Tritium

Contact: D. McMorrow - dmcmorrow@mitre.org

November 2011
JSR-11-345
Approved for public release; distribution unlimited.

JASON
The MITRE Corporation
7515 Colshire Drive
McLean, Virginia 22102-7508(703) 983-6997

Contents
1 INTRODUCTION

1

2 STATEMENT OF WORK

3

3 BRIEF ANSWERS TO SPECIFIC QUESTIONS

5

4 CONSTRAINTS OF BASIC PHYSICS
7
4.1 Neutronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.2 Tritium Burnup Fraction . . . . . . . . . . . . . . . . . . . . . 10
4.3 Tritium Inventory . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.4 Tritium Breeding Ratio . . . . . . . . . . . . . . . . . . . . . . 14
5 ADDITIONAL ISSUES
5.1 Deuterium-Rich Fueling . . . . . . . . . . . . . . . . . . . . .
5.2 Lithium and Lead-Lithium Blanket . . . . . . . . . . . . . . .
5.3 More Tritium is Better . . . . . . . . . . . . . . . . . . . . . .
5.4 Tritium Handling and Leakage . . . . . . . . . . . . . . . . . .
5.5 6 Li, Tritium and 3 He Economics . . . . . . . . . . . . . . . . .
5.6 Quantification of Margins and Uncertainties . . . . . . . . . .
5.7 Tritium Breeding Issues for ICF . . . . . . . . . . . . . . . . .
5.8 Sources of Tritium . . . . . . . . . . . . . . . . . . . . . . . .

iii

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Tritium

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13119022
Contact: D. McMorrow@dmcmorrow@mitre.org

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Approved for public release; unlimited distribution
13. SUPPLEMENTARY NOTES
14. ABSTRACT

Tritium breeding is an essential component of potential future GWE sources of electrical energy based on
nuclear fusion. Such reactors require kg quantities of tritium per year of operation which must be bred aspart of the overall reactor cycle. Traditionally, tritium is assumed to be bred from neutrons involved infusion energy-production processes of the particular type of reactor using a lithium (Li) “blanket” orrelated alloys such as the Pb-17Li eutectic. As such, tritium breeding is intimately connected with energy
production, thermal management, radioactivity management, materials properties, and mechanicalstructures of any plausible future large-scale fusion power reactor. JASON is asked to examine the current
state of scientific knowledge and engineering practice on the physical and chemical bases for large-scaletritium breeding.
15. SUBJECT TERMS
16. SECURITY CLASSIFICATION OF:

a. REPORT

Unclassified

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Unclassified

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OF ABSTRACT

19a. NAME OF RESPONSIBLE PERSON

Mr. Ed Synakowski
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301-903-8584

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1

INTRODUCTION
The first generation of controlled fusion devices are being designed toliberate heat from the fusion of a deuteron D and a triton T to form an alphaparticle, α, and a neutron, n, in the strongly exothermic nuclear reaction
D + T → α + n + Q,

(1)

The energy release per reaction is
Q = 17.6 MeV.

(2)

Using the energy release Q of (1) and neglecting the additional heating
due to neutron capture, which can add several MeV per reaction, we find thatto produce an average fusion (thermal) power PF would require a tritum massconsumption rate ofṀ1 = 56PF kg y−1 GWT−1 .

(3)

Here one Gigawatt thermal power has been abbreviated as GWT. A few tensof percent of this fusion (thermal) power can be converted into electrical
power, for example, in steam or gas turbines.
Radioactive tritium spontaneously decays to 3 He, an electron e− andan electron antineutrino ν̃e with a half life of 12.3 years in the process ofbeta-decay
T →3 He + e− + ν̄e + 18.6 keV.

(4)

The stable isotope 3 He, produced when tritium decays, has many uses already, for example, in neutron detectors, in 3 He-4He dilution refrigeratators to produce millikelvin temperatures, and in magnetic-resonance imaging.
Naturally occurring 3 He is so rare that virtually all of the current demandfor 3 He is met with gas collected from the radioactive decay of tritium, either manufactured for use in nuclear weapons by the United States and the1Russian Federation or recovered from the heavy-water of Candu fission reactors. A fusion economy would provide a substantial new resource of 3 He,
and would encourage new applications.
Unlike the stable isotope deuterium, which makes up 156 ppm of hydrogen on earth, tritium has a relatively short “shelf life” because of theradioactive decay (4), so tritium is most efficiently used within a few years
after its manufacture. The ITER experiment will make use of the 20 kg of Tthat has been accumulated from Candu reactors. A single, 1 GW(E) fusion
power plant, at 30% conversion efficiency from thermal to electrical energy,
would use 20 kg of tritium in less than two months.
With these facts in mind, the United States Department of Energy asked
JASON to respond to the following charge during the JASON Summer Studyof 2011:2

2

STATEMENT OF WORKThe MITRE Corporation will contract with DOE with funding supplied

through the United States Army (CECOM) to provide the necessary personnel, services, and facilities to support JASON until 31 January 2012. All
activities and deliverables called for in this paragraph shall be provided inaccordance with the schedule in paragraphs 5.1. Study funding will support
the annual integrated program across multiple agencies. All products will beshared subject to classification requirements.

Large-Quantity Tritium Production: Tritium breeding is an essential
component of potential future GWE sources of electrical energy based on
nuclear fusion. Such reactors require kg quantities of tritium per year ofoperation which must be bred as part of the overall reactor cycle. Traditionally, tritium is assumed to be bred from neutrons involved in fusionenergy-production processes of the particular type of reactor using a lithium(Li) “blanket” or related alloys such as the Pb-17Li eutectic. As such, tritium breeding is intimately connected with energy production, thermal management, radioactivity management, materials properties, and mechanicalstructures of any plausible future large-scale fusion power reactor. JASON
is asked to examine the current state of scientific knowledge and engineering
practice on the physical and chemical bases for large-scale tritium breeding.
In particular, JASON’s report should address the following questions andprovide answers with supporting analysis:

Specific questions:
1. How realistic are 1GWE-scale tritium breeding blankets from today’s
perspective?

32. What are the most important development issues from today’s perspective?
3. Do tritium breeding considerations favor certain classes of fusion reactors over other possible choices?

4

3

BRIEF ANSWERS TO SPECIFIC QUESTIONS
Brief answers to the specific questions are given here. Reasons for theseanswers will be outlined in the remainder of the report.

1. How realistic are 1GWE-scale tritium breeding blankets fromtoday’s perspective?
Blankets are in the advanced conceptual design stage. Some detailed
modeling and experimental tests have been done. This work shows thatin principle it is possible for a well-designed reactor to breed enough tritium to replace what it burns, to make up for losses in reprocessing, andto produce enough surplus every few years to fuel a new reactor. Many
important engineering issues need to be solved, for example, possible
corrosion of the pipes by circulating blanket material like molten Li or
PbLi metals, extraction and purification of tritium from the blanket,
tritium leakage, etc.
2. What are the most important development issues from today’s
perspective?
Since the detailed fate of 14 MeV neutrons from the fusion reaction(1) must be precisely known to predict tritium breeding, a sufficiently
accurate data base of neutron cross sections must be certified. In assembling this data base, we recommend using methods similar to thoseused in the stockpile stewardship program, “Quantification of Measurements and Uncertainties.” Cross sections deemed to be of insufficientaccuracy should be measured more carefully. Additional experiments
should be done to more accurately quantify the difference between predictions of the tritium-breeding codes and experimental measurements.
Requirements for tritium-breeding should be one of the key tradeoffs
5in reactor design. For example, maximizing the burnup fraction fb (aplasma-physics issue) and minimizing the reprocessing time tp of unburnt tritium (a chemical-engineering issue) are essential to minimize
both the required tritium inventory and the required tritium breeding
ratios.
3. Do tritium breeding considerations favor certain classes of fusion reactors over other possible choices?
Blankets of magnetic confinement fusion (MCF) reactors are constrainedin space by magnetic field coils, conduits for initial plasma heating
power, divertor placement, etc. Many of these elements also containneutron-absorbing structural materials. Inertial confinement fusion(ICF) designs, which are less mature than those of MCF, also have constraints, for example, paths for target injection and for driver beams
like lasers or heavy ions, the need for walls capable of withstanding
the periodic impulsive loads from exploding pellets, and openings toallow rapid clearing of the chamber debris after each pellet implosion.
All of these factors limit the fraction of neutrons that can participate
in breeding. At the present level of understanding, blanket design appears somewhat less constrained for ICF than for MCF machines. For
both MCF and ICF, adequate tritium breeding is feasible, and issues
other than tritium breeding are likely to be much more important inassessing relative advantages of MCF and ICF.

6

4

CONSTRAINTS OF BASIC PHYSICS
The feasibility of tritium breeding depends on both basic physics andengineering issues. In the two-body reaction (1), about 4/5 of the 17.6 MeV
energy release, or 14.1 MeV is carried by the neutron and 1/5 or 3.5 MeV
is carried by the alpha particle, which heats the magnetically or inertiallyconfined plasma. Most of the neutrons are absorbed in a breeding blanket,
where they produce more than one triton per neutron to make up for neutrons
that escape through gaps in blanket coverage or are absorbed by structural
material, to make up for losses in the tritium handling system, and to provide
excess tritium for new reactors. The tritium breeding ratio (TBR),
TBR =tritium bred
tritium burnt(5)

is defined as the average number of tritium atoms bred per tritium atom
burnt in the reaction (1). We must have TBR > 1, for a self-sustained fusion
economy.

Blankets with Pure Lithium. With proper design, it is possible to obtain TBR > 1 in lithium-containing blankets with some combination of thereactionsn +6 Li → T + α + 4.8 MeV,
n +7 Li + 2.5 MeV → T + α + n0.

(6)
(7)

The product neutron n0 of (7) has a smaller energy than the incident neutron
n. The per cent atomic abundances of naturally occurring Li are6

Li 7.5%;

and

7

Li 92.5%.

(8)

The exothermic reaction (6) has a very large cross section, 940 b, for neutrons
with a velocity of 2200 m/s [1]. The cross section scales very accurately as
7

1/v for energies up to about 60 keV. Consequently, with careful selectionof structural materials and geometry to minimize the loss of neutrons byabsorption or escape from the blanket, nearly all of the neutrons that slow
down to thermal energies from their initial 14.1 MeV can be absorbed by
6

Li and can generate tritium. The reaction (6) also makes a substantial

contribution to the thermal power output of the fusion reactor since theenergy release per reaction, 4.8 MeV, is 27% of the 17.6 MeV energy releaseof the primary fusion reaction (1).
The cross section of the second, endothermic reaction, (7) is heavily
suppressed because of the Coulomb barrier for charged product particles atenergies just above the 2.5 MeV threshold, but it has a cross section of order
0.3 b for neutrons with energies above 5 MeV. It can be readily driven by
the 14 MeV neutrons from the primary fusion reaction (1), and it allows asingle neutron to make two or more tritons. For example a 14 MeV neutron
can break up a 7 Li into a T and an α according to (7). If the slower, productneutron, n0 , happens to retain more than 2.5 MeV after breaking up a 7 Li
nucleus, it can break up a second 7 Li and release another T before falling
below the energy threshold for the reaction (7), when it can still be captured
on 6Li, in accordance with the reaction (6), to form a final T.

Blanket with neutron multipliers. A second way to get relatively large
tritium breeding ratios is to include neutron mutipliers, notably beryllium(Be) and lead (Pb), in lithium blankets. The most promising neutron multiplication reactions are
n +9 Be + 3 MeV → 2α + n0 + n00,

(9)

n + Pb + 10 MeV → Pb + n0 + n00.

(10)

One of the product neutrons n0 from the low-threshold, (n,2n) reaction (9)may occasionally retain enough kinetic energy to drive another cycle of thereaction (9) or (7), but in most cases the product neutrons will be be below
8Figure 1: Cross sections for the reactions (6), (7), (8) and (10). Other
important cross sections include elastic and inelastic scattering cross sections
for Li, Be and Pb, needed to model the slowing down (moderation) of the 14
MeV primary neutrons, and neutron absorption cross sections for structural
materials (Figure from M. Sawan).
thereshold and can make tritium only through capture on 6 Li in accordancewith (6). Therefore, when using the (n,2n) reactions of (9) and (10), one
can almost always increase the TBR by using lithium that has been enrichedin the isotope 6 Li. The energy-dependence of cross sections for the mostimportant reactions for tritium breeding are shown in Figure 1.

4.1

Neutronics

As discussed above, under ideal circumstances it is possible to produce
nearly two tritons for every 14 MeV neutron. In pure lithium of natural
isotopic composition this would give an ideal tritium breeding ratio, TBR
9≈ 2. But many practical engineering issues will limit the TBR to smaller
values. With sufficiently reliable values for the cross sections of key reactions
like (6), (7), (9), (10), etc., and with numerical methods that fully account for
the heterogeneous geometry and structural materials of the reactor, it should
be possible to calculate values of the TBR that will be within a per cent of
those that are observed. Analogous calculations for fission reactors predictthe multiplication factor and its dependence on control rod positions andother reactor parameters to a small fraction of a per cent. However, many
decades of work have gone into perfecting neutronic computational methods
for fission reactors and in “tuning” the codes by comparing their predictions
with observations. Analogous codes for tritium breeding have had less time
for perfection and less measured data to use for tuning.
Much progress is being made on tritium-breeding neutronics, notably
by University of Wisconsin Professors Mohammed Sawan, Laila El -Guebaly
and their collaborators in Madison, and by University of California Professor
Mohammed Abdou and his collaborators in Los Angeles. Work in this area
should be continued to identify any neutronics issues that differ substantiallyfrom those of fission reactors. Since tritium breeding depends critically on reactions with much faster neutrons than those normally encountered in fission
reactors, key fast-neutron cross sections of breeding and structural materials
need to be evaluated with particular care.

4.2

Tritium Burnup Fraction

The probability that a triton injected into a reactor is burned in thereaction (1) before it escapes the confinement region in the case of MFE, orbefore the capsule disassembles in the case if ICF, is called the tritium burnup
fraction, fb . Unburned tritium is collected and used again as fuel. As we will
discuss in more detail below, fb should be as close to unity as possible to10minimize the required inventory of tritium and to reduce the required valuesof the tritium breeding ratio.
Let the number densities of tritons and deuterons in the plasma be [T]and [D] respectively. The reaction (1) will cause [T] and [D] to decrease atequal rates

d[T]
d[D]
=
= −[T][D]hvσi.
dt
dt

(11)

where hvσi is the product of the velocity-dependent cross section σ for thereaction (1) and the relative velocity v of the colliding pairs, averaged over a
Maxwellian distribution of velocities at an ion temperature Ti , assumed to be
the same for D and T. The rate coefficient, in m3 s−1 , for ion temperatures
Ti in keV can be well approximated by [2]hvσi =

3.68 × 10−18
2/3

Ti

exp −

19.94
1/3

Ti

!

.

(12)

For a representative MFE ion temperature
Ti = 20 keV,

(13)

hvσi = 3.22 × 10−22 m3 s−1 .

(14)

we find from (12) that

Over the range of validity of (12), the reaction rate increases rapidly withtemperature sincedlnhvσi =
dTi

19.94

2
−
1/3
3
3Ti

!

d
ln Ti
dTi

(15)

At the the temperature Ti = 20 keV, we findddlnhvσi = 1.8
ln Ti
dTi
dTi

(16)

So at a nominal plasma temperature of 20 keV, a 1% increase in ion temperature will increase the reaction rate by 1.8%.

11

Suppose the reactor is stoichiometrically fueled so[N] = [T] = [D],(17)

where [N] is the common number density. Then one can readily solve (11) tofind that the number density [Nτ ∗ ] at time τ ∗ > 0 is related to the number
density [N0 ] at the time of fuel injection by[N0].
1 + hvσi[N0 ]τ ∗(18)

[Nτ ∗ ]
hvσi[N0 ]τ ∗
=
.
[N0 ]
1 + hvσi[N0 ]τ ∗(19)

[Nτ ∗ ] =The burnup fraction is
fb = 1 −For magnetic confinement fusion, the effective time for burning, τ ∗ , can bebigger than the ion confinement time τc of the plasma, because some fraction
R of the ions that escape the plasma can recombine and reenter the plasma
as neutral atoms. Then the effective confinement time τ ∗ is
τ ∗ = τc + τc R + τc R2 + · · · =

τc
.
1−R

(20)

Experimental evidence so far suggests that R  1 so τ ∗ will not be muchbigger than τc . Using (14) and (19) and representative numerical values formagnetic confinement machines,[N0 ] = 1020 m−3 ,we findfb =Ti = 20 keV and τ ∗ = 2 s,

(21)

0.064
= 6.02%.
1.064

(22)

The burnup fraction anticipated for the International Thermonuclear Experimental Reactor (ITER) is considerably smaller, less than 1%. Proponents ofinertial confinement fusion hope to achieve burnup fractions as high at 30%.
Large burnup fractions help to keep the required tritium inventory low, as
we will discuss in the next section.

12

4.3

Tritium Inventory

Unburnt fuel from the reactor is sent to a tritium reprocessing systemthat takes a mean time tp to clean up and recycle the tritium. The continually
reprocessed tritium is injected into the plasma with an efficiency η. The
efficiency can be relatively high, several tens of per cent, for frozen pellet
injection, but it appears to be relatively low, perhaps only a few percent, forgas injection at the edge of the plasma. Then to provide the burn rate (3),and to make up for radioactive decay at the rateγs =ln 2 −1
y ,
12.3

(23)

and the loss rate γr in the reprocessing of unburnt T, we must have
ηfb M0∗ T BR = Ṁ1 + (γs + γr )M0 ,
tp

(24)

where Ṁ1 , the burn rate needed to power the plant, was given by (3) and
M0 is the time-independent, rercirculating tritium inventory. As we discussin the next section, in addition to the recirculating inventory M0 , there will
normally be a growing inventory m of tritium being bred for additional reactors, with a separate processing and storage system. From (24) we see thatthe inventory is
M0 =

Ṁ1
.
T BR ∗ ηfb /tp − γs − γr(25)

From (25) we see that the relative tritium production, T BR ∗ ηfb/tp must atleast exceed the relative loss rate γr + γs from the reprocessing loop and fromradioactive decay. If the breeding rate is large compared to the loss rate, andT BR ≈ 1 we can approximate the mass inventory (25) by
M0 ≈tp Ṁ1.
ηfb

For example, if
fb = 0.05,
13

(26)

η = 0.5,
tp = 1 day,PF = 1 GWT,

(27)

M0 = 6.14 kg.

(28)

Equation (26) gives

This is a large amount of tritium, but much less than the 56 kg that must
be burnt per year to produce 1 GW of heat. We see from (26) that therecirculating inventory can be minimized by minimizing the reprocessing time
tp and by increasing the injection efficiency η and burn fraction fb withrespect to the representative values of (27).
The estimates above assumed no breeding of additional tritium, a topic
we address in the next section.

4.4

Tritium Breeding Ratio

The blanket is designed to breed enough tritium to at least make up forthat which is burnt, and what is lost in reprocessing and radioactive decay.
Moreover, after a desired doubling time td , typically a few years, enough extra
tritium should be produced to provide the initial inventory for an identical
reactor.
Denote the mass of the tritium inventory by
M = M0 + m,(29)

where the time-independent circulating mass, M0 , needed to run the reactor
was given approximately by (26) and m is the growing, time-dependent massthat is being bred for fueling the next reactor. Radioactive decay at the rate
γs , losses at the rate γr in the reprocessing loop, burning and breeding will

14

cause the refueling mass to change at the ratedm
= −γs m − (γs + γr )M0 − Ṁ1 + Ṁ1 ∗ TBR
dt= −γs m + κM0 .

(30)

where we can use (25) with (30) to write the net production rate coefficient
as
κ=

!

ηfb
− γs − γr ( TBR − 1) − γs − γr .
tp

(31)

For no breeding, m = 0 and dm/dt = 0, (30) gives (24). Solving (30) under
the assumption of a positive tritium production rate κ > 0, and assuming
m = 0 at time t = 0 and m = M0 at the doubling time, td > 0, we findκ=γs.
1 − e−γs td(32)

For certain ranges of the parameters η, fb , tp, td, γs and γr we can equate
the expressions (31) and (32) for κ to find the required tritium breeding
ratio TBR. For simplicity, consider sufficiently short doubling times td (a few
years) that there is negligible radioactive decay of the tritium and γs td  1.
Then we can approximate (32) by κ ≈ 1/td and neglect γs and γr in (31) tofind that the required tritium breeding ratio is
TBR − 1 ≈tp.
ηfb td(33)

For example, if we use the paramters of (27) in (33) with a doubling time,
td = 3 y, we find a required tritium breeding ratio
TBR ≈ 1.04.

(34)

From (33) we see that to have the least demanding requirements on thetritium breeding ratio it is necessary to use the longest possible doublingtimes, td, the largest tritium burn fraction fb , the largest injection efficiency
η and the smallest recycling time tp .

15

5

ADDITIONAL ISSUESIn this section we discuss issues related to tritium breeding that go

beyond the explicit questions of our charge.

5.1

Deuterium-Rich Fueling

The fusion community may have already considered deuterium-rich fuelmixtures, but we think this is worth serious consideration since deuteriumrich mixtures could be more favorable for tritium breeding than stoichiometric mixtures with equal atomic fractions of of D and T. For DT fueling, threeother fusion reactions that occur at the same time as (1) are
D + D → T + p + 4.04 MeV,(35)

D + D →3 He + n + 3.27 MeV,

(36)

T + T → α + 2n + 11.4 MeV.

(37)

The rate coefficients, hvσi, corresponding to the reactions (35) and (36) areabout 200 times smaller than for the main reaction (14) and the energy release
per reaction is substantially less[3]. The rate coefficient for the reaction (37)is about 90 times smaller than (14). Using non-stoichiometric, deuteriumrich fuel, which would enhance the contribution of the reactions (35) and (36)and supress the contribution of (37) to the burning, could be advantageous
to the breeding cycle because:• Deuterium-rich fuel could substantially increase the burnup fraction fbof the tritium. The larger the burnup fraction, the smaller the required
inventory of tritium and the smaller the required tritium breeding ratio.

17• The reaction (35) makes tritium directly, and the reaction (36) makes
the valuable isotope 3 He and a neutron which can convert 6Li to T in
the blanket.
For example, suppose that the number density [N0 ] of (21) is sufficient toprovide the desired thermal output of the reactor with stoichiometric fuel.
Then we would get the same thermal output from a non-stoichiometric fuelwith triton and deutron number densities give by[D][T] = [N0 ]2.

(38)

Call the relative deuterium enrichment
[D]
.
[N0]

=

(39)

The relative burn rate, γ , of tritium will then beγ = −

1 d[T]= γ1 .
[T] dt(40)

where the stoichiometric burn rate isγ1 = [N0 ]hvσi.

(41)

Other things being equal, the plasma pressure will scale as the sum of
the deuterium and tritium number densities, so enhancing the deuterium
content by  will cause the ion pressure p0 for a stoichiometric fuel mix toincrease top=orp − p0 ≈

p0
1
+
.
2



p0
( − 1)2 ,2if | − 1|  1.

(42)

(43)

For example, consider a modest, 30% D enrichment of = 1.3.
18(44)

We see from (40) that the tritium burn rate will increase by a factor of
30%. If the required 4.5% ion pressure increase from (43) has a negligible
effect on the ion confinement time, we would also get an approximately 30%
increase in burn fraction. According to (25) and (33) this would decrease
both the required tritium inventory M0 and the breeding-ratio excess, TBR1, by about 30%. The contribution of the reactions (35) and (36) to theburning would be increased by a factor of 1.32 = 1.69. But the rates (35)
– (36) are so small compared to the rate of the main DT fusion reaction(1), that their increased contribution from deuterium-rich fueling will not be
a very important factor compared to the substantially larger burn fraction
fb , and the resulting decreases of the required tritium inventory and tritium
breeding ratio.

5.2

Lithium and Lead-Lithium Blanket

Pure lithium and lithium-lead (Pb-Li) mixtures have been investigatedin some detail as potentially useful blanket materials, that could also provide some or all of the heat transfer to the balance of the plant for partial
conversion to electrical energy.
Pure lithium has a very high electric conductivity, and rapid pumpingof liquid lithium against the large magnetohydrodynamic (MHD) forces of
MCF reactors will be very difficult. Pure lithium metal is often envisaged as
a combined breeding and heat transfer medium for ICF reactors, which do
not require such large magnetic fields.
A currently interesting MCF design envisages using a homogeneous mixture of the liquid metals, Pb and Li, as the tritium breeding blanket and toprovide some heat transfer. The bulk of the heat transfer would be provided
by circulating helium gas for which there are no MHD issues. The phase
diagram of the Pb-Li system, shown in Figure 2. There is a eutectic compo19

Figure 2: Phase diagram of the PbLi system[5]. Many blanket designs envisage using the eutectic mixture of about 15.8% Li, with a melting point of
about 235 C.
sition, 15.8% (atomic) Li and 84.2% (atomic) Pb, with a minimum freezing
temperature of 235 ◦ C. In most of the briefings we received, the breedingblanket was assumed to have the eutectic composition. A NaK eutectic isused in experimental fast-neutron fission reactors to facilitate frequent refueling with a liquid-metal coolant that remains liquid at room temperatureor below. The Pb-Li eutectic melting point is well above room temperature
so it is not clear that the eutectic mixture would have any advantages overa mixture with a larger Li fraction and better tritium breeding potential.
We recommend that whatever considerations went into selecting the eutectic
composition for the Pb-Li blanket be reviewed.
Solid eutectics are easy to make in a reproducible manner. If a melt that
does not have the eutectic composition is cooled, the phase rich in whichever
component is more abundant than the eutectic composition will freeze first.
If Li-rich it will float to the surface; if Pb-rich it will sink to the bottom.
When the temperature reaches the eutectic point the remaining material, of20

eutectic composition, will freeze homogeneously. It is only necessary to cut
off the non-eutectic layer at the top or bottom of the solid ingot, and theremaining material will have the eutectic composition and can be repeatedly
remelted and refrozen as a homogeneous solid.
Liquid mixtures of non-eutectic composition can be easily made by melting weighed quantities of their components. In fusion breeders the temperature of the blanket material is supposed to range from about 500 ◦ C to
700 ◦ C, and for this range one can see from Figure 2 that compositions with
Li fractions up to 40 % (atomic) should remain liquid, and could have better
tritium breeding potential.
Initial melting and mixing is not trivial because of the large density
mismatch between Pb and Li, but once a liquid is mixed it remains mixed
until frozen. Once frozen, careful mixing is necessary to homogenize theremelted material if the eutectic composition is not used. Magnetohydrodynamic mixers have been developed [5] and could be useful for the initial
mixing of non-eutectic compositions.
For relatively inexpensive and non-hazardous tests of tritium breedingin Pb-Li, it would be useful to use solid, room temperature samples. Maintaining such samples above their melting point would introduce significant
additional costs and hazards. A suitable proxy material could consist of interleaved sheets of eutectic and pure materials (or of the two pure materials)
in the appropriate thickness ratios. The probing neutron beam should enter
the stack of sheets perpendicularly (or obliquely). Because the fast-neutroninteraction length in any solid-density material is several cm or more, sheetsof 1 cm thickness could provide a satisfactory approximation to homogeneity.
It is often remarked that the relative amount of the isotopes 6 Li and 7 Li
in Pb-Li blanket material can be chosen to optimize tritium breeding. It isalso true that the relative amounts of Pb and Li can be chosen to optimize
breeding and the eutectic composition probably has too little Li for optimum
21performance. As discussed above, there is no obvious reason to be limited tothe eutectic composition of a melt.

5.3

More Tritium is Better

There has been some consideration of deliberately decreasing the TBR,
for example, but adjusting the relative fraction of 6 Li and 7Li in blanket
material, to avoid producing more tritium than needed for fueling existing
reactors, providing fuel for additional reactors, and making up for losses fromprocessing and radioactive decay.
We doubt that overproduction of tritium is a real problem. Tritium isreadily stored as metal tritides, at modest cost and with no significant hazard.
Tritium is a valuable not only for fusion energy, but because it is the only
currently practical source of 3 He. Demand for 3 He far outstrips the supply.
The largest projected demand at present is for slow-neutron detectors, which
DHS wants to proliferate in great numbers to counter nuclear terrorism. An
additional growing use for 3He is in medical imaging of the lung. There is no
substitute.

5.4

Tritium Handling and Leakage

In steady-state operation relative small quantities of tritium must be
extracted from a much larger mass of blanket material. Although the quantity of tritium produced is relatively small, there will be stringent regulatory
constraints on its emission to the environment in any chemical form. Gaseous
HT and the vapor HTO are of most concern, the latter because of its readysubstitution for H2O in most chemical and biological systems. A plausible
regulatory limit is 1–3 g year−1 of tritium loss. This is about 10−4 of thetritium burnt in one year to make 1GW of thermal energy. Material control
22

at this level can be achieved with careful chemical engineering, but tritium
presents special problem because of its volatility, diffusivity in many materials, and the ready formation of mobile and reactive compounds like HTO.
Tritium extraction from the breeding material is complicated because
large amounts of heat may also need to be extracted through heat exchangers with significant tritium permeability. Thus tritium could contaminate theheat transfer medium (for example helium) in the secondary loops of heatexchangers. Materials with low-permeability to tritium at elevated temperatures are needed. A representative material is tungsten with a permeabilityof 1 × 10−7 in units of cm3(STP) [m s kPa1/2]−1 at 700 C. This extrapolates
to 10−23 in the same units at room temperature. To get the permeability
current in cm3 of T2 gas (at standard temperature and pressure) per second,
one must multiply the permeability by the difference in the square root of
the pressure in kPa times the ratio of the area of the barrier to its width.
The dependence on the square root of the pressure is called Sievert’s law,and it comes from the dissociation of T2 to atomic tritium in the metal. The
diffusion coefficient of T2 in alumina, where there is no dissociation of the T2
molecule, is 1 × 10−15 m2 s−1 at 700 ◦ C. The room-temperature value is extrapolated to be 10−31 m2 s−1 . Such extrapolations are necessarily uncertain
because they assume the temperature dependence of permeabilities follows
an Arrhenius law into temperature ranges far from those for which direct
measurements are available. Unrecognized transport mechanisms with small
prefactors but lower activation energies could give much larger permeation
coefficients at low temperature. Direct measurements extend to 1 × 10−10
cm3(STP) [m s kPa1/2]−1 for tungsten and to 10−20 m2 s−1 for alumina,
with no sign of deviation from Arrhenius temperature dependence. Some ofthese coefficients were measured for protium or deuterium, and the values
for tritium are expected to be smaller because tritium’s greater mass reduces
the tunneling that can play an important role diffusion and permeation ofhydrogen isotopes.

23

In principle, it is possible to reduce tritium leakage to negligible levels
with multiple barriers of small, well-characterized permeabilities. However, inpractice, things may go wrong. For example, material corrosion by tritiatedvapors (HTO, HT) may lead to leaks. Because of their ionizing radiation,
tritiated gases are known to be especially corrosive. There are bound to beunanticipated problems, as has been true for every new technology.
Detritiation of hydrogen-containing (such as water vapor) plant exhaustis, in principle, feasible to any desired degree of completeness with enoughstages of electrolytic or other isotopic separation. The basic performance(physical chemistry) parameters are known; this is not a new technology,
and can be engineered to any desired limits. As for any highly engineered
system, the issue is unanticipated failure, not the nominal calculated leakagerate.
In summary, the chemical engineering issues connected to tritium breeding will be a very challenging. While these are hard problems, we do not see
them as show-stoppers. Judging from the briefings we heard, the world fusion energy program is well aware of tritium handing issues and has effective
research and development programs underway to address uncertainties.

5.5

6

Li, Tritium and 3 He Economics

The cost of 60% enriched 6Li has been estimated to be $800/kg, or$1,333 kg−1 of 6Li in the enriched product [6]. As a first approximation,
we assume the cost of further enrichment is proportional to the additional
separative work units (SWU’s) required. Assuming a tails fraction of 0.0375(half the natural 6 Li abundance of 7 %) for both the enrichment to 60% andthe subsequent enrichment from 60% to 90%, we find that enrichment to 60%
requires 16.5 SWU per unit of 6 Li, while further enrichment to 90% requires
an additional 3.7 SWU per unit of 6Li. Hence we estimate a cost of 90%
24enriched 6 Li of $ 1,600 kg−1 of 6 Li in the enriched product. Of course this is
not a very refined estimate since the cost should include many other factors,
for example, the capital cost of equipment, which is larger at low enrichment
because more material must be handled.
With efficient conversion, one 6Li makes one triton. So to make 1 kg oftritium requires 2 kg of 6 Li, and if the 6 Li is from material enriched to 90 %,the contribution to the cost from enriched lithium is $3,200 kg−1 . The costof the lithium is definitely the “tail of the dog”, with tritium prices in therange $10,000–30,000 g−1 (g, not kg!), and a speculative future cost (Willms:
fire.pppl.gov/fesac dp ts willms.pdf) of $100,000–200,000 g−1 .
Fusion reactors may be a significant source of tritium for purposes otherthan fusion fuel. A 2.5 GWth, 1 GWe fusion plant with TBR = 1.10 and
33% efficiency for converting heat to electrical energy, would produce about
17 kg y −1 of tritium beyond the 170 kg needed to replace what must be
burnt. If the electric production of 3.16 × 107 GJ y−1 = 8.8 × 103 GWhr y−1
is valued at $0.10 kWhr−1 the electric power produced (at 100% duty cycle)
is worth $ 8.8 × 108 y−1 . At $100,000 g−1 for 17 kg y−1 of tritium, the valueof the tritium produced would be $1.7 × 109 y−1 , more than the value valueof the electrical energy. Although the price of $ 100,000 g−1 for tritium iscompletely unrealistic, the point is that overproduction of tritium could be asignificant contribution to the economics of the reactor. Before priorities atthe Department of Homeland Security made it difficult to purchase 3He at
any price, it was available commercially at around $100 per liter (at standard
temperature and pressure), or $ 2,240 per mole, or about $ 750 g−1 . We havesee prices quoted as high as $ 4,000 g−1 [7].
Of course, the prices mentioned above are artificial and not free market
prices. Should fusion power provide sources of tritium and 3 He that areorders of magnitude greater than present production, a real market for both
tritium and 3 He could develop, with prices completely different from those25

prevailing today. Abundant new supplies of tritium and 3 He will create new
applications. For example, escape path lighting (as on airplanes) could be
put in every building, just as public buildings now have exit signs, often
powered by tritum decay. We regularly hear of people, including firemen,dying in fires because the become disoriented in the smoke and cannot findtheir way out.

5.6

Quantification of Margins and Uncertainties

Although it is our judgement that adequate tritium breeding is possible for both MCF and ICF, we recommend that the key uncertainties ofbreeding be quantified. A well-established formal method for dealing withuncertainties in predictions of untested complex systems is called Quantification of Margins and Uncertainties [8, 9, 10]. The reader is referred tothese references for details. This methodology was developed to understandand quantify the confidence that can be placed in performance margins ofuntested systems in the presence of uncertainties. In the case of nuclear
weapons there is a moratorium on testing for the indefinite future; in thecase of fusion power reactors, there will be no reactors for full-scale tests formany years, probably several decades. So quantification margins and uncertainties will helpful to both the fusion energy and nuclear weapons programs
to point research and development toward problems of highest priority.

5.7

Tritium Breeding Issues for ICF

Research on inertial confinement fusion (ICF) has been focussed onachieving ignition, and little work has been done on the breeding issue beyond
some conceptual paper studies. Nevertheless, the overall neutron economy
of an ICF power plant would be broadly similar to a MCF plant, and much26

of the technical discussion already given in this report carries over to ICF.
This subsection will explain these similarities and highlight the differences.
The most expensive capital cost in an ICF plant is likely to be thedriver, whether it be a laser, a heavy-ion accelerator, or (more speculatively)a pulsed power machine. The driver must deliver energy to the fusion target,
which contains a capsule of DT fuel. The drive causes the fuel to implode,ignite, and deliver yield in the form of neutrons, alpha particles, x-rays, anddebris. Yield per pellet might be in the range 100 MJ - 1000 MJ, and apower plant of capacity 1000MWe would therefore need to inject and burnbetween 2 and 25 targets per second.
A fusion chamber several meters in diameter is required to contain thefuel capsule explosions. As with MCF, the first wall is a crucial component,
but in ICF it must tolerate pulsed energy deposition on sub-microsecond
timescales. In some conceptual designs, a buffer gas at low pressure (perhaps
xenon at 10 torr) helps protect the first wall from x-rays.
Behind the first wall, coolant flows and breeder blankets must operate,
just as in MCF. The coolant and breeder may well be the same material,
such as liquid Li or Li-Pb mixtures. In some conceptual designs, the firstwall is a “waterfall” of liquid lithium that serves both as a blanket and heattransfer medium while helping to protect the innermost solid wall.
In any case, tritium is bred in the blanket material, and must be recovered. Moreover, unburned tritium must be recovered from the fusion
chamber. The recovered tritium must be purified and used to manufacture
new targets, at high efficiency and low loss. Target manufacture would probably take place right at the plant, to minimize transport and delay, and islikely to represent the single largest operational cost for the plant.

27

Some of the principal differences in tritium breeding for MCF and ICF are:1. If ICF is to work at all as a power plant, the target must burn fuelat fairly high efficiency (30% has been projected), in contrast to MCF,
where the burnup of injected fuel may be only a few percent; thus thequantities of tritium recovered from ICF chamber would be smaller
than for MCF.
2. Since an ICF chamber needs no strong magnetic fields, flow of conducting coolant/breeder would not be impeded by magnetohydrodynamic
effects. (The exception might be pulsed-power ICF plants, where strongtransient fields might exist.)
3. Manufacture of targets for ICF is enormously more challenging thanmanufacture of fuel pellets for MCF. An ICF target is a precision part,which must survive injection at high speed (100s of m/s) into the hot
fusion chamber. In the case of indirect drive, the fuel capsule is enclosed
in a cm-sized hohlraum.
4. An ICF chamber will not need a central post and will have different
penetrations in its first wall compared to MCF, changing the geometrical neutron losses. Some ICF conceptual designs envisage relatively
small geometrical losses compared to those of MCF.

5.8

Sources of Tritium

To indicate the scale of the problem, recall that a full-scale fusion reactor
generating 3 gigawatts thermal burns about 150 kilograms of tritium per year.
We note the following issues:
1. Fission reactors. A basic disadvantage of fusion when compared withfission is that even the most energetic fusion reaction (1) produces
28about 20 MeV energy per neutron while fission produces about 200
MeV per neutron. At present, tritium is produced in fission reactors,
but if fission is used to breed fuel for fusion, the tail would be wagging
the dog.
• If a fission reactor is dedicated to producing tritium, the maximum
yield is about one atom T per fission. 10 watts of thermal fission
energy will produce tritium fuel for 1 watt of fusion energy. This
makes no economic sense, unless the tritium is used as a temporary
input to get a fusion reactor started. The fusion reactor must bea breeder with a breeding ratio greater than unity.
• CANDU reactors. The only source of non-military tritium is the
CANDU reactors, 21 operating in Canada, 4 in Korea and one or
two in India, China, Rumania, Pakistan, and Argentina. From allof these, about 1.8 kilograms tritium per year is recovered fromthe heavy water that is used for cooling and moderation. About
100 grams of tritium per year are sold at a price of $ 30K per gram.
The CANDU are mostly scheduled to retire around the year 2025.
The stockpile remaining in Canada is about 20 kilograms. This
will be just sufficient to supply the ITER machine, which is not abreeder, with tritium for 10 years of experiments. There will not
be enough left over to make a significant contribution to future
fusion reactors.
• Other commercial fission reactors, using light rather than heavy
water, require substantial modification if they are to be used fortritium production. For example, much of the boron and gadolinium, currently used burnable neutron poisons to stabilize the reactivity over the lifetime of the fuel load, could be replaced bylithium. The modifications would be expensive and would requirea lengthy process of development and regulatory certification.
In 2003 a commercial TVA reactor at Watts Bar began irradiat29

ing Li-containing rods for tritium production for the U.S. nuclear
weapons stockpile. However, an October 2010 GAO report[11]notes that NNSA has not been able to irradiate as many tritiumproducing burnable absorber rods (TPBAR) as it had scheduled
because of problems with tritium permeation– an indication of the
difficulty of controlling the leakage of tritium.
2. An earlier JASON study, (JSR-95-310, unclassified), studied in detail anumber of schemes for producing tritium with accelerators. In 1995 werecommended one such scheme to DOE as a practical solution of a DOE
supply problem concerned with tritium for nuclear weapons. In that
context, the quantity of tritium required was small and predictable,
and a high cost per gram was acceptable. If tritium is to be produced
for fusion energy, the quantities are much larger and the affordable
cost per gram is much smaller. Accelerator schemes suffer from thesame circumstances that make tritium production in fission reactors
uneconomic. If the accelerator is used to provide a spallation sourceof neutrons which are absorbed directly to make tritium, the input ofenergy required to run the accelerator is greater than the output ofenergy produced by the tritium. If the spallation source is amplified
by surrounding it with a sub-critical fission reactor, then the fission
reactor might as well be operated as an ordinary critical reactor, andthe accelerator becomes superfluous.
3. The migmatron promoted by Bogdan Maglich. The migratron is a proposal to run a fusion reactor with ordinary hydrogen and boron as fuel,so that all the energy goes into charged ions and none into neutrons.
This scheme would have many advantages as an energy source, if it
could be made to work. It would incidentally produce small amountsof tritium as a by-product of its operation. Unfortunately, it has nevercome close to a practical demonstration. In event that a migma reactor
could actually work, it would probably make DT reactors obsolete and30

would enormously reduce the demand for tritium. The migma reactor
would then be used directly as an energy source and not as a breederof tritium.
4. Requirements for lithium and beryllium. A fusion power reactor
generating 3 gigawatts thermal will require about 500 tons of lithium fora breeding blanket using lithium 7 as the source of secondary neutrons.
A breeder with the same power using beryllium as neutron source will
require about 250 tons of lithium and about 100 tons of beryllium.
These materials must be reprocessed periodically but will not be usedup.
• Lithium resources. World production of lithium in 2010 was
about 20,000 tons, mostly used for ceramics, but increasingly forlithium batteries. Production is expected to rise rapidly if the
population of electric automobiles expands. Proven reserves in2010 were about 4,000,000 tons, mostly in Argentina, Chile andBolivia. Estimated resources were about 16,000,000 tons. Compared with these resources, the requirements for tritium breeding
are small. Blankets for 100 full-scale fusion breeders would requireless than one percent of the resources. If the producers of lithium
should try to raise the price dramatically, the electric automobile industry would be priced out of the market before the fusion
industry would be seriously affected.
• Beryllium resources. World production of beryllium in 2010
was about 300 tons. Proven reserves were 16,000 tons, mostly in
the USA, and estimated world resources were about 80,000 tons.
If all fusion reactors were using beryllium blankets, the provenreserves would be sufficient for 160 full-scale reactors each using
100 tons. If the beryllium production capacity was insufficient or
if the price of beryllium was too high, fusion reactors could use
alternative blankets using lithium-lead or liquid lithium. In any
31

case, it is unlikely that shortage of beryllium would be a factor
limiting the growth of fusion energy.

32

References[1] http://www.ncnr.nist.gov/resources/n-lengths/[2] S. Glasstone and R. Loveberg, Controlled Thermonuclear Reactions, Van
Norstrand, Princeton (1960), p. 20.
[3] S. Atzeni and J. Meyer-ter-Vehn, Inertial Fusion Oxford University
Press (2004)[4] Ihle, H., and Wu, C., Chemical thermodynamics of fusion reactorbreeding materials and their interaction with tritium. J. Nucl. Materials
130 (3), 454–464 (1985).
[5] Freibergs, J., et al., MHD technology for the production of Pb–Li eutectic alloys. The 15th Riga and 6th PAMIR Conference on Fundamental
and Applied MHD Fusion I, 259–262 (nd)[6] http://www-ferp.ucsd.edu/ARIES/MEETINGS/1104/ElGuebaly1.pptx[7] http://www.lunarpedia.org/index.php?title=He3[8] Goodwin, B., and Juzaitis, R., National Certification Methodology for
the Nuclear Weapon Stockpile. (2003) (OUO).
[9] Pilch, M., Trucano, T. G., and Helton, J. C., Ideas Underlying Quantification of Margins and Uncertainties (QMU): A White Paper. Sandia
Report SAND2006-5001 (2006)[10] National Research Council, Evaluation of Quantification of Margins andUncertainties Methodology for Assessing and Certifying the Reliabilityof the Nuclear Stockpile, National Academies Press (2008).
[11] http://www.gao.gov/products/GAO-11-100

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