r, E) and c$.&&, El are the (n, T) and (n, n’T) reactions in llB, respectively.
S. Zimin / Estimations of ‘Tprodtccliorl
6
The equations for average densities after integrating (2.2.1) by the energy and zone volume can be written as follows: dp”( t)/dt
= -pll(
t) $‘(t),
dpT(t)/dt
=p”(t)
*J+‘(t),
(2.2.2)
where J+‘(t) = &dEj--dl’.
[ u,,‘,‘,‘,(r, E) -t o-&~(
r, E)] * +( r, E, t).
However the depletion of “B is not necessary to be evaluated because this process is negligibly small and, correspondingly, does not influence the 3T generation. If the neutron flux does not depend on time, the equation for the 3T generation from (2.2.2) can be solved analytically. Let ph’ be the density of llB at the moment t = 0. The solution can be written as follows: p’(r)
(2.2.3)
=&[l-exp(-J+‘t)].
Thus the final formula for tritium evaluation can be written by combining (2.1.6) and (2.2.3) as follows: pT(f)=p~o{(J,7,T/J,‘o)‘[1-exp(-~~ot)]
+Jn7,Tt}+P~o[1-exp(-J,‘P,t)]
+&[l-em(-.f+‘t)]. (2.2.4)
The total amount of 3T generated in ‘rB after 5 FTY in all the volume of the inboard shielding blanket which consists of 98 v/o of SS/H,O and 2 v/o of B (enriched with 90% “B) is estimated to be less than 3 g, in comparison with 60 g generated in l”B (see Section 2.1). Obviously “B plays a minor role in comparison with “B. However, in the case of natural boron (80 v/o of llB and 20 v/o of “B) the role of llB can not be neglected. 2.3. Concerning neutron spectrum infzuence The neutron spectrum is highly dependent on the system configuration of concern and has to be taken into account if a proposed simplified method is going to be used. The method is proposed to be used for boronized shielding materials only. The neutron spectrum in the shielding zone behind a breeding blanket is expected to be well softened and sensitive only to an employed breeding blanket type because the contents of the shielding materials are expected to vary insignificantly design by design [S]. Figure 4 shows the material composition to be placed behind the breeding blanket, namely the semipermanent
ZONE I
2 3
Rcdius, cm 215 230 232
4
5
272
6
297
7
322
392
Fig. 4. One-dimensional calculational model of the build-up of an experimental thermonuclear reactor. &planation of zoner: (1) plasma (14-MeV neutron source, (2) scrape-off layer, (3) first wall, (4) blanket, (5) semipermanent shield, (6) vacuum vessel, (7) TF magnets;(1,2) void, (3,5,6) 70% SS and 30% water, (7) 50% SS and 50% Cu.
S. Zimin lo~5
of 3Tproduction
/ Estimations
7
NEUTRON AN0 GAMMA RAY FLUX
lo+=i$--J
“g?zg , , , I 100
150
DISTANCE
Fig. 5. Variations
200
250
300
350
400
FROM THE PLASMA AXIS (CM)
in the neutron and gamma fluxes along the radius of the geometrical model (shown in Fig. 4) with ceramic breeder blanket (zone 4 in Fig. 4) with Be multiplier (60% Be, 15% SS, 10% H,O and 15% Li,O).
shield and vacuum vessel. The contents and design of above zones are usually determined by shielding requirements and thermal-hydraulic constraints, respectively. Therefore, usually the semipermanent shield and vacuum vessel consist of well heterogeneous zones of steel and water. These zones can be modelled well by a homogeneous mixture of about 70% SS and 30% water. Further, a wide circle of possible driver blankets for the ITER design has been narrowed to four designs, namely three designs of a ceramic breeder concept with Be multiplier (the layered configuration, the pebble bed design, and the breeder in-tube configuration) and one design of a Pb-Li breeder concept (the water-cooled blanket with the Li,,Pb,, breeding material) [8]. The content of the above-mentioned three blanket options with a ceramic breeder and Be multiplier is changed design by design insignificantly [8] and could be considered from the shielding point of view as a homogeneous mixture of about 60% Be, 15% SS, 10% H,O and 15% Liz0 (or Li,ZrO,). Variations in the neutron and gamma fluxes along the radius of geometrical model (shown in Fig. 4) with the ceramic breeder (60% Be, 15% SS, 10% Hz0 and 15% Liz01 and the Pb-Li breeder (65% Li,,Pb,,, 15% H,O and 20% SS> blankets are shown in Figs. 5 and 6, respectively. The neutron spectra behind the above-mentioned ceramic breeder blanket and Pb-Li blankets (see Fig. 4, R = 272 cm) are shown in Figs. 7 and 8, respectively. The neutron spectra at the first wall (see Fig. 4, R = 230 cm>, behind the semipermanent shield (see Fig. 4, R = 297 cm> and behind the vacuum vessel (see Fig. 4, R = 322 cm) are shown in Figs. 7 and 8 as well. According to Figs. 7 and 8, the neutron spectra behind both considered blanket types are well soften and the difference between above spectra is rather small. Therefore, the proposed simplified method can be applied to both blanket types. 2.4. Tritium generation in structural materials
There are many reactions to produce 3T by neutron reactions with structural materials, such as Mn, Ni, MO, V, Zr etc. However, all above-mentioned elements can produce 3T only by a (n, T> threshold
S. Zimin
/ Estimations
of -‘Tproduction
-TOTAL N. GAMMARAY
IO4’
, bl
I
100
150
200
DISTANCE
250
300
350
FROM THE PLASMA
AXlS
400 (CM)
Fig. 6. Variations in the neutron and gamma fluxes along the radius of the geometrical model (shown in Fig. 4) with Pb-Li breeder blanket (zone 4 in Fig. 4) with Pb multiplier (6.5% Li,,Pb,, 15% Hz0 and 20% SS).
type reaction. Further, the threshold of above reactions is usually more or barely less than 14.1 MeV [lo]. On the contrary, the threshold of the (n, T2a) reaction in r”B of the (2.1.1) reaction is less than 0.5 MeV. Curves of neutron cross-sections for some main components of SS316, namely Mn, Ni and MO, widely used as the construction material of an experimental thermonuclear reactor, are shown in ref. [lo]. It is ,o~5,
NEfJTRPN FNEYGY kPE$TRt
,
,
y
,
-R=230CM -bR=272CM -R=297CM
lo-310-*lo-‘loo
IO’ IO2 103 IO4 IO’ IO6 IO’ loa NEUTRON
ENERGY (eV1
Fig. 7. Neutron spectra at different distances from the plasma axis of the calculational model of Fig. 4 with a homogeneous model of ceramic breeder blanket with Be multiplier (60% Be, 15% SS, 10% Ha0 and 15% Li,O).
S. Zimin
of
/ Estimations
3Tproduction
9
NEUTRON ENERGY SPECiRA
r IO81 ’ r*b 10-310-210-'100
’ ’ ’ ’ ’ ’ ’ ’
IO' IO2 IO3 IO4 IO5 IO6 IO7 IOB
NEUTRON
ENERGY (eV)
Fig. 8. Neutron spectraat different distancesfrom the plasmaaxisof the calculationalmodel of Fig. 4 with a homogeneousmodel of Pb-Li breederblanket with Pb multiplier (65% Li,,Pb=, 20% SSand 15%H20).
worth to underline that the Fe, main component of SS316, has the (n, T) reaction in 54Fe (6% in natural Fe) and 56Fe (92% in natural Fe) isotopes as well [12]. However, the cross-sections for the 54Fe(n, T) [Q = - 12.42 MeV] and 56Fe(n, T) [Q = - 11.92 MeV] reactions are relatively small, namely about 10 pb and 30 pb, respectively, according to the data library of REAC-ECN [12]. Among other main components of SS316 only 61Ni (1.25% in natural Nil, “Mn (100% in natural Mn) and “MO (15.7% in natural MO) have a threshold of (n, T) reaction barely less than 14.1 MeV. Curves of neutron cross-sections for those isotopes are shown in ref. [lo]. Therefore, 3T could be produced in SS316 by four reactions: S6Fe + n “Mn + n 61Ni + n g5Mo + n -
54Mn+T 53Cr+T
(E= (E=
-11.92MeV), -12MeV),
5gCo+T g3Nb+T
(E= -14.05 MeV), (EG -14.08 MeV).
(2.4.1) (2.4.2) (2.4.3) (2.4.4)
However, the cross-sections of the reactions (2.4.1)-(2.4.4) are one to two order of magnitude less than that associated with llB, namely 3.0 X 10 -’ barns, 9.2 x 10s4 barns, 9.0 X lob5 barns and 8.5 x 10m5 barns, respectively. The volume fractions of “Mn, ‘j’Ni and “MO in SS316 are small as well, namely about 2%, 0.1% and 0.2%, respectively [13]. Macro cross-sections of the (n, t) reaction, such as the (n, 2cu) reaction in the case of iOB, for 14-MeV neutrons are calculated for “B, rlB, 56Fe, “Mn, 61Ni and “MO, namely 5.46 x lo-’ cm-‘, 3.27 x 10e5 cm-‘, 2.2 x lo-’ cm-‘, 1.82 X 10m6 cm- ‘, 1.23 X lo-’ cm-’ and 1.97 X 10s8 cm-‘, respectively. Therefore, it is expected that 3T production in Fe, Mn, Ni and MO in boronized SS316 will be negligibly small in comparison with the 3T production in boron isotopes. In the case of non-boronized steel, the 3T production for 3 MW a/m* operation time of an experimental thermonuclear reactor like ITER is estimated to be less than 0.2 g throughout the whole volume of its shielding blanket.
S. Zimin
/ Estimations
of 3Tproduction
.O Neutron Energy (MeV 1 Fig. 9. JENDLJ
3. Lithium
cross-sections of neutron reactions in 6Li versus neutron energy.
burn-up in blankets
3.1. Survey of main nuclear reactions in lithium isotopes
Numerous nuclear reactions in lithium are possible in lithium-bearing reactors [lO,lll. The main reactions can be written as follows:
blankets of thermonuclear
6Li+n
d
‘Li + y,
(3.1.1)
6Li+n
-
3T +4He,
(3.1.2)
6Li+n
-
4Hefp+2n,
(3.1.3)
6Li+n
-
6He+p,
(3.1.4)
6Li+n
-
4He +*D + n’,
(3.1.5)
7Li+n
-
‘Li
(3.1.6)
‘Li+n
-
4He +3T + n’,
(3.1.7)
‘Li+n
-
6He +*D,
(3.1.8)
7Li+n
-
4He +*D + 2n,
(3.1.9)
7Li+n
-
6Li + 2n.
-
24He+-y,
Cross-sections of some above-mentioned 10. 3.2. Analytical
(3.1.10) reactions versus a neutron energy are shown in Figs. 9 and
consideration
Let a&, and a&, be the sum of the cross-sections of the nuclear reactions (3.1.2)-(3.1.5) and (3.1.6)-(3.1.9), respectively. If u&,) and u:,~,,) are the cross-sections of (3.1.1) and (3.1.10) nuclear
11
S. Zimin / Estimations of ‘Tproduction
‘;; lo-’ E x .z lo-2 i m 1 22 - 1o-3
I
I
i
_s--------me_ ,/ t’
I I
-I
’O-L.0
,
i
I 2
10.0
.O
Neutron Energy (MeV 1 Fig. 10. JENDL-3 cross-sections of neutron reactions in ‘Li versus neutron energy.
reactions, respectively, and c#I(~,E, t) the neutron flux spectrum at position r and time t which includes the neutron energy information, the equations for the densities of 6Li and ‘Li could be written as follows:
dt-+(r, t)/dt=P’(c #&,, dp’(r,
t)/dt
=#(r,
(r, E) .4(r,
E, t) dE -#(r,
(r, E) -c$(r, E, t) dE -p’(r,
f)/qf,,u)
t)j&&(r, t)/c&(r,
E) -4(r, E) .4(r,
E, t) dE, E, t) dE.
(3.2.1) According to ref. [ll], the cross-section of the (3.1.1) reaction for fast and average energy neutrons is negligibly small in comparison with the sum of the cross-sections of the reactions (3.1.6)~(3.1.9). Thus it seems to be possible to simplify (3.2.1) as follows:
(r, E)*Hr, E,t>dE-#(r, t>/q&,(r,E)*di(r,E,f) dE, d#(r, Wdt =p’(c t>/qi,~,~ dp’(r,
t)/dt=
-p’(r,
t)/q&(r,
E) *4(r,
E, t) dE.
(3.2.2) The equations for the average densities after integrating (3.2.2) by energy and volume can be written as follows: d#(t)/dt
=P’@) *J&,)(t)
dp’( t)/dt
= --p’(t)
*J&< t>,
-P%)
%&)Y
(3.2.3)
S. Zimin / Estimations of ‘Tprodrtction
12
where
If the neutron flux does not depend on time, the equations (3.2.3) can be solved analytically as follows:
(3.2.4)
where pz and pi are the densities of 6Li and ‘Li at the moment r = 0, respectively. However, if it is taken into account that the cross-section of nuclear reaction (3.1.10) is at least by one order of magnitude less than the sum of the cross-sections of the nuclear reactions (3.1.2)-(3.151, the equation for 6Li density from (3.2.4) can be simplified as follows: &r>
=P: em( -J&r).
(3.2.5)
Further for thermal and average energy, namely less than 0.1 MeV, neutrons the cross-section of the (3.1.2) reaction is expected to be dominant in comparison with cross-sections of the (3.1.3)-(3.15) and the (3.1.10) reactions. Thus, if we neglect, for more simplification, the (3.1.3)-(3.15) and the (3.1.10) nuclear reactions in comparison with the (3.1.2) reaction, equation (3.2.5) can be written as follows: bW> =d
exp( -J&T+)r
(3.2.6)
where J&)(r)
=/fdE/d~-$,,n(r, E) -4(r, E, r). ” It should be underlined again that above simplification could be valid for lithium zones in blankets where neutron spectrum is determined by thermal and average energy neutrons. Such a spectrum is expected to appear in most blanket concepts because of desire of blanket designer to use the advantage of the (3.1.2) reaction for lithium production (the cross-section of this reaction follows to the well-known law u - l/u). Equation (3.2.6) is used for rough estimation of 6Li depletion in the Japanese option of Li,O-bearing ITER blanket with Be multiplier (see Figs. 11 and 12). More information on the blanket design can be found in ref. [14]. The estimated average lithium depletion for the first lithium layer at the outboard midplane is found to be - 4% per 1.2 MW a/m*. More detail analysis of lithium depletion is carried out in ref. [14]. According to ref. [14], the maximum and minimum depletions are found to be 6.6% and 2.9% at the surface and near the center of the first breeder layer, respectively. Both the results of rough estimation of 6Li depletion by the proposed formula (3.2.6) and results obtained in ref. [14] are shown in Fig. 13. However the TBR changes negligibly small because of using lithium enriched with ‘jLi by 50%. It should be underlined that formula (3.2.6) is proposed for a simple evaluation of lithium burn-up in the blanket of SSTR thermonuclear reactor in ref. [7] as well. The burn-up rate of 6Li in ref. [7] is found
S. Zimin / Estimations of ‘Tproduction
-1: IggTJ
Stainless Steel : Be
FI
: Cooling Panel
II
: Water
m:Li20 * All dimensions are shown in mm. Fig. 11. Calculational model of Japanese outboard blanket (midplane) proposed for the ITER project. Blanket Coolant Manif
Fig. 12. Schematic view of layered pebble bed blanket proposed for ITER by Japan.
13
S. Zimin
/ Estimations
of 3Tproduction
Position in Breeder Zone , cm [See Fig. I I , first Lip0 layer behind the first wall 1 Fig. 13. 6Li burn-up profile in the first Liz0 layer at the outboard midplane of the layered pebble bed blanket proposed for ITER by Japan.
from calculation to be about 4% per 1 MW a/m*. These results are in consistence both with the above presented estimation and more detailed calculations in ref. [14] for the Japanese pebble bed blanket with Be multiplier. The TBR decreasing for 5 MW a/m* operating time of SSTR is evaluated to be about 2% [71.
4. Conclusion The analytical result by the system integral equations developed to evaluate boron generation in the boronized shield of thermonuclear reactors shows the importance of this phenomena for relatively long terms of reactor operation, namely for more than 2-3 MW a/m* operating time. If a boronized shielding driver blanket is to be designed for an ITER-like project of thermonuclear reactor only for the inboard zone, the total amount of tritium in this shielding blanket after 3 MW a/m* of operation is expected to be about 60 g. In the case of implementation of the boronized driver blanket for both inboard and outboard reactor zones, the total amount of tritium generated in the blanket is expected to be even more, namely 100-200 g. Thus this phenomena should be taken into account for the safety, maintenance and decommissioning analyses of both experimental and DEMO thermonuclear reactors. The proposed method of tritium evaluation can be easily used for this purpose. There are also many reactions to produce 3T by neutron reactions with other major structural materials, such as Fe, Mn, Ni, MO, V, Zr, etc. The comparative analysis carried out in this study for components of non-boronized SS316 shows that Mn will play a main role in 3T production. However, in the case of boronized steel, the 3T production in Mn is estimated to be negligibly small. The total amount of 3T to be produced in the constructional material of an experimental thermonuclear reactor like ITER CDA for 3 MW a/m* operation time is estimated to be less than 0.2 g. However, for DEMO thermonuclear reactors, whose operation time is expected to be lo-20 MW a/m*, the above phenomena has to be seriously considered. The system of integral equations is obtained for the process of lithium depletion (burn-up) in blankets as well. This system of integral equations is solved analytically with reasonable simplifications. The analysis of a Li,O-bearing blanket (enriched with 50% of ‘jLi) with Be multiplier proposed by Japan [14]
S. Zimin / Estimations of ‘Tproduction
15
Breeder ConfiguratIon : BOCT (pebble) MultIplier Thlcknerr : 5cm In front Of
m .s .t 1.04I= 3 1.02 J ““0
20I 40 Lithium-6
60I 80I 100 Enrichment 1%)
Fig. 14. Effect of 6Li enrichment on the Tritium Breeding Ratio of ceramic breeder blanket with beryllium multiplier ref. [15]).
(taken from
for ITER shows a small depletion rate per year for 6Li and a negligibly small one for ‘Li. However, if natural lithium is to be used in the blanket, the 6Li depletion could decrease TBR by some percents just after 2-3 MW a/m* operation time. Therefore the main conclusion can be drawn from this consideration about the necessity for today’s generation of experimental thermonuclear reactors of lithium enrichment with ‘jLi at least up to 20-30%. The necessity of Li enrichment with ‘Li has been discussed in numerous studies, e.g. in Japan [U-17], etc. For instance, the quantitative evaluation of TBR for various Li enrichments with (jLi for the ceramic breeder blanket developed in Japan for Fusion Power Reactor (BOCT concept) is shown in Fig. 14. This understanding is taken into consideration in many state-of-art blanket concepts, e.g. lithium enriched with 50% of ‘jLi has been used in the above-mentioned layered pebble bed blanket proposed for ITER EDA by Japan [14]. For DEMO reactors whose operation time is expected to be more than 10 MW a/m*, the necessity of lithium enrichment with 6Li seems to be important even more.
Acknowledgements
The author gratefully acknowledges the helpful discussions with Professor M. Nakazawa and Dr. G. Shatalov on part 2 of this study. The author also wishes to thank Dr. Y. Seki for advices, discussions and encouragement. Attention to this study and support from Drs. S. Mori, K. Maki, H. Takatsu, and S. Matsuda is acknowledgemented as well. This work was supported by the Japan Atomic Energy Research Institute.
References [l] ITER Conceptual Design Report, IAEA, ITER-DS-No. 18, Vienna (1991). [2] V.V. Orlov, The design of an experimental thermonuclear reactor, VANT, Thermonuclear Fusion 2 (1988) 3-5 (in Russian). [3] S. Zimin, A study on radiation shielding analysis for toroidal field coils of a tokamak type fusion reactor, PhD, University of Tokyo, Japan (1992). [4] INTOR International Tokamak Reactor, Phase One, IAEA, Vienna, p. 469-473 (1982).
16
S. Zimin
/ Estimations
of 3Tproduction
[5] Y. Seki, Gas production rates in lithium oxide of fusion reactor blanket, J. of Nucl. Sci. and Technol. 12, NO. 12 (1975) 769-722. [6] T. Kobayashi et al., Japanese contributions to IAEA INTOR Workshop, Phase Two A, Part 3, Chapter VIII: Blanket and first wall, JAERI-M 87-219 (1988). [7] Concept study of the Steady State Tokamak Reactor (SSTR), JAERI-M 91-081 (1991) p. 247-249. [8] D. Smith et al., ITER blanket, shield and material data base, IAEA, ITER-DS No. 29, Vienna (1991). [9] ITER EDA agreement signed, Fusion Canada, Bulletin of the National Fusion Program, Issue 18 (August 1992). [lo] T. Nakagawa, T. Asami and T. Yoshida, Curves and tables of neutron cross sections - Japanese Evaluated Nuclear Data Library, Version 3, JAERI-M 90-099 (1990). [ll] D.I. Garber and R.R. Kinsey, Neutron cross sections, Volume II, Curves, Information Analysis Center Report, National Neutron Cross Section Center Brookhaven National Laboratory Upton, New York 111973 (1976). [12] H. Gruppelaar et al., The REAC-ECN3 data library with neutron activation and transmutation cross-sections for use in fusion reactor technology, Report ECN-207 (ECN, Petten, 1988). [13] Y. Seki et al., Low activation steels for contact operation after cooling period of 30 years and 120 years, Proceedings of the Workshop on Low Activation Materials, Culham Laboratory, UK, April 8-12, 1991. [14] H. Takatsu et al., Layered pebble bed concept for ITER breeding blanket, 17th SOFT, Roma, Sep. 14-18, 1992. [15] T. Tone et al., Technical evaluation of major candidate blanket systems for fusion power reactor, JAERI-M 87-017. [la] K. Maki and T. Okazaki, Effect of blanket structure on tritium breeding ratio in fusion reactors, Nucl. Technol./Fusion 4 (Nov. 1983) 468-478. [17] K. Maki, Increase of tritium breeding ratio by blankets having front breeder zone in fusion reactors, Fusion Technol. 8 (Nov. 1985) 2655-2664.
Simplified methods for estimations of 3T production in boronized shielding materials and Li burn up in breeder blankets Sergei Zimin Department Naka-gun,
of ITER Ibaraki-ken,
Project, Japan
Naka
Fusion
Research
Establishment,
Japan
Atomic
Energy
Research
Institute,
Naka-machi
Submitted 6 November 1992, revised version 22 January 1993; accepted 19 April 1993 Handling Editor: M. Ohta
The systems of integral equations are developed to evaluate tritium generation in boronized shields and lithium burn-up in blankets of thermonuclear reactors. These systems of integral equations are solved analytically with reasonable simplifications. By so doing, relatively simple methods to evaluate both the tritium generation in a boronized shield and the lithium depletion in blankets are developed and proposed for future work under thermonuclear reactor projects. The method obtaining ‘T production in boronized shielding materials is checked for various blanket designs of ITER CDA, namely ceramic breeder concepts and a Pb-Li breeder concept. The amount of tritium generated in the inboard boronized shielding blanket of ITER/OTR and lithium depletion in the outboard LisO-bearing blanket of ITER/FER are evaluated by the proposed methods to demonstrate practical usefulness of these evaluation procedures.
1. Introduction Neutrons originating from fusion reactions in the plasma region of thermonuclear reactors interact in the blanket and shielding regions that surround the plasma. The interactions of the neutrons in the blanket have to provide some useful functions, e.g. the deposition of the fusion neutrons kinetic energy plus the release of additional nuclear energy from exothermic reactions, the production of tritium in the 6Li and ‘Li isotopes in the lithium-bearing blankets of thermonuclear reactors, etc. However, the neutron interactions in thermonuclear reactors have also many negative side effects, e.g., radiation damage effects, induced radioactivity and radiation doses, some transmutations etc. In addition to these factors, 3T (tritium) production in the region out of the breeder blanket becomes a serious factor. An employment of boronized shields is considered in a number of projects of thermonuclear reactors, e.g. ITER CDA [l] and ITER/OTR [2]. However, if the boronized shield is to be used in thermonuclear reactor designs, 3T can be generated in the shield region [3] due to tritium production reactions in i”B and llB. The amount of 3T produced depends on both the level of boronization and the total volume of boronized shield. The production of 3T in a shield negatively affects the reactor safety by creating undesirable 3T leakages from the shield region to other reactor zones. These 3T leakages have to be taken into account during maintenance and decommissioning of shield modules. The bum-up of 6Li and ‘Li in blankets depletes lithium density and may lead to a decrease of the tritium breeding ratio (TBR) with operating time. The depletion depends on both the level of lithium enrichment and the method used to confine the breeder. Only in a few studies [4-71 has the problem of lithium depletion been addressed. Ref. [5] shows, for example, that the maximum and average 6Li depletion in Li,O-bearing blanket can reach for 1 MW a/m2 about 1% and OS%, respectively. The TBR decrease for 3 MW a/m2 is estimated to be about 1% [61. 0920-3796/93/$06.00
0 1993 - Elsevier Science Publishers B.V. All rights reserved
2
S. Zimin / Estimations of 3Tproduction
By imposing thermal-hydraulic, economic and structural-mechanic constraints, the total amount of lithium in the blanket, lithium enrichment, and the number and thickness of lithium zones can be substantially restricted and do not necessarily follow the optimized configuration determined by neutronits requirement. Numerous penetrations in a vacuum chamber decrease a total TBR as well. Thus, usually the total TBR of an experimental thermonuclear reactor ranges from 0.6 to 0.9. For instance, in ref. [8] for all blankets proposed for ITER CDA, the total TBR was estimated to be less than 0.9. Therefore, just 1% of TBR decreasing is to be considered as a serious problem for the blanket design. These processes are to be taken into account in the design of current experimental thermonuclear reactors like ITER EDA [9] whose total operating time is expected to be about 1 MW a/m*. For the next generations of a thermonuclear reactor like DEMO and future commercial thermonuclear power plants, the above-mentioned processes are expected to be much more important because of relatively large operating time, namely more than 10 and 25 MW a/m*, respectively. The present work attempts to provide simplified methods for estimations of above-mentioned nuclear processes by creating and solving analytical equations of neutron balance for each of the above-mentioned processes separately. Major nuclear reactions on both lithium and boron isotopes are surveyed for this purpose. Two main parts of this paper are dedicated to the tritium generation in l”B and “B of the boronized shield and the depletion of 6Li and ‘Li in breeder blankets. 2. Tritium
generation in boronized shields
2.1. Tritium generation in “B Utilization of boron is studied in many thermonuclear reactor projects, e.g. ITER [l], ITER/OTR [2], etc. This material is very effective for the neutron absorption. Therefore, it helps to suppress the neutron absorption in Fe (the neutron absorption in Fe is a negative nuclear process from the view point of shielding because it leads to a high energy photon flux in the shield). However, tritium can be generated in the boronized shield by the reaction: 24He. “B+n 3T + *Be The cross-section of this reaction [lo] versus neutron energy is shown in Fig. 1. In addition, 7Li is generated by the reaction: “B+n 4He+7Li+y Therefore, the reaction:
(2.1.1)
(E=0.478MeV).
(2.1.2)
7Li+n n’ +4He +3T (2.1.3) can be the additional source of 3T generation. Let p”(r, t) be the density of “B, p7(r, t) be the density of 7Li and pT(r, t) be the density of 3T. Let a,“(r, E) be the absorption cross-section of “B, c$.(r, E) be the cross-section of the (2.1.1) reaction and o&(r, E) be the cross-section of the (2.1.3) reaction. The decay of 3T is not taken into account for simplification. In that case the system of integral equations could be written for densities of “B, 7Li and 3T as follows: dp”(r,
t)/dt
= -p”(r,
r)/$‘(r,
E) *4(r,
E, t) dE,
i
I
dp7(r, t)/dt=p”(r,
(dpT(r,
t)/dt=P7(r,
r)/o,1’(r,
E) *4(r,
E, t) dE,
t)/+(r,
E) *4(r,
E, t) dE+p”(r,
(2.1.4) t)/+(r,
E)*4(r,
E> t) dE,
S. Zimin / Estimations of ‘Tproduction IO'
IO0 is g ,o-' .-s 5 " 1g2 z v IO-:
IO-;
I
0
I
10.0 Neutron Energy ( MeV1
20.0
Fig. 1. JENDL-3 cross-sections of neutron reactions in “B versus neutron energy.
where &, E, t) is the neutron flux spectrum at a position r, and a time t which contains neutron energy information. The major boron depletion is expected by the (2.1.2) reaction [3]. Therefore, in the first equation of (2.1.4) we can neglect the reaction (2.1.1). This assumption will be justified in Section 2.3 where neutron spectra in the region of interest are discussed. In the second equation of (2.1.4) we neglect the depletion of ‘Li, reaction (2.1.31, for simplification as well. Therefore, the equations for average densities after integrating (2.1.4) by the zone volume can be written as follows:
I
dp”( t)/dr = -pl’( t) *J,“(t), dp’(t)l/dt =p”(t) *J;‘(t), dp=(t)/dt
=P’@) ‘&(t>
+P”(t)
(2.1.5) ‘.$r(f),
where
V = the total volume. If the neutron flux does not depend on time (this is validated by the fact that 3T is generated mostly in ‘Li by fast neutrons, where the neutron spectrum is not changed with l”B burning down), the equations
S. Zimin
/ Estimations
of
3Tproductiotl
Fig. 2. The nuclear densities of “B, ‘Li and T versus reactor operating time without taking into account T decay.
(2.15) can be solved analytically. Let pk” be the density of “B at the moment t = 0. The solution can be written as follows: p?(t)
.I
= pA” exp( -JJ”t ),
p’(t)
=pkO(l,-
exp( -JJOf)),
p’(t)
=p~“[(J,7,T/J,‘o)(1-exp(-J,‘o~))
(2.1.6) +./i,Tt]
+p~“(l-ew(-J,‘!+)).
Figure 2 shows the densities of “B, ‘Li and 3T versus the operation time of ITER/OTR thermonuclear reactor. The equations (2.1.6) are used for obtaining these curves. The neutron flux is calculated for the inboard ITER/OTR configuration [3] with the ANISN code. After 5 full time years CITY) operation with an average neutron wall load of 1 MW/m2, the densities of “B, ‘Li and 3T are obtained as follows: pl” = 0.99pk” = 2.97 p'= 3.0
1021 cmm3,
1019 cmm3,
X
p* = 1.28
X
X
10” cme3.
Therefore, about 60 g of 3T is expected to be generated after 5 FTY in all volume of the inboard shielding blanket which consist of 98 v/o of SS/H,O and 2 v/o of B (enriched with 90% loBI. The total amount of 3T generated in “B for the same conditions is estimated to be less than 3 g as described in Section 2.2. Obviously llB plays a minor role in comparison with “B. However, in the case of natural boron (80% of llB and 20% of “B) the underestimation of 3T generation could be rather large. This problem is discussed in the next section. The main. error of the proposed simplified method, in which 3T generation has been estimated for both l”B and “B isotopes, is expected to be connected with the neglection of the 3T decay. For instance, neglecting 3T decay for 3 MW a/m2 and 5 MW a/m2 operation times can lead to more than 10% and 15% decrease of 3T, respectively. Therefore, the error depends on the operation time. For an experimental thermonuclear reactor like ITER whose operation time is expected to be 1 MW a/m2, the total error of the proposed method is expected to be less than 5%. On the contrary, in the case of
S. Zirnin
/
Eslimations
of 3Tproduction
5
Neutron Energy ( MeV1 Fig. 3. JENDL-3 cross-sections of neutron reactions in “B versus neutron energy.
DEMO reactors whose operation time is expected to be more that 10 MW a/m2, a correction connected with 3T decay will have to be made. 2.2. Tritium generation in “B The (n, T) and (n, n’T) reactions are possible in “B as well [lO,ll] (see Fig. 3). However, the cross sections of these reactions in the 14-MeV energy region are less than the cross section of the (2.2.1) reaction (n, T2a) in i”B by about 4 and 50 times, respectively. On the other hand, the thresholds of these reactions are closed to 11 MeV and 13 MeV, respectively. However, the threshold of (n, T2a) reaction in l”B is less than 1 MeV. Thus, the (n, l’2a) reaction in l”B will play a main role in the generation of 3T in the boronized shield, if B is enriched with “B. As it is mentioned above, the utilization of an enriched boron is studied in many thermonuclear reactor projects, e.g. ITER and ITER/OTR. Therefore, the (n, T) and (n, n’T) reactions is ilB are not considered in Section 2.1 for simplification. The underestimation of 3T generation in the extreme case of natural boron (80% of “B and 20% of “B) is expected to be less than 20-30%. In the case of 50% and 90% enrichment, the underestimation of tritium production is expected to be 8-16% and 4-8%, respectively. However, if necessary, the tritium generation in “B can be evaluated separately. Let pll(r, t) and pT(r, t) be the densities of “B and 3T, respectively. If we do not take into account for simplification of the decay of 3T, the equations could be written for densities of “B and 3T as follows: dp”(r,
t)/dt=
-+(c
t)/[a,‘,\(r,
E) +q&q+,
E)]4(r,
E, c) dE, (2.2.1)
L where +(r, E, t) is the neutron flux spectrum at position r, and time t which contains the neutron energy information, and a,‘;r(r, E) and c$.&&, El are the (n, T) and (n, n’T) reactions in llB, respectively.
S. Zimin / Estimations of ‘Tprodtccliorl
6
The equations for average densities after integrating (2.2.1) by the energy and zone volume can be written as follows: dp”( t)/dt
= -pll(
t) $‘(t),
dpT(t)/dt
=p”(t)
*J+‘(t),
(2.2.2)
where J+‘(t) = &dEj--dl’.
[ u,,‘,‘,‘,(r, E) -t o-&~(
r, E)] * +( r, E, t).
However the depletion of “B is not necessary to be evaluated because this process is negligibly small and, correspondingly, does not influence the 3T generation. If the neutron flux does not depend on time, the equation for the 3T generation from (2.2.2) can be solved analytically. Let ph’ be the density of llB at the moment t = 0. The solution can be written as follows: p’(r)
(2.2.3)
=&[l-exp(-J+‘t)].
Thus the final formula for tritium evaluation can be written by combining (2.1.6) and (2.2.3) as follows: pT(f)=p~o{(J,7,T/J,‘o)‘[1-exp(-~~ot)]
+Jn7,Tt}+P~o[1-exp(-J,‘P,t)]
+&[l-em(-.f+‘t)]. (2.2.4)
The total amount of 3T generated in ‘rB after 5 FTY in all the volume of the inboard shielding blanket which consists of 98 v/o of SS/H,O and 2 v/o of B (enriched with 90% “B) is estimated to be less than 3 g, in comparison with 60 g generated in l”B (see Section 2.1). Obviously “B plays a minor role in comparison with “B. However, in the case of natural boron (80 v/o of llB and 20 v/o of “B) the role of llB can not be neglected. 2.3. Concerning neutron spectrum infzuence The neutron spectrum is highly dependent on the system configuration of concern and has to be taken into account if a proposed simplified method is going to be used. The method is proposed to be used for boronized shielding materials only. The neutron spectrum in the shielding zone behind a breeding blanket is expected to be well softened and sensitive only to an employed breeding blanket type because the contents of the shielding materials are expected to vary insignificantly design by design [S]. Figure 4 shows the material composition to be placed behind the breeding blanket, namely the semipermanent
ZONE I
2 3
Rcdius, cm 215 230 232
4
5
272
6
297
7
322
392
Fig. 4. One-dimensional calculational model of the build-up of an experimental thermonuclear reactor. &planation of zoner: (1) plasma (14-MeV neutron source, (2) scrape-off layer, (3) first wall, (4) blanket, (5) semipermanent shield, (6) vacuum vessel, (7) TF magnets;(1,2) void, (3,5,6) 70% SS and 30% water, (7) 50% SS and 50% Cu.
S. Zimin lo~5
of 3Tproduction
/ Estimations
7
NEUTRON AN0 GAMMA RAY FLUX
lo+=i$--J
“g?zg , , , I 100
150
DISTANCE
Fig. 5. Variations
200
250
300
350
400
FROM THE PLASMA AXIS (CM)
in the neutron and gamma fluxes along the radius of the geometrical model (shown in Fig. 4) with ceramic breeder blanket (zone 4 in Fig. 4) with Be multiplier (60% Be, 15% SS, 10% H,O and 15% Li,O).
shield and vacuum vessel. The contents and design of above zones are usually determined by shielding requirements and thermal-hydraulic constraints, respectively. Therefore, usually the semipermanent shield and vacuum vessel consist of well heterogeneous zones of steel and water. These zones can be modelled well by a homogeneous mixture of about 70% SS and 30% water. Further, a wide circle of possible driver blankets for the ITER design has been narrowed to four designs, namely three designs of a ceramic breeder concept with Be multiplier (the layered configuration, the pebble bed design, and the breeder in-tube configuration) and one design of a Pb-Li breeder concept (the water-cooled blanket with the Li,,Pb,, breeding material) [8]. The content of the above-mentioned three blanket options with a ceramic breeder and Be multiplier is changed design by design insignificantly [8] and could be considered from the shielding point of view as a homogeneous mixture of about 60% Be, 15% SS, 10% H,O and 15% Liz0 (or Li,ZrO,). Variations in the neutron and gamma fluxes along the radius of geometrical model (shown in Fig. 4) with the ceramic breeder (60% Be, 15% SS, 10% Hz0 and 15% Liz01 and the Pb-Li breeder (65% Li,,Pb,,, 15% H,O and 20% SS> blankets are shown in Figs. 5 and 6, respectively. The neutron spectra behind the above-mentioned ceramic breeder blanket and Pb-Li blankets (see Fig. 4, R = 272 cm) are shown in Figs. 7 and 8, respectively. The neutron spectra at the first wall (see Fig. 4, R = 230 cm>, behind the semipermanent shield (see Fig. 4, R = 297 cm> and behind the vacuum vessel (see Fig. 4, R = 322 cm) are shown in Figs. 7 and 8 as well. According to Figs. 7 and 8, the neutron spectra behind both considered blanket types are well soften and the difference between above spectra is rather small. Therefore, the proposed simplified method can be applied to both blanket types. 2.4. Tritium generation in structural materials
There are many reactions to produce 3T by neutron reactions with structural materials, such as Mn, Ni, MO, V, Zr etc. However, all above-mentioned elements can produce 3T only by a (n, T> threshold
S. Zimin
/ Estimations
of -‘Tproduction
-TOTAL N. GAMMARAY
IO4’
, bl
I
100
150
200
DISTANCE
250
300
350
FROM THE PLASMA
AXlS
400 (CM)
Fig. 6. Variations in the neutron and gamma fluxes along the radius of the geometrical model (shown in Fig. 4) with Pb-Li breeder blanket (zone 4 in Fig. 4) with Pb multiplier (6.5% Li,,Pb,, 15% Hz0 and 20% SS).
type reaction. Further, the threshold of above reactions is usually more or barely less than 14.1 MeV [lo]. On the contrary, the threshold of the (n, T2a) reaction in r”B of the (2.1.1) reaction is less than 0.5 MeV. Curves of neutron cross-sections for some main components of SS316, namely Mn, Ni and MO, widely used as the construction material of an experimental thermonuclear reactor, are shown in ref. [lo]. It is ,o~5,
NEfJTRPN FNEYGY kPE$TRt
,
,
y
,
-R=230CM -bR=272CM -R=297CM
lo-310-*lo-‘loo
IO’ IO2 103 IO4 IO’ IO6 IO’ loa NEUTRON
ENERGY (eV1
Fig. 7. Neutron spectra at different distances from the plasma axis of the calculational model of Fig. 4 with a homogeneous model of ceramic breeder blanket with Be multiplier (60% Be, 15% SS, 10% Ha0 and 15% Li,O).
S. Zimin
of
/ Estimations
3Tproduction
9
NEUTRON ENERGY SPECiRA
r IO81 ’ r*b 10-310-210-'100
’ ’ ’ ’ ’ ’ ’ ’
IO' IO2 IO3 IO4 IO5 IO6 IO7 IOB
NEUTRON
ENERGY (eV)
Fig. 8. Neutron spectraat different distancesfrom the plasmaaxisof the calculationalmodel of Fig. 4 with a homogeneousmodel of Pb-Li breederblanket with Pb multiplier (65% Li,,Pb=, 20% SSand 15%H20).
worth to underline that the Fe, main component of SS316, has the (n, T) reaction in 54Fe (6% in natural Fe) and 56Fe (92% in natural Fe) isotopes as well [12]. However, the cross-sections for the 54Fe(n, T) [Q = - 12.42 MeV] and 56Fe(n, T) [Q = - 11.92 MeV] reactions are relatively small, namely about 10 pb and 30 pb, respectively, according to the data library of REAC-ECN [12]. Among other main components of SS316 only 61Ni (1.25% in natural Nil, “Mn (100% in natural Mn) and “MO (15.7% in natural MO) have a threshold of (n, T) reaction barely less than 14.1 MeV. Curves of neutron cross-sections for those isotopes are shown in ref. [lo]. Therefore, 3T could be produced in SS316 by four reactions: S6Fe + n “Mn + n 61Ni + n g5Mo + n -
54Mn+T 53Cr+T
(E= (E=
-11.92MeV), -12MeV),
5gCo+T g3Nb+T
(E= -14.05 MeV), (EG -14.08 MeV).
(2.4.1) (2.4.2) (2.4.3) (2.4.4)
However, the cross-sections of the reactions (2.4.1)-(2.4.4) are one to two order of magnitude less than that associated with llB, namely 3.0 X 10 -’ barns, 9.2 x 10s4 barns, 9.0 X lob5 barns and 8.5 x 10m5 barns, respectively. The volume fractions of “Mn, ‘j’Ni and “MO in SS316 are small as well, namely about 2%, 0.1% and 0.2%, respectively [13]. Macro cross-sections of the (n, t) reaction, such as the (n, 2cu) reaction in the case of iOB, for 14-MeV neutrons are calculated for “B, rlB, 56Fe, “Mn, 61Ni and “MO, namely 5.46 x lo-’ cm-‘, 3.27 x 10e5 cm-‘, 2.2 x lo-’ cm-‘, 1.82 X 10m6 cm- ‘, 1.23 X lo-’ cm-’ and 1.97 X 10s8 cm-‘, respectively. Therefore, it is expected that 3T production in Fe, Mn, Ni and MO in boronized SS316 will be negligibly small in comparison with the 3T production in boron isotopes. In the case of non-boronized steel, the 3T production for 3 MW a/m* operation time of an experimental thermonuclear reactor like ITER is estimated to be less than 0.2 g throughout the whole volume of its shielding blanket.
S. Zimin
/ Estimations
of 3Tproduction
.O Neutron Energy (MeV 1 Fig. 9. JENDLJ
3. Lithium
cross-sections of neutron reactions in 6Li versus neutron energy.
burn-up in blankets
3.1. Survey of main nuclear reactions in lithium isotopes
Numerous nuclear reactions in lithium are possible in lithium-bearing reactors [lO,lll. The main reactions can be written as follows:
blankets of thermonuclear
6Li+n
d
‘Li + y,
(3.1.1)
6Li+n
-
3T +4He,
(3.1.2)
6Li+n
-
4Hefp+2n,
(3.1.3)
6Li+n
-
6He+p,
(3.1.4)
6Li+n
-
4He +*D + n’,
(3.1.5)
7Li+n
-
‘Li
(3.1.6)
‘Li+n
-
4He +3T + n’,
(3.1.7)
‘Li+n
-
6He +*D,
(3.1.8)
7Li+n
-
4He +*D + 2n,
(3.1.9)
7Li+n
-
6Li + 2n.
-
24He+-y,
Cross-sections of some above-mentioned 10. 3.2. Analytical
(3.1.10) reactions versus a neutron energy are shown in Figs. 9 and
consideration
Let a&, and a&, be the sum of the cross-sections of the nuclear reactions (3.1.2)-(3.1.5) and (3.1.6)-(3.1.9), respectively. If u&,) and u:,~,,) are the cross-sections of (3.1.1) and (3.1.10) nuclear
11
S. Zimin / Estimations of ‘Tproduction
‘;; lo-’ E x .z lo-2 i m 1 22 - 1o-3
I
I
i
_s--------me_ ,/ t’
I I
-I
’O-L.0
,
i
I 2
10.0
.O
Neutron Energy (MeV 1 Fig. 10. JENDL-3 cross-sections of neutron reactions in ‘Li versus neutron energy.
reactions, respectively, and c#I(~,E, t) the neutron flux spectrum at position r and time t which includes the neutron energy information, the equations for the densities of 6Li and ‘Li could be written as follows:
dt-+(r, t)/dt=P’(c #&,, dp’(r,
t)/dt
=#(r,
(r, E) .4(r,
E, t) dE -#(r,
(r, E) -c$(r, E, t) dE -p’(r,
f)/qf,,u)
t)j&&(r, t)/c&(r,
E) -4(r, E) .4(r,
E, t) dE, E, t) dE.
(3.2.1) According to ref. [ll], the cross-section of the (3.1.1) reaction for fast and average energy neutrons is negligibly small in comparison with the sum of the cross-sections of the reactions (3.1.6)~(3.1.9). Thus it seems to be possible to simplify (3.2.1) as follows:
(r, E)*Hr, E,t>dE-#(r, t>/q&,(r,E)*di(r,E,f) dE, d#(r, Wdt =p’(c t>/qi,~,~ dp’(r,
t)/dt=
-p’(r,
t)/q&(r,
E) *4(r,
E, t) dE.
(3.2.2) The equations for the average densities after integrating (3.2.2) by energy and volume can be written as follows: d#(t)/dt
=P’@) *J&,)(t)
dp’( t)/dt
= --p’(t)
*J&< t>,
-P%)
%&)Y
(3.2.3)
S. Zimin / Estimations of ‘Tprodrtction
12
where
If the neutron flux does not depend on time, the equations (3.2.3) can be solved analytically as follows:
(3.2.4)
where pz and pi are the densities of 6Li and ‘Li at the moment r = 0, respectively. However, if it is taken into account that the cross-section of nuclear reaction (3.1.10) is at least by one order of magnitude less than the sum of the cross-sections of the nuclear reactions (3.1.2)-(3.151, the equation for 6Li density from (3.2.4) can be simplified as follows: &r>
=P: em( -J&r).
(3.2.5)
Further for thermal and average energy, namely less than 0.1 MeV, neutrons the cross-section of the (3.1.2) reaction is expected to be dominant in comparison with cross-sections of the (3.1.3)-(3.15) and the (3.1.10) reactions. Thus, if we neglect, for more simplification, the (3.1.3)-(3.15) and the (3.1.10) nuclear reactions in comparison with the (3.1.2) reaction, equation (3.2.5) can be written as follows: bW> =d
exp( -J&T+)r
(3.2.6)
where J&)(r)
=/fdE/d~-$,,n(r, E) -4(r, E, r). ” It should be underlined again that above simplification could be valid for lithium zones in blankets where neutron spectrum is determined by thermal and average energy neutrons. Such a spectrum is expected to appear in most blanket concepts because of desire of blanket designer to use the advantage of the (3.1.2) reaction for lithium production (the cross-section of this reaction follows to the well-known law u - l/u). Equation (3.2.6) is used for rough estimation of 6Li depletion in the Japanese option of Li,O-bearing ITER blanket with Be multiplier (see Figs. 11 and 12). More information on the blanket design can be found in ref. [14]. The estimated average lithium depletion for the first lithium layer at the outboard midplane is found to be - 4% per 1.2 MW a/m*. More detail analysis of lithium depletion is carried out in ref. [14]. According to ref. [14], the maximum and minimum depletions are found to be 6.6% and 2.9% at the surface and near the center of the first breeder layer, respectively. Both the results of rough estimation of 6Li depletion by the proposed formula (3.2.6) and results obtained in ref. [14] are shown in Fig. 13. However the TBR changes negligibly small because of using lithium enriched with ‘jLi by 50%. It should be underlined that formula (3.2.6) is proposed for a simple evaluation of lithium burn-up in the blanket of SSTR thermonuclear reactor in ref. [7] as well. The burn-up rate of 6Li in ref. [7] is found
S. Zimin / Estimations of ‘Tproduction
-1: IggTJ
Stainless Steel : Be
FI
: Cooling Panel
II
: Water
m:Li20 * All dimensions are shown in mm. Fig. 11. Calculational model of Japanese outboard blanket (midplane) proposed for the ITER project. Blanket Coolant Manif
Fig. 12. Schematic view of layered pebble bed blanket proposed for ITER by Japan.
13
S. Zimin
/ Estimations
of 3Tproduction
Position in Breeder Zone , cm [See Fig. I I , first Lip0 layer behind the first wall 1 Fig. 13. 6Li burn-up profile in the first Liz0 layer at the outboard midplane of the layered pebble bed blanket proposed for ITER by Japan.
from calculation to be about 4% per 1 MW a/m*. These results are in consistence both with the above presented estimation and more detailed calculations in ref. [14] for the Japanese pebble bed blanket with Be multiplier. The TBR decreasing for 5 MW a/m* operating time of SSTR is evaluated to be about 2% [71.
4. Conclusion The analytical result by the system integral equations developed to evaluate boron generation in the boronized shield of thermonuclear reactors shows the importance of this phenomena for relatively long terms of reactor operation, namely for more than 2-3 MW a/m* operating time. If a boronized shielding driver blanket is to be designed for an ITER-like project of thermonuclear reactor only for the inboard zone, the total amount of tritium in this shielding blanket after 3 MW a/m* of operation is expected to be about 60 g. In the case of implementation of the boronized driver blanket for both inboard and outboard reactor zones, the total amount of tritium generated in the blanket is expected to be even more, namely 100-200 g. Thus this phenomena should be taken into account for the safety, maintenance and decommissioning analyses of both experimental and DEMO thermonuclear reactors. The proposed method of tritium evaluation can be easily used for this purpose. There are also many reactions to produce 3T by neutron reactions with other major structural materials, such as Fe, Mn, Ni, MO, V, Zr, etc. The comparative analysis carried out in this study for components of non-boronized SS316 shows that Mn will play a main role in 3T production. However, in the case of boronized steel, the 3T production in Mn is estimated to be negligibly small. The total amount of 3T to be produced in the constructional material of an experimental thermonuclear reactor like ITER CDA for 3 MW a/m* operation time is estimated to be less than 0.2 g. However, for DEMO thermonuclear reactors, whose operation time is expected to be lo-20 MW a/m*, the above phenomena has to be seriously considered. The system of integral equations is obtained for the process of lithium depletion (burn-up) in blankets as well. This system of integral equations is solved analytically with reasonable simplifications. The analysis of a Li,O-bearing blanket (enriched with 50% of ‘jLi) with Be multiplier proposed by Japan [14]
S. Zimin / Estimations of ‘Tproduction
15
Breeder ConfiguratIon : BOCT (pebble) MultIplier Thlcknerr : 5cm In front Of
m .s .t 1.04I= 3 1.02 J ““0
20I 40 Lithium-6
60I 80I 100 Enrichment 1%)
Fig. 14. Effect of 6Li enrichment on the Tritium Breeding Ratio of ceramic breeder blanket with beryllium multiplier ref. [15]).
(taken from
for ITER shows a small depletion rate per year for 6Li and a negligibly small one for ‘Li. However, if natural lithium is to be used in the blanket, the 6Li depletion could decrease TBR by some percents just after 2-3 MW a/m* operation time. Therefore the main conclusion can be drawn from this consideration about the necessity for today’s generation of experimental thermonuclear reactors of lithium enrichment with ‘jLi at least up to 20-30%. The necessity of Li enrichment with ‘Li has been discussed in numerous studies, e.g. in Japan [U-17], etc. For instance, the quantitative evaluation of TBR for various Li enrichments with (jLi for the ceramic breeder blanket developed in Japan for Fusion Power Reactor (BOCT concept) is shown in Fig. 14. This understanding is taken into consideration in many state-of-art blanket concepts, e.g. lithium enriched with 50% of ‘jLi has been used in the above-mentioned layered pebble bed blanket proposed for ITER EDA by Japan [14]. For DEMO reactors whose operation time is expected to be more than 10 MW a/m*, the necessity of lithium enrichment with 6Li seems to be important even more.
Acknowledgements
The author gratefully acknowledges the helpful discussions with Professor M. Nakazawa and Dr. G. Shatalov on part 2 of this study. The author also wishes to thank Dr. Y. Seki for advices, discussions and encouragement. Attention to this study and support from Drs. S. Mori, K. Maki, H. Takatsu, and S. Matsuda is acknowledgemented as well. This work was supported by the Japan Atomic Energy Research Institute.
References [l] ITER Conceptual Design Report, IAEA, ITER-DS-No. 18, Vienna (1991). [2] V.V. Orlov, The design of an experimental thermonuclear reactor, VANT, Thermonuclear Fusion 2 (1988) 3-5 (in Russian). [3] S. Zimin, A study on radiation shielding analysis for toroidal field coils of a tokamak type fusion reactor, PhD, University of Tokyo, Japan (1992). [4] INTOR International Tokamak Reactor, Phase One, IAEA, Vienna, p. 469-473 (1982).
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[5] Y. Seki, Gas production rates in lithium oxide of fusion reactor blanket, J. of Nucl. Sci. and Technol. 12, NO. 12 (1975) 769-722. [6] T. Kobayashi et al., Japanese contributions to IAEA INTOR Workshop, Phase Two A, Part 3, Chapter VIII: Blanket and first wall, JAERI-M 87-219 (1988). [7] Concept study of the Steady State Tokamak Reactor (SSTR), JAERI-M 91-081 (1991) p. 247-249. [8] D. Smith et al., ITER blanket, shield and material data base, IAEA, ITER-DS No. 29, Vienna (1991). [9] ITER EDA agreement signed, Fusion Canada, Bulletin of the National Fusion Program, Issue 18 (August 1992). [lo] T. Nakagawa, T. Asami and T. Yoshida, Curves and tables of neutron cross sections - Japanese Evaluated Nuclear Data Library, Version 3, JAERI-M 90-099 (1990). [ll] D.I. Garber and R.R. Kinsey, Neutron cross sections, Volume II, Curves, Information Analysis Center Report, National Neutron Cross Section Center Brookhaven National Laboratory Upton, New York 111973 (1976). [12] H. Gruppelaar et al., The REAC-ECN3 data library with neutron activation and transmutation cross-sections for use in fusion reactor technology, Report ECN-207 (ECN, Petten, 1988). [13] Y. Seki et al., Low activation steels for contact operation after cooling period of 30 years and 120 years, Proceedings of the Workshop on Low Activation Materials, Culham Laboratory, UK, April 8-12, 1991. [14] H. Takatsu et al., Layered pebble bed concept for ITER breeding blanket, 17th SOFT, Roma, Sep. 14-18, 1992. [15] T. Tone et al., Technical evaluation of major candidate blanket systems for fusion power reactor, JAERI-M 87-017. [la] K. Maki and T. Okazaki, Effect of blanket structure on tritium breeding ratio in fusion reactors, Nucl. Technol./Fusion 4 (Nov. 1983) 468-478. [17] K. Maki, Increase of tritium breeding ratio by blankets having front breeder zone in fusion reactors, Fusion Technol. 8 (Nov. 1985) 2655-2664.