capabilities of a dt tokamak fusion neutron source for driving a...

Capabilities of a DT tokamak fusion neutron source for driving a spent nuclear fuel

transmutation reactor

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Capabilities of a DT tokamak fusion neutron source

for driving a spent nuclear fuel transmutation reactor

W.M. StaceyFusion Research Center, Georgia Institute of Technology,Atlanta, Georgia, United States of America

Abstract. The capabilities of a DT fusion neutron source for driving a spent nuclear fuel transmu-

tation reactor are characterized by identifying limits on transmutation rates that would be imposed

by tokamak physics and engineering limitations on fusion neutron source performance. The need for

spent nuclear fuel transmutation and the need for a neutron source to drive subcritical fission trans-

mutation reactors are reviewed. The likely parameter ranges for tokamak neutron sources that could

produce an interesting transmutation rate of 100s to 1000s of kg/FPY (where FPY stands for full

power year) are identified (Pfus ≈ 10–100 MW, βN ≈ 2–3, Qp ≈ 2–5, R ≈ 3–5 m, I ≈ 6–10 MA). The

electrical and thermal power characteristics of transmutation reactors driven by fusion and accelerator

spallation neutron sources are compared. The status of fusion development vis-a-vis a neutron source

is reviewed.

1. Introduction

There is an ongoing worldwide planning, analy-sis and R&D activity dedicated to mitigating thenuclear waste problem by neutron transmutation oflong lived actinides and fission products in spentnuclear fuel. The objective of neutron transmutationof spent nuclear reactor fuel is to reduce the amount(70 000 t will have been produced in the USA by2015) and the time of high radiotoxicity (from hun-dreds of thousands to hundreds (or thousands) ofyears) of the material that must be stored in highlevel radioactive waste repositories. Such a reduc-tion in the amount and the time of high radiotox-icity of stored high level waste could eliminate theone remaining obstacle — waste disposal — to thefull-scale deployment of nuclear power to meet theworld’s growing energy demands without dramati-cally increasing CO2 levels. At the same time, thedestruction of actinides by fission would eliminatea potential proliferation risk and produce electricalpower, which would provide a source of revenue tooffset the operating cost of the transmutation facility.

The OMEGA project motivated the largest inter-national R&D activity since 1988 on separation andtransmutation of actinides and fission products, withJapan and France as the principal participants. Fur-ther motivation was provided by an IAEA Meet-ing in 1991 and the GLOBAL Meeting in Seattlein 1993. The major elements of this R&D have beensystems studies to evaluate transmutation scenariooptions and the development of technologies for sep-arating actinides and fission products from the waste

stream of reprocessed fuel. A formal program ofinformation exchange among OECD countries, underthe auspices of the OECD Nuclear Energy Agency(NEA), has produced five International InformationExchange Meetings on the subject in the past decade,each with about 100 participants and proceedings[1, 2].

In the USA, there has been considerable interestin the use of accelerator spallation neutron sourcesin conjunction with subcritical transmutation reac-tors for the transmutation of spent nuclear fuel (see,e.g., Refs [3–5]). This interest has led to the estab-lishment of the accelerator transmutation of waste(ATW) activity [5], in which the major emphasis ison the use of a subcritical reactor driven by an accel-erator spallation neutron source.

In contrast to the US ATW activity, the inter-national OECD/NEA activity has emphasized recy-cling of spent fuel first in commercial light waterreactors (LWRs) and then in dedicated fast reactors.However, there is a general consensus that, even withextensions of the presently available aqueous process-ing technology, critical reactors alone cannot achievesufficient levels and rates of net actinide destructionto qualitatively change the waste disposal issue andthat subcritical reactors driven by neutron sourcesare needed to achieve this goal. While acceleratorspallation neutron sources have been mentioned inmost such studies, fusion neutron sources could playthe same role.

The physics [6] and technology [7–13] designbasis for a good tokamak DT fusion neutron sourceexists today and will be advanced over the next few

Nuclear Fusion, Vol. 41, No. 2 c©2001, IAEA, Vienna 135

W.M. Stacey

years. The ‘conventional’ tokamak physics database(including the more than 10 MW level of DT oper-ating experience in TFTR (USA) and JET (EU))and the existing technology database (including thetechnology which has already been demonstratedon existing tokamaks and the advanced technol-ogy which has been developed and tested in theUS M$750 ITER R&D programme) are sufficientto allow the design and construction at present ofneutron sources with modest annual neutron fluencecapability. The ‘advanced tokamak’ physics databasethat is rapidly accumulating is extending the designbasis for continuous operation, reduced cost andannual neutron fluence accumulation.

A limited number of studies (see, e.g. Refs [14–19]) of transmutation systems with fusion neutronsources have been performed. These studies andother considerations would seem to indicate that theminimum requirements for a tokamak DT fusion neu-tron source for a transmutation facility are energyamplification Q ≈ 2–5, neutron wall load Γ <

1 MW/m2, very long pulse operation and availability≈40–50%. The present tokamak physics and technol-ogy database is sufficient to design a device satisfyingthe Q and Γ requirements (which are less demand-ing than those for ITER). A substantial advance inthe database for long pulse operation will be sup-plied by KSTAR (Republic of Korea), but withoutthe integration needed with burning plasma phenom-ena. However, a prototype tokamak experiment thatintegrates the burning plasma physics, long pulsephysics and advanced technology is required, particu-larly to provide the design database for achieving 40–50% availability. Such a prototype would necessarilybe almost at the ITER [20] level, and that devicewould in fact serve as a prototype for a tokamak neu-tron source for a transmutation facility. Furthermore,it would be technically feasible to test prototypicaltransmutation reactor modules (without fissionablematerial or fission products) in ITER.

Several fuel/moderator/coolant and process-ing/separation technologies are being developedand/or evaluated in the ATW process [5] and in theOECD/NEA R&D activities [1, 2], based on exten-sions of nuclear reactor technology and taking intoaccount the accumulated experience with nuclearsafety and nuclear licensing requirements. For afusion driven transmutation facility, an additionaltechnical issue is the adaptation of these technologiesto tokamak geometry and to achieving tritium self-sufficiency. The evaluation of fusion driven transmu-tation facilities based on the adaptation of the same

‘nuclear’ technologies (fuel/moderator/coolant andprocessing/separation technologies) that are beingdeveloped/evaluated in the ATW and OECD/NEAactivities remains to be done.

Some idea of the ‘window of opportunity’ fordeveloping a fusion neutron source for transmuta-tion applications can be obtained by considering theschedule for the development of an accelerator spalla-tion neutron source for this application [5]. The ATWactivity initiated a six year programme in f.y. 2000to perform scenario systems studies and to evaluate‘reactor’ technology options. This initial programmeis intended to be followed by about ten years of R&Dand technology testing, which would in turn be fol-lowed by the construction, operation and continualupgrading of a demonstration plant over a period of15 years, leading to an accelerator neutron sourcebased transmutation facility coming on-line in about30 years.

If ITER is constructed and operated more or lesson schedule, or if a different neutron source proto-type on a somewhat smaller scale is built and oper-ated on about the same schedule, then it should bepossible to design and construct a tokamak fusionneutron source based transmutation facility to comeon-line within about 30 years, consistent with thepresent ATW schedule, particularly if the designwas performed and validated during the prototypeoperating period.

The transmutation of spent nuclear fuel could bean important, intermediate term, international mis-sion for magnetic fusion which directly contributes tothe long term objective of fusion energy. A tokamakfusion neutron source could be as suitable, perhapsmore suitable, as an accelerator spallation neutronsource for the transmutation of spent nuclear fuel ina subcritical reactor, and the further R&D neededfor a tokamak fusion neutron source that meets therequirements for a transmutation facility may be nomore than the R&D required for an accelerator neu-tron source that meets the same requirements, giventhe recent internationally funded (7.5× 108 US dol-lars) ITER R&D activity and the possibility that aninternationally funded ITER could serve as the pro-totype fusion neutron source. It is important thatboth the accelerator spallation and the fusion neu-tron source technologies be fully evaluated for thisapplication.

Since the neutron spectrum in a subcritical reac-tor driven by a neutron source will depend moreon the moderating and absorption properties, andhence on the material composition, of the subcritical

136 Nuclear Fusion, Vol. 41, No. 2 (2001)

Article: DT tokamak fusion neutron source

reactor than on the energy spectrum of the sourceneutrons, the material composition in the subcriticalreactor can be optimized for the transmutation taskat hand, without the criticality and safety constraintsthat would be present in a critical reactor. Thus, thephysics characteristics of a subcritical reactor shouldbe more or less independent of whether a fusion oran accelerator spallation neutron source is used. Theengineering design and the economics, however, willsurely depend on the choice of neutron source.

The purpose of this article is to characterize thecapabilities of a DT tokamak as a fusion neutronsource for a subcritical reactor for the transmutationof spent nuclear fuel. The need for transmutation ofspent nuclear fuel and the need for neutron sourcesto drive subcritical fission reactors is reviewed in Sec-tion 2. The thermal and electrical power character-istics of neutron sources based on DT fusion andon accelerator spallation are compared in Section 3.Physics and engineering limitations on the capabil-ities of a tokamak fusion neutron source for driv-ing a subcritical transmutation reactor are discussedin Section 4, and a likely range of tokamak neutronsource parameters is presented. The status of DTtokamak neutron source development, vis-a-vis therequirements identified in Section 4, is reviewed inSection 5. Finally, some conclusions are presented inSection 6.

2. Transmutationof spent nuclear fuel

The once through cycle (OTC), in which slightlyenriched UO2 fuel (235U increased from 0.72% innatural U to 3–5%) is irradiated to 30–50 GWd/t(gigawatt days per metric ton) in a commercial reac-tor and then disposed of totally as high level waste(HLW), is the reference nuclear fuel cycle in theUSA and a few other countries. With the presentlow U prices, this is the cheapest fuel cycle, in theshort term. Moreover, the present US governmentpolicy against reprocessing, motivated by prolifera-tion concerns, is consistent only with OTC. How-ever, the long term implications of OTC are ratherunfavourable. The potential energy content of resid-ual fissile material (about 1% each Pu and 235U)and of the 238U (>90%) in spent fuel, which con-stitutes more than 90% of the potential energy con-tent of mined uranium, is lost in the OTC. Moreover,all the nuclides that can contribute to the potentialradiotoxicity of the spent fuel are retained together

with a much greater volume of depleted U (mostly238U), which makes a relatively small contributionto the potential radiotoxicity, resulting in the largestpossible volume of HLW, which must be stored ingeological repositories for hundreds of thousands tomillions of years.

At the current level of nuclear energy productionin the USA using OTC, a new repository on the scaleof the presently proposed Yucca Mountain site wouldhave to be installed about every 30 years. The objec-tive of transmutation of spent fuel is to reduce boththe mass of HLW that must be stored in geologicalrepositories and the time of high radiotoxicity of thatHLW, thus reducing the requirements for both thenumber of repositories and the duration of securedstorage. A National Research Council (NRC) study[21] recently concluded that the need for a geolog-ical repository could be reduced, but would not beeliminated, by transmutation.

The short term radiotoxicity of the spent fuelis dominated by fission products, but after 300–500 years only long lived radionuclides (particularly99Tc and 129I, but also 135Cs, 93Zr, etc.) remain [22]— unfortunately some of these are relatively mobileand contribute disproportionately to the potentialradiological hazard from spent fuel. However, thelong term potential radiotoxicity of spent fuel arisesprincipally from the presence of transuranic actinides(Pu and the so-called minor actinides Np, Am, Cm,etc.) produced by transmutation–decay chains orig-inating with neutron capture in 238U, which consti-tute a significant radiation source for hundreds ofthousands of years.

Processing of spent UO2 fuel to recover the resid-ual U and Pu reduces the potential long termradiotoxicity of the remaining HLW (minor actinides,fission products, activated structure, etc.) by a factorof 10 and reduces the volume by a much larger factor,and aqueous processing technology (PUREX) capa-ble of 99.9% efficient recovery of U and Pu is commer-cially available in a number of countries (UK, France,Japan, India, Russian Federation and China). A fuelcycle in which the recovered Pu and U was recy-cled as a mixed oxide (MOX) UO2–PuO2 commer-cial reactor fuel has been envisioned since the begin-ning of the nuclear energy era, and at present anumber of commercial reactors are operating withrecycled Pu in Western Europe. (Reprocessed U isnot being significantly recycled because of the lowcost of fresh U which does not contain the neutronabsorbing 236U that decreases the reactivity of recy-cled U.) Taking into account the further production

Nuclear Fusion, Vol. 41, No. 2 (2001) 137

W.M. Stacey

of minor actinides and fission products in the recy-cled Pu, a single recycle of the Pu in spent fuelreduces the potential radiotoxicity of the HLW asso-ciated with the original spent fuel only by a factor of3 (rather than 10). Repeated recycling of the MOXfuel is technically feasible and would result in betterfuel utilization, but the potential radiotoxicity of theHLW associated with the original spent fuel wouldactually increase relative to that of OTC because ofthe further production of minor actinides and fissionproducts [1].

It is clear from the above discussion that in orderto reduce the potential radiological hazard associatedwith spent fuel or the length of time that hazardexists, it is necessary

(a) To destroy the actinides (Pu and the minoractinides),

(b) To destroy the potentially hazardous long livedfission products.

The destruction of the minor actinides and long livedfission products, as well as the Pu, by neutron trans-mutation implies the requirement for separation ofthese nuclides from the waste stream of processedspent fuel for recycling with subsequent fuel load-ings. Effective separation of Pu with 99.9% efficiencyis achieved commercially with the PUREX process.The effective separation of Np is technically feasi-ble with a modified PUREX process, but practi-cal separation methods for Am, Cm and the longlived fission products are still in the research stage.The pyrometallurgical (PYRO) separation technol-ogy presently under development would, unlike thePUREX process, allow separation of Np, Am andCm along with Pu into a co-deposited metallic prod-uct that could be recycled in a metal fuel fast reac-tor, resulting in a waste stream essentially free ofactinides.

Since all actinides are potentially radiotoxic andsince neutron capture (n,γ) reactions in actinides justproduce other actinides, the only effective way todestroy actinides is by neutron fission (n,f) reactions.Some of the actinides are effectively not fissionable ina thermal neutron spectrum such as exists in almostall commercial nuclear reactors, and the probabilityof fission per neutron absorbed is greater for all theactinides in a fast neutron spectrum [22]. The neu-tron absorption cross-sections for the troublesomelong lived fission products are small in a thermalneutron spectrum and even smaller in a fast neutronspectrum, implying the advantage of a very high flux

of thermal neutrons for their effective destruction(effective destruction of 135Cs may prove impracticalbecause of the presence of other neutron absorbingCs isotope fission products).

Several studies of minor actinide transmutationin nuclear reactors have been performed (see, e.g.,Refs [1, 2, 5]). They indicate that recycling of indus-trial levels of minor actinides as well as of Pu inthermal neutron spectrum commercial reactors doesnot significantly reduce the overall radiotoxicity andrequires an increase in fuel enrichment, with a cor-responding increase in the cost of energy. On theother hand, recycling minor actinides as well as Puin fast reactors is predicted to reduce the overallradiotoxicity of HLW, but the maximum loading ofminor actinides is limited by reactor safety consider-ations. The possibility of recycling Pu and the minoractinides first in thermal neutron spectrum commer-cial LWRs and then in dedicated fast reactors hasbeen calculated to be able to reduce the radiotoxicinventory in HLW by a factor of about 100 relativeto that of OTC [1].

Such studies generally indicate that the transmu-tation of Pu, minor actinides and fission productsin critical nuclear reactors would be ultimately lim-ited by criticality or safety constraints. While fastreactors could, in principle, burn the mixture of Puplus minor actinides and some of the fission products,the available PUREX process does not separate theminor actinides with the plutonium from the wastestream for recycling. Moreover, it would be difficultto fabricate MOX fuel containing the highly radioac-tive minor actinides in existing facilities. This has ledin Europe and Japan to consideration of remote fuelfabrication facilities to supply fuel containing minoractinides for destruction in dedicated subcritical‘transmuter’ reactors driven by accelerator spallationneutron sources, while the Pu would be consumedin dedicated fast reactors [1].

The US ATW concept [5] is to use remote fabri-cation of fuel containing separated Pu plus minoractinides, but no 238U, for destruction in a criti-cal ‘transmuter’ reactor driven by an external neu-tron source. A variant of this concept would involvefirst irradiating this Pu plus minor actinide fuelby repeated recycling in a critical reactor beforethe final irradiation in a subcritical ‘transmuter’reactor.

The small delayed neutron fraction of the minoractinides and the generally positive reactivity coef-ficient of fast reactors without 238U dictates thatthese actinide destruction, or ‘transmuter’, reactors



must remain well below subcriticality. The reactivitycoefficient could be made negative by the addition of238U, which would allow the possibility of actinidedestruction in critical fast reactors, but that wouldlead to the production of additional Pu and minoractinides by transmutation of 238U, and hence to adecreased net actinide destruction rate.

The development of the PYRO separation tech-nology would allow separation of Np, Am and Cmalong with Pu, all of which could be recycled in ametal fuel fast reactor, resulting in a waste streamessentially free of actinides. However, it would benecessary to include 238U (or another resonanceabsorber) in the fuel to avoid the safety problemsmentioned in the previous paragraph, which wouldreduce the net destruction rate of actinides.

Thus, safety or net destruction rate constraintson the transmutation of actinides in critical reac-tors could be relaxed by operating the reactorssubcritically with a neutron source. Several stud-ies of subcritical reactors driven by acceleratorspallation neutron sources [1–5] and a few stud-ies of subcritical reactors driven by fusion neu-tron sources [14–19] have predicted significantlyhigher levels of Pu, and minor actinide and/orlong lived fission product destruction than thosethat are predicted to be achievable in criticalnuclear reactors. The optimum scenario for recy-cling Pu, minor actinides and long lived fissionproducts in commercial thermal neutron spectrumreactors, in dedicated fast neutron spectrum reac-tors and in subcritical transmutation reactors drivenby neutron sources remains the subject of activeinvestigation.

It should be noted that there will be significanttechnical challenges associated with the implemen-tation of fission waste transmutation in either fusionor accelerator based neutron source subcritical facili-ties, and, indeed, in critical fission reactor transmuta-tion schemes. There will be a tendency to large powerdensity swings during the transmutation cycle due tochanges in fissionable fuel density and composition.There will be materials damage and materials com-patability issues to be addressed, and there will besafety issues associated with high power densities andlarge fission waste inventories. These concerns will bepresent for any transmutation system. Detailed stud-ies are required to address these issues and to evalu-ate both which transmutation scheme offers the bestsolution and whether or not any transmutation sys-tem is superior to long term monitored retrievablestorage.

3. Comparison of electricalpower characteristics of fusionand accelerator neutron sourcetransmutation facilities

3.1. Computational model

We use a simple, global particle balance to modelsource driven subcritical reactors. The point kineticsmodel describing the dynamics of the total neutronpopulation N in a nuclear reactor with an externalsource S is [23]

dN

dt=

k − 1− β

`N +

I∑i=1

λiCi + S (1)

anddCi

dt=

βiN

`− λiCi, i = 1, ..., I (2)

where the Ci represent the population of fission prod-ucts of species i which decay with half-life t1/2 =√

2/λi to release ‘delayed’ neutrons, βi is the fissionyield of delayed neutron precursor species i, β =∑

βI , k is the multiplication constant of the reac-tor assembly and ` = 1/(v

∑a) is the prompt neu-

tron lifetime, where v is the average neutron speedand

∑a is the macroscopic absorption cross-section

averaged over the neutron energy distribution. Theasymptotic solution of Eqs (1) and (2) yields theequilibrium neutron population in the reactor,

N =S`

1− k=

S/(v∑

a)1− k

. (3)

The effective multiplication constant can be writ-ten as the ratio of the neutron production rate to theneutron destruction rate,

k =(ν∑

f +2∑

n,2n +3∑

n,3n)∑Fa +

∑Lia +

∑Pa

PNL

≡ νγ∑

f PNL∑Fa +

∑Lia +

∑Pa

(4)

where ν is the average number of neutrons per fission,the factor γ takes into account the neutrons producedin (n,2n) and (n,3n) reactions, PNL is the non-leakageprobability that a neutron remains in the reactor tobe absorbed, and

∑xa is the macroscopic absorption

cross-section for the fissionable material (x = F), thelithium needed to breed tritium for the fusion neu-tron source (x = Li), and for absorption in the struc-ture and other parasitic material (x = p).

We assume that with the fusion neutron sourceit is necessary to produce tritium fuel, which


W.M. Stacey

requires a tritium breeding ratio (TBR) greater thanunity,

TBR =ΣLi

a Nv

S> 1. (5)

Combining Eqs (3) and (5) yields

ΣLia = Σa(1− k)TBR (6)

which can be used with Eq. (4) to relate the effec-tive multiplication constant with no Li present (k0

for TBR = 0) to the effective multiplication constantwhen Li is present in a reactor that is otherwise iden-tical,

k0 = k[1 + (1− k)TBR] (7)

The effective transmutation (fission) rate (TR) isdefined as

TR = vΣfN =S

1− k

Σf

Σa' Sk

ν(1 − k)(8)

since the non-fission capture of a neutron by anactinide essentially just converts that actinide intoanother actinide.

3.2. Input electrical power requirement

The input electrical power required to produce S

spallation neutrons per second is

P atwin,e =

EspallSatw

ηatwb

+P atw

aux

ηatwaux

=EspallSatw

ηatwb

[1 +

(P atw

aux

EspallSatw

)(ηatw

b

ηatwaux

)]

(9a)

where Espall is the energy on target per spalla-tion neutron produced, ηatw

b is the ratio of electricalenergy to energy on target (i.e. the beamline effi-ciency), P atw

aux is the power required to operate theauxiliary systems for the accelerator spallation neu-tron source transmutation facility and ηatw

aux is theefficiency of delivery of this energy to end use.

The input electrical power required to produce S

fusion neutrons per second is

P fusin,e =

EfusSfus

ηfusb Qp

+P fus

aux

ηfusaux

=EfusSfus

ηfusb Qp

[1 +

(P fus

aux

EfusSfus

)Qp

(ηfus

b

ηfusaux

)]

(9b)

where Efus/Qp is the injected plasma heating energyper fusion neutron produced, ηfus

b is the ratio of elec-trical energy into the heating system to the energyinto the plasma (i.e. the heating efficiency), P fus

aux isthe power required to operate the auxiliary systemsfor the fusion neutron source transmutation facilityand ηfus

aux is the efficiency of delivery of this energy toend use.

We will evaluate the ratio of input electrical powerrequired for fusion and accelerator spallation neutronsource transmutation facilities that produce the sametransmutation rate

Rin ≡P fus

in,e

P atwin,e

=(

Efus

Espall

)(ηatw

b

ηfusb

)(ξfusQp

)

×

[1 +

(P fus

aux

EfusSfus

)Qp

(ηfus

b

ηfusaux

)][1 +

(P atw

aux

EspallSatw

)(ηatw

b

ηatwaux

)]

(10)

Efus = 17.6 MeV/n and we use Espall = 25 MeV/n,corresponding to the production of 40 spallation neu-trons per 1 GeV ion. We assume the same efficien-cies for the plasma heating and accelerator systems,so that ηfus

b /ηatwb = 1.0. We assume ηfus

b /ηfusaux =

ηatwb /ηatw

aux = 0.8. We assume that 50 MW auxiliarypower is needed for a transmutation system that pro-duces 2.5× 1019 n/s and use Paux/S = 12.5 MeV/nfor both the fusion and the accelerator spallationtransmutation systems.

The requirement to breed tritium in the fusiontransmutation facility consumes neutrons that couldotherwise be used for transmutation. We considertwo different scenarios with regard to the treatmentof this tritium breeding requirement. In the first sce-nario, it is assumed that the transmutation facilityused with the fusion neutron source differs from thetransmutation facility used with the accelerator spal-lation neutron source only by the addition of suffi-cient Li to achieve TBR = 1.05. Thus, if the fusiontransmutation facility has a multiplication constantk, the ATW facility has a larger multiplication con-stant k0 given by Eq. (7), and the fusion facility mustproduce a neutron source larger by the factor

ξfus ≡ Sfus

Sspall=

1− k

1− k0=

1 + (1− k)TBR(1− k)TBR

(11)

in order for both facilities to have the same transmu-tation rate. We use γ = 1.05, ν = 2.9 and PNL = 0.95



INPUT ELECTRICAL POWER REQUIREMENT RATIO FUSION/ATW FOR SAME TRANSMUTATION RATE

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5 6 7 8 9 10

Qp

Pin

fus

/Pin

AT

W

Figure 1. Ratio of input electrical power required for the operation of fusion and ATW

neutron sources which produce the same transmutation rate in a subcritical transmutation

reactor. (Espall = 25 MeV/n, Efus = 17.6 MeV/n, Paux/S = 12.5 MeV/n, ν = 2.9, γ = 1.05,

ηfusb = ηatw

b = ηfuse = ηatw

e = 0.40, ηfuse /ηblkt

e = ηatwe /ηblkt

e = 0.9, ηatwb /ηatw

aux = ηfusb /ηfus

aux = 0.8:

k = 0.90 is the same with fusion and ATW neutron sources.)

to calculate k0 and ξfus . In the second scenario, weassume that the transmutation reactors used withthe fusion and accelerator neutron sources have thesame multiplication constant k, and hence the sameneutron source levels to produce the same transmu-tation rates. This would be accomplished by replac-ing a parasitic absorber with Li or by increasingthe fissionable material in the transmutation reactorfor the fusion neutron source relative to the ATWfacility.

The ratio of input electrical powers required toproduce the same transmutation rates in fusion andaccelerator spallation neutron source transmutationfacilities is shown as a function of plasma gain forthe second of the above Li scenarios in Fig. 1, forthe above parameters and k = 0.90. (The results fork = 0.85 and 0.95 differ only slightly.) For a plasmagain Qp greater than about 1.0–1.5, the requiredinput electrical power is less for a fusion neutronsource transmutation facility than for a similar ATWwhich produces the same transmutation rate. AtQp > 5, the input electrical power requirement fora fusion transmutation facility is about half or less

the requirement for an ATW with the same transmu-tation rate, for the parameters assumed above, andthe improvement is slight for Qp > 5. The resultsshown in Fig. 1 are in semi-quantitative agreementwith the results of a similar analysis based on a some-what simpler model [24].

3.3. Comparison of waste thermal energy

The thermal energy dissipated in the ATW andfusion neutron sources are EspallSatw and (1 +1/Qp)EfusSfus , respectively, and the thermal energygenerated by the fission and other exoergic processesin the transmutation reactor is (1+ε)EfisSx/(1−kx),where x = fus or atw, and ε is the ratio of energyproduced by other (than fission) exoergic reactionsto the energy produced by fission. The ratio of theamount of thermal energy that must be removedfrom transmutation facilities with fusion and accel-erator spallation neutron sources which produce thesame transmutation rate is


W.M. Stacey

Rth =Pfus,th/Satw

Patw,th/Satw= ξfus

(1 +

1Qp

)Efus

Espall

×

[1+

(1+ε)(1−kfus)

kfus

ν

(Efis

Efus

)(1

1+1/Qp

)][1+

katw

ν

(1+ε)(1−katw )

(Efis

Espall

)]

≡ Rsourceth

[1+

(1+ε)(1−kfus)

kfus

ν

(Efis

Efus

)(1

1+1/Qp

)][1+

katw

ν

(1+ε)(1−katw)

(Efis

Espall

)].

(12)

The ratio Rsourceth = ξfus(1 + 1/Qp)Efus/Espall of

the thermal energies dissipated in the fusion andaccelerator neutron sources has been calculated forthe two scenarios discussed earlier for treating thetritium breeding requirement for the fusion neu-tron source. A fusion neutron source will dissipatesomewhat more thermal energy at low Qp (<2) andsomewhat less thermal energy at higher Qp than anaccelerator neutron source, when both sources aredriving subcritical reactors with the same k valuesthat are producing the same transmutation rates(kfus = katw ).

The thermal energy produced in the transmuta-tion reactor by fission (Efis = 195 MeV/fission) is somuch greater than the thermal energy produced inthe neutron source that the ratio of the total ther-mal energy produced in fusion and accelerator spal-lation neutron transmutation facilities with the sametransmutation rate, given by Eq. (12), is essentiallyunity.

3.4. Comparison ofplant electrical energy gain

If the waste energy from the spallation neutronproduction (i.e. target heating) is collected and con-verted to electricity with efficiency ηspall

e and theenergy of the fission and other exoergic reactions inthe subcritical transmutation reactor is collected andconverted to electricity with efficiency ηblkt

e , the out-put electrical energy from a transmutation facilitydriven by an accelerator spallation neutron sourceis

P atwout,e =

(Espallη

atwe +

katw

ν

(1 + ε)Efisηblkte

1− katw

)Satw

(13a)

where ε = 0.05 accounts for the enhancement of thefission energy release by other exoergic reactions.

Assuming that the efficiency ηblkte of collecting

and converting to electricity the energy producedin the subcritical reactor assembly is the same withthe fusion and accelerator spallation neutron sources,the output electrical energy from a transmutationfacility driven by a fusion neutron source is

P fusout,e =

[Efusη

fuse

(1+

1Qp

)+

kfus

ν

(1+ε)Efisηblkte

1− kfus

]Sfus

(13b)

where ηfuse is the efficiency of collecting and convert-

ing to electricity the plasma heating energy and theenergy produced by fusion.

If the input power, fusion power and fission powerare recovered and converted to electricity, the ratioof the output electrical power to the input electricalpower

Qxe ≡

P xout,e

P xin,e

(14)

is known as the electrical Q value, or gain, of thesystem. For a fusion neutron source transmutationfacility this expression becomes

Qfuse = ηfus

e ηfusb

×

{1 + Qp

[1 +

kfus

ν

(1 + ε)(1− kfus)

(Efis

Efus

)(ηblkt

e

ηfuse

)]}[1 + Qp

(P fus

aux

SfusEfus

)(ηfus

b

ηfusaux

)].

(15)

We assume the same efficiencies for collectingand converting fusion and spallation heat, so thatηfus

e /ηatwe = 1.0, and we assume somewhat better

heat recovery from the transmutation blanket thanfrom the spallation target or the fusion plasma, sothat ηblkt

e /ηfuse = ηblkt

b /ηatwe = 0.9. The quantity Qfus

e

is plotted in Fig. 2, for three different values of themultiplication constant of the transmutation reactor.Clearly, net electrical power (Qe > 1) is possible forQp values even much below unity, for the parametersdiscussed above.



ELECTRICAL Q FOR TRANSMUTATION FACILITY WITH FUSION NEUTRON SOURCE

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5 6 7 8 9 10

Qp

Qe

k=0.85

k=0.90

k=0.95

Figure 2. Electrical energy gain Qfuse for a subcritical transmutation reactor plant with

fusion neutron source. (Efis = 195 MeV/fis, Efus = 17.6 MeV/n, Paux/S = 12.5 MeV/n,

ν = 2.9, γ = 1.05, ε = 0.05, ηfusb = ηfus


e = 0.9, ηfusb /ηfus

aux = 0.8.)

ELECTRICAL Q RATIO FUSION/ATW FOR SAME TRANSMUTATION RATE

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6 7 8 9 10

Qp

Qe

fus

/Qe

AT

W

Figure 3. Ratio of subcritical transmutation reactor plant electrical energy gain for the same

transmutation rate with fusion and ATW neutron sources. (Efis = 195 MeV/fis, Espall =

25 MeV/n, Efus = 17.6 MeV/n, Paux/S = 12.5 MeV/n, ν = 2.9, γ = 1.05, ε = 0.05,

ηfusb = ηatw

b = ηfuse = ηatw


e = ηatwe /ηblkt

e = 0.9, ηatwb /ηatw

aux = ηfusb /ηfus

aux = 0.8;

k = 0.90 is the same with fusion and ATW neutron sources.)


W.M. Stacey

The ratio of the electrical gains for fusion trans-mutation and ATW reactor systems which achievethe same transmutation rates is given by

Qfuse

Qatwe

=(

ηfuse

ηatwe

)(ηfus

b

ηatwb

)

×

{1 + Qp

[1 +

(1 + ε)(1− kfus)

kfus

ν

(Efis

Efus

)(ηblkt

e

ηfuse

)]}[1 +

(1 + ε)(1− katw )

katw

ν

(Efis

Espall

)(ηblkt

e

ηatwe

)]

×

[1 +

(P fus

aux

EspallSatw

)(ηatw

b

ηatwaux

)][1 + Qp

(P fus

aux

EfusSfus

)(ηfus

b

ηfusaux

)]. (16)

This ratio is plotted in Fig. 3 for the parametersdescribed above and for kfus = katw . For theseparameters, the plant electrical gain is greater forfusion transmutation plants with Qp > 1 thanfor ATW plants with the same transmutation rate.These results are in good semiquantitative agreementwith the results obtained in a similar analysis usinga somewhat simpler model [24].

We have checked the sensitivity of the calcula-tions to some of the input parameters. Doubling theauxiliary power per neutron reduces the Qe ratio byabout 33% at high Qp, but has little effect at lowQp. Increasing ηatw

b from 0.4 to 0.45 or decreasingηspall

e from 0.4 to 0.35 reduces this ratio by about15% at high Qp, but has little effect at low Qp, andchanging both the ratios ηfus

b /ηfusaux and ηatw

b /ηatwaux a

like amount has a negligible effect. Thus, the gen-eral nature of the comparisons of fusion and accel-erator spallation neutron source transmutation facil-ities shown in Figs 1 and 3 would seem to be rel-atively insensitive to modest uncertainties in plantparameter values, although a parameter such as theelectrical Qe for either system will vary linearly withηe and ηb.

We recognize that a comparison of transmuta-tion efficiency and neutron cost, as well as a com-parison of electrical and thermal power character-istics, is needed to fully evaluate a fusion neutronsource vis-a-vis an accelerator neutron source forspent fuel transmutation. However, a comparison ofefficiency and neutron cost depends not only on theneutron source but also on the subcritical transmu-tation facility, and is beyond the scope of this article.We have, however, begun such a study.

4. Limitations onfusion neutron source capabilitiesfor transmutation reactors

The factors determining the effect of possible neu-tron source limitations on the transmutation rate in asubcritical transmutation reactor can be understoodby examining Eq. (8). This equation can be put intodifferent forms to illustrate the effect of various pos-sible limitations of the neutron source capability onthe transmutation rate. We stress that we are exam-ining only limitations on transmutation rate thatwould be caused by limitations in neutron sourcecapability, not by engineering and safety constraintson the transmutation reactor itself.

4.1. Radiation damage limits to the first wall

Writing the neutron source in terms of the powerPn of En = 14 MeV neutrons through the first wallrelates the neutron source strength to the neutronwall load, or flux, Γn and first wall area Aw,

S =Pn

En=

(Pn/Aw)Aw

En=

Γavn Aw

En. (17)

This relation may be used in Eq. (8) to write thetransmutation rate as

TR =S

1− k

k

ν=

Γavn Aw(k/ν)En(1 − k)

(18a)

from which the annual transmutation rate TRA(kg/FPY) may be written in terms of the annualfluence, the area of the first wall and the effectivemultiplication constant of the transmutation reactor

TRA [g/FPY] =

5.55(k/ν)(Γavn t) [MW−FPY/m2] Aw [m2]

1− k(18b)

where FPY refers to full power year.A given transmutation rate can obviously be

achieved in a number of ways by making trade-offsbetween neutron wall load and first wall area on theone hand and the effective multiplication constanton the other. The upper limit on the effective mul-tiplication constant is set by safety considerations; k

should be sufficiently less than unity that no credibleevent could cause a reactivity increase ∆k that wouldmake the transmutation reactor prompt critical; i.e.k + ∆k must remain less than 1 + β for any credi-ble accident, where β is the delayed neutron fraction(β = 0.0020 for 239Pu, 0.0029 for 240Pu and 0.0054for 241Pu). The wall area depends on the size of the



neutron source, of course, which can be made as largeas desired for a fusion neutron source.

The first wall will fail when the accumulated neu-tron fluence Γmax

n t reaches some limiting value (1–3 MW FPY/m2 for existing austenitic stainless steeland considerably more for advanced structural alloyspresently under development). A practical require-ment might be that the first wall lifetime be as longas the refuelling interval for the transmutation reac-tor. Assuming a 1 FPY refuelling interval and tak-ing a limiting neutron fluence of 2 MW FPA/m2

and a first wall area of 450 m2 (representative ofan R ≈ 5 m tokamak), a transmutation reactor withk = 0.90 driven by a fusion neutron source wouldbe limited by materials damage to a transmutationrate of TRA ≈ 50 000 kg/FPY. Assuming a first wallarea of 100 m2 (perhaps representative of advancedconfinement concepts in the early stages of develop-ment), radiation damage in an austenitic stainlesssteel first wall would limit the transmutation rateto TRA ≈ 10 000 kg/FPY. Such large transmuta-tion rates are unrealistic for other reasons (handlingthe engineering challenges of such a large thermalpower output and the safety challenges of such alarge mass of fissile material in the transmutationreactor being foremost among them). As a point ofreference, the present ATW plan is to fission less than2000 kg/FPY of actinides in a single transmutationreactor, and studies of critical fission transmutationreactors typically have transmutation rates of lessthan 1000 kg/FPY. The main points are that:

(a) A practical fusion neutron source is unlikely tobe limited by radiation damage to the first wall,even for the presently available austenitic stain-less steels;

(b) A fusion neutron source for transmutation couldmeet its objectives operating at rather low neu-tron wall loads (�1 MW/m2).

We will make a more quantitative investigation ofthese points later in this section.

4.2. Thermal limits to the first wall

The thermal power Pth which must pass throughthe first wall of the fusion neutron source is thesum of Eα = 3.5 MeV alpha particle energy perfusion and the input plasma heating power, whichmay be related to the fusion power Pfus = SEfus byQp = Pfus/Pheat . A fraction fdiv of this power will beexhausted in the divertor, and a fraction 1−fdiv willbe incident on the first wall of the neutron source as

a heat flux. Thus, the fusion neutron source may bewritten as

S =Pth

(Eα + Efus/Qp)(1 − fdiv )

=ΓthAw

Efus

(Eα

Efus+

1Qp

)(1− fdiv )

(19)

and the corresponding form for the transmutationrate becomes

TR =(k/ν)S1− k

=(k/ν)ΓthAw

Efus

(Eα

Efus+

1Qp

)(1−k)(1−fdiv)

.

(20a)

In terms of transmutation rate per FPY thisbecomes

TRA (kg/FPY) =4.44(k/ν)Γth [MW/m2] Aw [m2](

1Qp

+15

)(1 − k)(1− fdiv )

.

(20b)

The maximum surface heat flux for an austeniticstainless steel first wall is about 0.5 MW/m2. Takingan average heat flux of half this value to accountfor peaking, assuming a diverted heat fraction offdiv = 0.5 and assuming Qp = 5, Aw = 450 m2 andk = 0.90, the transmutation rate would be limited toabout 25 000 kg/FPY by first wall heat flux removallimitations. Assuming instead Aw = 100 m2, thefirst wall thermal limit on the transmutation rate foraustenitic steel is about 5500 kg/FPY. Again, theseare quite large transmutation rates, and the pointis that thermal limitations on an austenitic stain-less steel first wall of the neutron source should notlimit the transmutation rate achievable in a trans-mutation reactor driven by a fusion neutron source.This point will be investigated more quantitativelyin Section 4.3.

4.3. Tokamak physics limits

The plasma physics of the fusion neutron sourcealso imposes certain constraints on the realizablesource performance. The existing physics basis for atokamak neutron source is well characterized by thetokamak physics database compiled for ITER [6]. Forour purposes, we can consider five such physics con-straints to characterize the physics limitations on atokamak neutron source.


W.M. Stacey

Assurance of MHD stability of existing tokamakplasmas can be characterized by the requirementthat the normalized beta parameter

βN =β%

IMA/amBT(21)

does not exceed 2.5–3.0 and that the safety factorevaluated at the 95% flux surface

q95 =5BT Rm

2A2IMA[1 + κ2(1 + 2δ2 − 1.2δ3)]

×(

1.17− 0.65/A

1−A−2

)(22)

be not less than about 3. Here BT is the toroidalmagnetic field in teslas, IMA is the plasma current inmegamps, A = R/a is the ratio of the plasma majorto minor radii, κ is the elongation of the plasma,δ is a parameter known as the triangularity whichcharacterizes the degree of D shape of the plasmaand β is the ratio of the plasma kinetic pressure tothe pressure of the magnetic field,

β =nDTTDT + neTe + nimpTimp + nfEf

B2/2µ0. (23)

The DT ions, electrons (e), impurities (imp) and fast(f) beam and alpha particles contribute to the kineticpressure of the plasma.

The plasma must have adequate energy confine-ment to achieve a power balance between the self-heating from the fusion alpha particles plus anyauxiliary (NBI or RF) heating and losses due totransport and radiation. Consideration of the plasmapower balance indicates that the energy confinementtime must be about τign = 5 s to maintain the powerbalance at about 10 keV average temperature in theabsence of auxiliary heating and that the energy con-finement time must be about τign/(1 + 5/Qp) whenauxiliary heating is present. The tokamak databasefor ELMy H mode discharges is well correlated tothe tokamak parameters by the ITER-98H scalinglaw τ = τ98(I, B, Pfus , ...). Thus, achieving suffi-cient energy confinement to maintain power balanceimposes the confinement constraint

τign

1+5

Qp

= 0.05H I0.91MA B0.15

T n0.4419

[Pfus

(15

+1

Qp

)]−0.65

× R2.05κ0.72M0.13A−0.57 (24)

where H is the confinement enhancement factor, M

is the plasma ion mass in amu, A is the ratio of themajor to minor axes of the tokamak, n19 is the den-sity in units of 1019 m3, Pfus is in megawatts and

the units of the other quantities are indicated by thesubscripts.

The fusion power

Pfus = 14n2

DT 〈σv〉Uα(πκa2)(2πR) (25)

not only depends on the density, which is constrainedby the MHD and confinement constraints, but isalso involved in the confinement constraint, so thatEq. (25) is actually a fourth physics constraint. Here,〈σv〉 is the Maxwellian averaged fusion rate andUα = 3.5 MeV is the energy of the DT fusion alphaparticle which remains in the plasma to heat it.

A fifth physics constraint, thought to be due tothermal instabilities in the plasma, is an upper limiton the achievable plasma density. This upper limit onthe density can be correlated remarkably well over awide range of tokamak experiments with the simple‘Greenwald limit’,

n ≤ nGW ≡ IMA

πa2m

(26)

although there are many examples of tokamak oper-ation well above (up to about twice) the Greenwaldlimit.

In order to understand how these physics limitsmight constrain the performance of a fusion neu-tron source for a subcritical transmutation reac-tor, we have fixed various parameters (B = 5.5 T,q95 = 4, A = 3, T = 12 keV) and solved Eqs (21),(22), (24) and (25) for (I, n, R, Pfus) as a functionof Qp and δN . For this purpose we assumed β =2.1nDTTDT/(B2/2µ0). We carried out the calcula-tions with a set of confinement and shape parame-ters characteristic of the present tokamak database(H = 1, κ = 1.7, δ = 0.5) and with a second‘advanced’ set characteristic of improved confine-ment regimes presently under intensive investigationand a higher degree of shaping (H = 1.5, κ = 2.0,δ = 0.8). We considered several values of the param-eter βN , including values within the presently estab-lished database of βN < 3 and values within theadvanced range βN > 3 that is presently under inves-tigation.

In order to relate these calculations of physicsperformance to the transmutation rate, we write

TRA =(k/ν)S1− k

=4.44(k/ν)Pfus (MW)

1− k(kg/FPY).

(27)

We choose k = 0.90 for the calculations because thisvalue of the multiplication constant provides a largemargin to criticality and allows for the processing



TRANSMUTATION RATE

104

103

102

10

1

1 2 3 4 5 6 7 8 9 10

Qp

H=1,βN=1

H=1,βN=2

H=1,βN=3

H=1,βN=4

H=1.5,βN=1

H=1.5,βN=2

H=1.5,βN=3

H=1.5,βN=4

TR

A (

kg/F

PY

)

Figure 4. Transmutation rate in subcritical transmutation reactor driven by a toka-

mak fusion neutron source (k = 0.90, B = 5.5 T, q95 = 4, τign = 5 s, T = 12 keV).

of spent fuel with large concentrations of parasiticabsorbers present. The transmutation (fission) rateis, of course, directly related to the fission thermalpower production rate in the transmutation reactor

Pfis =k

ν

Pfus

1− k

Efis

Efus=

11.11− k

k

νPfus . (28)

Each kg/FPY transmutation rate corresponds to afission thermal power production rate of about 2.48MW, when k = 0.90.

In order to relate the physics performance to theneutron wall load/radiation damage limit and thethermal limit on the first wall discussed above, wewrite

Γn =45Pfus√

12 (1 + κ2)(2πa)(2πR)

(29)

and

Γth =15Pfus(1 − fdiv )√

12 (1 + κ2)(2πa)(2πR)

(30)

and carry out the calculation for fdiv = 0.5.The results of these calculations are plotted in

Figs 4–10, study of which leads to several interest-ing conclusions. Foremost among these is the con-clusion that parameters routinely achieved in oper-ating tokamaks (i.e. those that are part of the present

tokamak database (H = 1, βN = 2–3)) are sufficientfor a tokamak neutron source operating with den-sities below the Greenwald limit to produce trans-mutation rates of several hundred to several thou-sand kg/FPY in a reactor with k = 0.9. Suchtokamak neutron sources would have major radii inthe range R = 3–5 m, produce fusion power in therange Pfus = 10–100 MW and drive transmutationreactors that produce fission thermal power in therange Pfis ≈ 1000–10000 MW. Achieving improvedconfinement (H = 1.5) will enable these same trans-mutation rates to be achieved with smaller (andpresumably less expensive) neutron sources.

As a point of reference, the proposed ATW plantwould use two 45 MW proton beams to produce840 MW thermal energy in each of eight target trans-mutation assemblies, for a total thermal power out-put of 6720 MW, in order to produce a transmutationrate of 1760 kg/FPY.

A second important conclusion is that Qp = 2–5is adequate for the neutron source, since the trans-mutation rate increases only slowly above Qp = 5but drops sharply below Qp = 2. Furthermore, theinput electrical power requirement and the wasteheat production rate for a fusion neutron source,relative to an accelerator spallation neutron source,


W.M. Stacey

FUSION POWER

0.1

1

10

100

1000

1 2 3 4 5 6 7 8 9 10

Qp

Pfu

s (

MW

) H=1,βN=1

H=1,βN=2

H=1,βN=3

H=1,βN=4

H=1.5,βN=1

H=1.5,βN=2

H=1.5,βN=3

H=1.5,βN=4

Figure 5. Fusion power in tokamak fusion neutron sources for subcritical transmu-

tation reactors (k = 0.90, B = 5.5 T, q95 = 4, τign = 5 s, T = 12 keV).

MAJOR RADIUS

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10

Qp

H=1,βN=1

H=1,βN=2

H=1,βN=3

H=1,βN=4

H=1.5,βN=1

H=1.5,βN=2

H=1.5,βN=3

H=1.5,βN=4

R (

m)

Figure 6. Major radii of tokamak fusion neutron sources for subcritical trans-

mutation reactors (k = 0.90, B = 5.5 T, q95 = 4, τign = 5 s, T = 12 keV).

both become much more favourable above aboutQp = 1.5–2 but are relatively insensitive to furtherincreases in Qp beyond about 5.

A third important conclusion is that βN = 2–3seems to be the correct range for achieving theseinteresting transmutation rates (with k = 0.9), since

βN = 1 leads to transmutation rates that are too lowto be interesting and βN = 4 leads to transmutationrates that are so large as to imply large size, fissileinventory and heat removal challenges in the designof the transmutation reactor. We note in this regardthat since the transmutation rate shown in Fig. 6



PLASMA CURRENT

0

2

4

6

8

10

12

14

16

1 2 3 4 5 6 7 8 9 10

Qp

I (M

A)

H=1&1.5,βN=1

H=1&1.5,βN=2

H=1&1.5,βN=3

H=1&1.5,βN=4

Figure 7. Plasma current in tokamak fusion neutron sources for subcritical transmutation

reactors (k = 0.90, B = 5.5 T, q95 = 4, τign = 5 s, T = 12 keV).

scales as (1 − 0.9)k/0.9(1− k), interesting transmu-tation rates could also be achieved at βN < 2 intransmutation reactors with k > 0.9 and at βN > 3in transmutation reactors with k < 0.9.

The basis of these calculations, the estimatedcharacteristic parameters allowed by physics con-straints for tokamak neutron sources based on nom-inal (H = 1) and advanced (H = 1.5) confinementphysics is summarized in Table 1.

4.4. Engineering limits on a tokamak fusionneutron source

The smaller end of the size range indicated inFig. 6 and Table 1 would have to use copper mag-netic technology rather than superconducting mag-net technology, and even then some of the casesshown may be excluded by engineering limits. Forexample, at R = 2 m and a = 0.67 m (A = 3), a5 MA inductive current capability (for backup andtesting) would require about 8.5 V/s, which wouldnecessitate a flux core radius afc ≈ 0.5 m at a maxi-mum field of 10 T in the ohmic heating coil, leavingonly 2−0.67−0.5 = 0.83 m for the ohmic heating coil,the toroidal field coil and any inboard section of thetransmutation reactor, which at most would be justa very thin neutron shield. (See Ref. [25] for a dis-cussion of the engineering limitations on the size oftokamaks.) With such a small-R neutron source, that

Table 1. Characteristic parameters of tokamak fusion

neutron sources that produce transmutation rates of hun-

dreds to thousands of kg/FPY in transmutation reactors

with k = 0.9

Nominal AdvancedParameter

database database

H confinement 1.0 1.5

βN 2–3 2–3

Qp 2–5 2–5

B (T) 5.5 5.5

τign (s) 5 5

κ, δ 1.7, 0.5 2.0, 0.8

q95 4 4

n/nGW 0.4–1.0 0.2–0.6

R (m) 3–5 2–3

I (MA) 6–10 6–10

Pfus (MW) 10–100s 10–100s

Γn (MW/m2) 0.1–0.3 0.15–0.5

Γth (MW/m2) 0.02–0.09 0.03–0.15

the fraction (perhaps 20%) of the neutrons directedinwards (towards the major axis of the tokamak)would be absorbed in the copper magnets and shield,effectively reducing the neutron source to the trans-mutation reactor proportionately.

At R = 4 m and a = 1.33 m, a 5 MA induc-tive current capability would require about 35 V/s,which would necessitate afc ≈ 1.05 m, leaving about


W.M. Stacey

DENSITY NORMALIZED TO GREENWALD

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 2 3 4 5 6 7 8 9 10

Qp

n/n

GW

H=1,βN=1

H=1,βN=2

H=1,βN=3

H=1,βN=4

H=1.5,βN=1

H=1.5,βN=2

H=1.5,βN=3

H=1.5,βN=4

Figure 8. Greenwald normalized densities in tokamak fusion neutron sources for

subcritical transmutation reactors (k = 0.90, B = 5.5 T, q95 = 4, τign = 5 s, T =

12 keV).

NEUTRON WALL LOAD

0.001

0.01

0.1

1

10

1 2 3 4 5 6 7 8 9 10

Qp

H=1,βN=1

H=1,βN=2

H=1,βN=3

H=1,βN=4

H=1.5,βN=1

H=1.5,βN=2

H=1.5,βN=3

H=1.5,βN=4

Γ n (

MW

/m2 )

Figure 9. Neutron wall loads in tokamak fusion neutron sources for subcritical

transmutation reactors (k = 0.90, B = 5.5 T, q95 = 4, τign = 5 s, T = 12 keV).

1.6 m on the inboard side for the ohmic and toroidalcoils and the shielding. This is still neither enoughspace on the inboard side for shielding to enable useof superconducting magnet technology nor enough

space for placing transmutation assemblies on theinboard ≈20% of the neutron source. Thus, the effec-tive neutron source for transmutation would again bereduced by ≈20%.



THERMAL WALL LOAD

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

1 2 3 4 5 6 7 8 9 10

Qp

H=1,βN=1

H=1,βN=2

H=1,βN=3

H=1,βN=4

H=1.5,βN=1

H=1.5,βN=2

H=1.5,βN=3

H=1.5,βN=4

Qth

(M

W/m

2 )

Figure 10. Thermal wall loads in tokamak fusion neutron sources for subcritical

transmutation reactors (k = 0.90, B = 5.5 T, q95 = 4, τign = 5 s, T = 12 keV).

At R = 5 m and a = 1.67 m, a 5 MA inductivecurrent capability would require about 44 V/s, whichwould necessitate afc ≈ 1.18 m, leaving about 2.15 mon the inboard side for ohmic and toroidal coils andan inboard transmutation blanket or shield. At thissize, superconducting technology could be used if ashield was place on the inboard ≈20% of the toka-mak surface, once again reducing the neutron sourceto the transmutation reactor by≈20%. Alternatively,copper magnet technology could be used and someof this inboard volume could be occupied by trans-mutation assemblies.

Thus, except for the larger end of the range ofR shown in Table 1 and Fig. 6, the effective neu-tron source to the transmutation reactor would bereduced by as much as about 20% by engineering lim-itations on the inboard ‘radial build’ of the tokamakneutron source. Even with this reduction in effectiveneutron source level, the transmutation rates for therange of devices indicated in Table 1 remain veryinteresting for transmutation reactors.

5. Status of fusion developmentvis-a-vis a neutron source

Substantial progress has been made in recentyears in achieving the plasma conditions required

for a tokamak fusion neutron source. Using DT fuel,fusion powers exceeding 10 MW have been pro-duced in both TFTR and JET. DT plasmas in thesedevices have approached the conditions required forQp = 1. Operating with deuterium plasmas, JT60-Uhas reached parameters exceeding those required forQp = 1.

These recent experimental accomplishmentsreflect a rapid growth in the understanding of thephysics of anomalous transport in thermonuclearplasmas and of other aspects of tokamak behaviour.Coupled with an extensive tokamak physics databasegathered from dozens of tokamaks around the world[6], there now exists a knowledge base sufficient todesign tokamak reactors or neutron sources that willachieve Qp � 1, with high confidence.

Several concepts have been proposed for machinescapable of reaching Qp � 1 or even ignition, wherethe power produced by alpha particles in DT fusionreactions balances all energy losses from the plasma.While economic considerations dictate that electric-ity producing fusion reactors operate with very largeenergy gain Qp � 10, fusion neutron source appli-cations such as spent nuclear fuel transmutationrequire only modest Qp to be competitive. As we sawin the last section, Qp ≈ 2–5 is needed for a fusionneutron source coupled to a transmutation reactor


W.M. Stacey

with k = 0.9, and even smaller values of Qp could beused with larger values of k. An upgrade of the JETfacility has been proposed which, if approved, couldachieve Qp ∼ 2 within a few years. From the plasmaperformance standpoint, fusion has demonstrated alevel of performance where fusion neutron sourceapplications can be seriously considered. The remain-ing physics development required is associated withachieving higher annual neutron fluence accumula-tion, which involves a combination of achieving muchlonger burn pulses and higher reliability/availability.

The classical tokamak is a pulsed device with thecurrent driven inductively. Although inductive burnpulses of 1000 s or more can be envisioned in a reac-tor size (R > 5–6 m) tokamak, the plasma dischargemust ultimately be terminated while the inductivecoil is recharged. High fluence accumulation applica-tions requiring very long pulse or nearly steady stateoperation, such as may be the case for transmutationof spent fuel, require that inductive current drive besupplemented, if not entirely replaced, by some formof non-inductive current drive.

Non-inductive methods for driving current intokamaks on the basis of injection of energetic parti-cles or RF waves are well developed. Since such meth-ods are less efficient than inductive current drive, acentral issue is the achievable gain Qp. By optimiz-ing the conditions favourable to the generation ofthe bootstrap current driven by pressure gradients,the current required to be driven by RF or beamsources can be minimized, greatly enhancing the pos-sibility of achieving Qp � 1. Significant progress hasbeen made in developing well confined tokamak oper-ational regimes with high bootstrap current fraction.Extending these regimes to true steady state pro-vides the focus for much of present day tokamakresearch. The status of resolving this most impor-tant (availability relies upon it) remaining physicsissue is summarized in Ref. [26].

It is planned to build the successor to the presentgeneration of large tokamaks, ITER [20], through aninternational collaboration supported by the govern-ments of Europe, Japan and the Russian Federation.The present ITER design is for a device that canoperate in DT with an energy gain Qp ≥ 10 in theinductive mode and Qp ∼ 5 in the non-inductive orsteady state mode. The inductive mode is based onthe type of tokamak operation that resulted in thehigh performance regimes obtained in JET and JT-60U. Non-inductive operation is based on the steadystate operating modes that are now in an advancedstate of development. Total fusion power in either

case will be ∼500 MW and the neutron wall load-ing will be 0.5 MW/m2. These ITER plasma perfor-mance parameters are considerably more demandingthan those identified in the previous section for atokamak fusion neutron source for spent nuclear fueltransmutation (fusion power ≈10–100 MW, neutronwall loading ≈0.1–0.5 MW/m2).

A substantial (7.5×108 US dollars) tokamak tech-nology R&D programme for ITER has been carriedout in parallel with the design effort. All technolo-gies required for steady state operation of a burn-ing DT plasma were developed and tested in (nearfull scale for ITER, larger than full scale for a neu-tron source) test facilities, including superconduct-ing magnets, plasma heating, DT fuel processing,vacuum vessel fabrication, remote maintenance andboth plasma and nuclear heat removal systems. Suc-cessful validation of these technologies has provideda high degree of confidence that a machine in theITER class (and a smaller neutron source) can bebuilt and reach its design performance parameters.

The timescale for construction of ITER is about10 years, and the capital cost is expected to be in therange of (3–4)×109 US dollars. Should this device bebuilt, it would demonstrate the integration in a singlefacility of the critical fusion physics and technologiesrequired for a tokamak fusion neutron source for thespent nuclear fuel transmutation application. ShouldITER not be built, a (smaller) neutron source proto-type would be necessary to integrate the physics andtechnology, and to demonstrate the potential for highavailability operation.

Existing austenitic steels which could be usedfor the first wall between the plasma and thesurrounding material are estimated to have a life-time against material damage by 14 MeV neu-trons of 1–3 MW a/m2, and ferritic steels and vana-dium alloys which are under development for thisapplication may have a considerably longer lifetime.Our estimates of the minimum first wall 14 MeVneutron annual fluence needed from a fusion neu-tron source for a subcritical transmutation reactorare ≤0.5 MWFPY/m2 (as low as 0.05 MWa/m2),which are significantly lower than the annual flu-ence requirements (∼1–2 MWa/m2) which are usu-ally projected for an electric power demonstrationtokamak reactor [25]. However, there will be a sig-nificant fluence of fission neutrons on the first wall,as well as the 14 MeV fusion neutrons. Nevertheless,it would seem that existing austenitic stainless steelshould be adequate for the structural material in afusion neutron source for a transmutation reactor,



and it does not appear that a materials developmentprogramme for advanced first wall materials wouldbe required in support of a fusion neutron source fora transmutation reactor.

The nuclear (fuel, coolant, separation) technol-ogy being evaluated and developed in the ATW [5]and OECD/NEA [1] activities must be adapted toprovide for tritium self-sufficiency of the fusion neu-tron source and to accommodate the tokamak neu-tron source geometry. For Pb–Bi coolant, one of theleading candidates under consideration, the additionof Li would seem to be a relatively straightforwardadaptation, although the safety implications remainto be examined. Moreover, MHD effects for a liquidmetal in a magnetic field is an additional issue thatmust be resolved. In any case, the requirement is toadapt technology otherwise being developed in theATW nuclear programme, not to take on the entiredevelopment of such technology.

6. Conclusions

The most significant conclusion of this study isthat the parameters routinely achieved in operat-ing tokamaks (i.e. are part of the present tokamakdatabase (H = 1, βN = 2–3)) are sufficient fora tokamak neutron source operating with densitiesbelow the Greenwald limit to produce transmutationrates of several hundred to several thousand kg/FPYin a transmutation reactor with k = 0.9. Such toka-mak neutron sources would have major radii in therange of 3–5 m, produce fusion power in the range oftens to thousands of megawatts and drive transmu-tation reactors that produce fission thermal power inthe range ≈103–105 MW. Achieving improved con-finement (H = 1.5) will enable these same transmu-tation rates to be achieved with smaller (and pre-sumably less expensive) neutron sources.

A second important conclusion is that Qp = 2–5 isadequate for the neutron source, since the transmu-tation rate increases only slowly above Qp = 5 butdrops sharply below Qp = 2. Furthermore, the inputelectrical power requirement and the waste heat pro-duction rate for a fusion neutron source, relativeto the same quantities for an accelerator spallationneutron source, both become much more favourableabove about Qp = 1.5–2 but are relatively insensitiveto increases in Qp beyond about 5.

A third important conclusion is that βN = 2–3seems to be the right range for achieving these inter-esting transmutation rates (with k = 0.9).

Fusion plasma performance and technology havenow been developed and demonstrated to a levelwhere fusion neutron source applications can be seri-ously considered. The remaining physics develop-ment required is associated with achieving higherannual neutron fluence accumulation, which involvesa combination of achieving much longer burnpulses by means of non-inductive current drive andachieving higher reliability/availability. The princi-pal remaining technology development needed forusing a fusion neutron source to drive a subcriti-cal fission transmutation reactor is associated withadapting the transmutation reactor nuclear technol-ogy to produce the tritium fuel needed for the fusionneutron source and to accommodate the tokamakgeometry. Existing austenitic stainless steel shouldsuffice as the structural material for a fusion neu-tron source. A prototype experiment to integratethe physics and technology and to demonstrate thepotential for high availability operation is neededprior to construction of a fusion neutron source for atransmutation reactor.

A DT fusion neutron source operating in the rangeQp = 2–5 would require significantly less electri-cal input power but would produce greater thermalenergy than an accelerator spallation neutron sourcewhich produces the same transmutation rate in atransmutation reactor. If the thermal energy is con-verted to electricity, a transmutation reactor drivenby a DT fusion neutron source operating in the rangeQp & 2 would have a significantly larger plant electri-cal energy gain than a similar transmutation reactordriven by an accelerator spallation neutron source.

Other than availability/reliability considerations,the requirements for a fusion neutron source for spentfuel transmutation are significantly lower than therequirements for an electrical power demonstrationplant [25]. This conclusion suggests that such a fusionneutron source would be an appropriate intermedi-ate term objective in the international fusion pro-gramme. This would utilize fusion for an importantinternational project, while at the same time provid-ing a less costly (in the near term) path for advanc-ing the status of fusion development towards theultimate goal of electrical power production.

We conclude with a recognition that the ‘devil isalways in the details’ and that detailed studies areneeded to confirm the promising characteristics oftokamak fusion neutron sources for spent nuclear fuelthat have been identified by the rather broad analysisof this article.


W.M. Stacey

Acknowledgements

The material in Sections 1, 2 and 5 of this articlewas developed in the process of preparing a WhitePaper [27] on the subject. The author is grateful tohis co-authors on the White Paper — D. Baldwin,R. Parker and J. Schmidt — for their contributionsto, and comments on, the White Paper, to D. Wadeand J. Laidler for their comments on drafts of theWhite Paper, and to G. Van Tuyle for discussionsabout the US ATW programme.

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[4] Sailor, W.C., et al., Prog. Nucl. Energy 28 (1994)

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[7] Parker, R.R., Nucl. Fusion 40 (2000) 473.

[8] Chuyanov, V.A., Nucl. Fusion 40 (2000) 495.

[9] Mondino, P.L., et al., Nucl. Fusion 40 (2000) 501.

[10] Zhil’tsov, V.A., et al., Nucl. Fusion 40 (2000) 509.

[11] Yamanishi, T., et al., Nucl. Fusion 40 (2000) 515.

[12] JET Team, Nucl. Fusion 39 (1999) 611.

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[14] Parish, T.A., Davidson, J.W., Nucl. Technol. 47

(1980) 324.

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[19] Qiu, L.J., et al., Nucl. Fusion 40 (2000) 629.

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[23] Ibid, Ch. 6.

[24] Jassby, D.L., Schmidt, J.A., Electrical Energy

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[25] Stacey, W.M., Nucl. Fusion 35 (1995) 1369.

[26] Engelmann, F., Nucl. Fusion 40 (2000) 1025.

[27] Stacey, W.M., Baldwin, D.E., Parker, R.R.,

Schmidt, J.A., Neutron Transmutation of Spent

Nuclear Fuel — an Intermediate Term Objective for

Magnetic Fusion, White Paper (2000).

(Manuscript received 19 June 2000Final manuscript accepted 19 October 2000)

E-mail address of W.M. Stacey:[email protected]

Subject classification: N0, Tt


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