PAPER • OPEN ACCESS
Hyb id hyd ogen-elec ici y p oduc ion using
sphe ical okamaks: a cos -d i e sensi i i y s udy
and echno-economic analysis
To ci e his a icle: J. Hidalgo-Sala e i
e al
2025
Nucl. Fusion
65 036027
View he a icle online o upda es and enhancemen s.
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In e na ional A omic Ene gy Agency
Nuclea Fusion
Nucl. Fusion 65 (2025) 036027 (15pp) h ps://doi.o g/10.1088/1741-4326/adaa01
Hyb id hyd ogen-elec ici y p oduc ion
using sphe ical okamaks: a cos -d i e
sensi i i y s udy and echno-economic
analysis
J. Hidalgo-Sala e i1,a,∗, T. G i i hs2,a, Z. Xue eb Con i3, P. Cano-Megias4,
R. Chaca egui5, M. Bluck2, J. Ayllon-Gue ola1, A. Mancini6, M. Ga cia-Munoz6
and E. Viezze 6
1Depa men o Mechanical Enginee ing and Manu ac u ing, Uni e si y o Se ille, Se ille, Spain
2Depa men o Mechanical Enginee ing, Impe ial College London, London, Uni ed Kingdom o G ea
B i ain and No he n I eland
3Da a-Cen ic Enginee ing, The Alan Tu ing Ins i u e, London, Uni ed Kingdom o G ea B i ain and
No he n I eland
4Max-Planck Ins i u ü Plasmaphysik, Ga ching, Ge many
5Depa men o Ene gy Enginee ing, Uni e si y o Se ille, Se ille, Spain
6Depa men o A omic, Molecula and Nuclea Physics, Uni e si y o Se ille, Se ille, Spain
E-mail: jhsala[email p o ec ed]
Recei ed 22 Janua y 2024, e ised 27 No embe 2024
Accep ed o publica ion 14 Janua y 2025
Published 18 Feb ua y 2025
Abs ac
Hyb id usion powe plan s, which p oduce bo h hyd ogen and elec ici y, a e p oposed as a
way o deca bonise he ossil- uel-domina ed p ima y ene gy ma ke and imp o e plan
economics. The main cos d i e s o a usion powe plan based on a sphe ical okamak ha e
been iden i ied using s a is ical analysis (Mo is and Sobol me hods) om a wide ange o cases
ob ained wi h he sys ems code PROCESS. The analysis e eals he impo ance o plasma
physics and eac o geome y on powe plan economics. Th ee scena ios o ad ancing
echnophysical assump ions (conse a i e, mode a e and op imis ic) ha e been chosen o s udy
he in eg a ion o he usion eac o wi h he powe block (Rankine, He-B ay on o
supe -c i ical-CO2-Fehe ) and wi h he PEM elec olyse . The supe -c i ical-CO2cycle e u ns
he bes esul s o he s udied empe a u e ange (500 ◦C–800 ◦C), wi h an e iciency be ween
40%–56%. The modelled PEM is in line wi h cu en comme cial models wi h a consump ion
o 51.97 kWh kg−1H2. The economic easibili y o hese scena ios has been explo ed o a se
o lea ning ac o s ha conside he cheapening o he capi al cos s ied o expe ience. The
LCOE o hese scena ios ha e been compa ed agains cu en p ice anges o sola , wind and
ission powe and he LCOH agains PEM p ices, showing ha he mode a e and op imis ic
aEqual con ibu ion
∗Au ho o whom any co espondence should be add essed.
O iginal Con en om his wo k may be used unde he
e ms o he C ea i e Commons A ibu ion 4.0 licence. Any
u he dis ibu ion o his wo k mus main ain a ibu ion o he au ho (s) and
he i le o he wo k, jou nal ci a ion and DOI.
1741-4326/25/036027+15$33.00 P in ed in he UK 1 © 2025 The Au ho (s). Published by IOP Publishing L d on behal o he IAEA
Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Sala e i e al
scena ios could be compe i i e o lea ning ac o s lowe han 0.5 and capaci y ac o s la ge
han 0.7. An ex apola ion o he op imis ic scena io shows ha he hyb id usion powe plan in
he F ench and Ge man ma ke can imp o e he plan p o i s by 15% and 66% espec i ely.
Keywo ds: PROCESS, sphe ical okamaks, comme cial powe plan s, echnoeconomics,
hyb id hyd ogen p oduc ion, powe plan sensi i i y s udy, s a is ical analysis
(Some igu es may appea in colou only in he online jou nal)
1. In oduc ion
In 2019, elec ici y made up 20% o global p ima y ene gy
consump ion and is p edic ed o ise o 25% by 2040 [1].
This means ha h ee qua e s o he ene gy demand needs
o be me by non-elec ic ene gy esou ces. The majo i y o
hese non-elec ic esou ces a e he mally consumed, i.e. a
uel is used o gene a e hea ha may be an in e media e s ep
o he inal p oduc . I is also likely ha by 2050, due o
pushes o global deca bonisa ion, he elec ici y ma ke will
al eady be sa u a ed wi h low-ca bon echnologies. Nuclea
usion can se e as he co ne s one o ca bon- ee ene gy
gene a ion. Howe e , a ge ing he elec ici y ma ke alone
will no add ess he emaining 75% o non-elec ic p ima y
ene gy consump ion. Fusion powe , owing o i s he mal o i-
gin, has been sugges ed o di e se applica ions beyond elec-
ici y gene a ion [2]. P oposals include he de elopmen o
DEMO-like usion powe plan s capable o ensu ing ene gy
secu i y ac oss a spec um o applica ions. These applica ions
span om low- empe a u e powe needs, like dis ic hea ing
[3], desalina ion [4,5], and hyd ogen p oduc ion [6]. In his
s udy, he la e is p oposed.
In he ques o deca bonisa ion, clean hyd ogen eme ges
as a e sa ile solu ion. I s p oduc ion, whe he ha nessed om
enewable o nuclea ene gy sou ces, o de i ed om ossil
uels wi h ca bon cap u e, p esen s a pa hway o mi iga e
emissions ac oss challenging sec o s such as long-haul ans-
po , chemicals, and he manu ac u ing o i on and s eel [7,
8]. These sec o s pose conside able emission educ ion chal-
lenges. Signi ican ly, he in eg a ion o hyd ogen-powe ed
sys ems in indus ial ehicles and eigh /shipping ope a ions
no only holds he p omise o simul aneously dec easing ca -
bon emissions and enhancing ai quali y bu also add esses a
c i ical limi a ion o shipping, whe e ba e ies migh no be a
easible solu ion [9,10]. Fu he mo e, hyd ogen’s ole ex ends
o acili a ing he seamless in eg a ion o a iable enewables
wi hin he elec ici y sys em [11], and se ing as one o a ew
aluable op ions o s o ing ene gy o e ex ended pe iods.
In he con ex o p o iding a comp ehensi e echno-
economic analysis, his s udy e alua es usion powe as
an ene gy sou ce o he hyb id gene a ion o elec ici y
and hyd ogen h ough elec olysis. Whils holding a well-
es ablished posi ion wi hin he indus ial landscape, elec o-
lysis has a compa ably low-ca bon p o ile, pa icula ly in con-
as o p ocesses such as ossil uel e o ming. Impo an ly,
i o e s a s eamlined echnological con igu a ion, se ing i
apa om un-es ablished and complex al e na i es such as he
he mo-chemical sulphu -iodine cycle. Elec olysis ope a es
solely h ough elec ical p ocesses, elimina ing any eliance
on nuclea hea sou ces. This in insic ea u e opens a enues
o he co-gene a ion o hyd ogen and elec ici y p oduc ion.
Such a syne gy could seamlessly ma ch peak ene gy demand
in an ene gy pa adigm whe e usion se es as he consis en
base load powe , complemen ed by enewable sou ces. I can
also ensu e ha he plan speci ica ions a e aligned wi h hose
equi ed o elec ici y p oduc ion, meaning ha de elopmen
pa hways o elec ici y p oduc ion e o s s ill emain alid
un il a choice can be made on which pa hway is bes o usion
o exploi . S udies om She ield e al and Nicholas e al u -
he in es iga e his na a i e h ough cogene a ion be ween
hyd ogen and elec ici y [4,12,13].
The deploymen ime o usion powe plan s is c ucial o
hei e ec i e in eg a ion in o he ene gy mix. In his con ex ,
sphe ical okamaks (STs) a e po en ially quicke o inco po -
a e han con en ional okamaks due o hei ela i ely smalle
size, which po en ially esul s in sho e cons uc ion imes and
educed capi al cos s- wo common challenges in he deploy-
men o ission powe plan s. Howe e , i is impo an o no e
ha he smalle size o STs can also in oduce inc eased com-
plexi y in hei design and ope a ion, which should be ca e-
ully conside ed in he e alua ion o deploymen imelines.
STs a e cha ac e ised by an aspec a io (A), he a io be ween
he majo (R) and mino ( ) adius, <2. In gene al, lowe aspec
a io okamaks a e designed wi h lowe o oidal ield (BT) han
con en ional okamaks. This is due o how BTscales such ha
BT=BmaxRTF
RP, whe e Bmax is he maximum ield a he o oidal
ield coil, RTF is he inne adius o he o oidal ield coil, and
RPis he majo adius o he plasma [14]. In sphe ical oka-
maks The inne adius o he TF coil (RTF) is small. The majo
plasma adius (RP) is also small bu la ge ela i e o RTF.
Toge he , hese ac o s educe he achie able BT o a gi en
Bmax [14].
This dec eases he usion powe as P usion ∝B4
T. Howe e ,
by le e aging high be a, compac design, and e icien cu -
en d i e, STs emain compe i i e agains con en ional oka-
mak designs. This is why many cu en esea ch e o s ocus
on op imising STs o imp o e hei scalabili y and o e all
pe o mance. Following his easoning, mul iple public and
p i a e p og ammes a e unding ST pilo plan s wi h he a ge
o ene gy p oduc ion by he 2040–2050 s [15–18].
F om a physics pe spec i e, ST plasmas can each a highe
con inemen , achie ing ele a ed alues o a io o he plasma
2
Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Sala e i e al
p essu e o he magne ic p essu e, β, elonga ion (κ), and sa e y
ac o , (q) [19]. In he con ex o β, i is no ewo hy ha
ST plasmas can exceed he T oyon limi , exempli ied by he
START ST achie ing β alues exceeding 30% [20]. A dis-
inc i e cha ac e is ic o STs is he balance be ween he mag-
ne ic ields, pa icula ly he simila i y o he poloidal ield (Bp)
and he o oidal ield (BT) in he ou e ield egion. This equi-
lib ium induces pa icles o ollow high-pi ched ajec o ies,
esul ing in educed ime spen in egions o un a ou able
cu a u e and, consequen ly, ea u ing a be e pa icle con-
inemen . Mo eo e , STs na u ally ea u e elonga ed plasma
shapes, cha ac e ised by he pa ame e κ, which ep esen s
he a io o he hal o he plasma heigh o mino adius,
accoun ing o he o al e ical size o he plasma. This inhe -
en elonga ion subs an ially diminishes he ene gy needed o
achie e his ad an ageous con igu a ion. ST plasmas a e able
o achie e high boo s ap cu en s, inc easing plasma s abil-
i y and pe o mance. A high boo s ap ac ion indica es ha
a signi ican po ion o he equi ed plasma cu en is gen-
e a ed in e nally. In u n, he plasma emains a he neces-
sa y empe a u e and densi y o usion eac ions, educing
he need o addi ional ene gy in ensi e ex e nal hea ing and
cu en d i e me hods, imp o ing he o e all e iciency o he
usion eac o . Reduced eliance on ex e nal cu en d i e sys-
ems can lowe he ope a ional cos s o a usion eac o , mak-
ing i mo e economically iable o long- e m usion powe
gene a ion [21,22].
The ad an ages o ST designs a e no wi hou hei ade-
o s. Achie ing a highe usion gain (Q) in a mo e compac
machine ansla es o a g ea e hea lux impac ing he eac o ’s
i s wall and, no ably, he di e o , which mus endu e hea
luxes eaching magni udes in he ange o ens o MW m−2
[23,24]. The compac con igu a ion also esul s in limi ed
space wi hin he cen al s ack. This egion accommoda es he
cen al solenoid, inne leg o he poloidal ield coils, shield-
ing ma e ials, and he b eede blanke ( hough no all designs
inco po a e a b eede blanke in he high ield egion, a chal-
lenge when aiming o a sel -sus aining i ium b eeding a io).
Ce ain designs add ess his conce n by minimising he cen -
al solenoid’s spa ial occupancy (i is exclusi ely employed
o s a up, wi h ex e nal means and he boo s ap cu en sup-
plying plasma cu en ) o by i s comple e emo al, as seen in
solenoid- ee s a up designs such as [25,26]. The heigh ened
olume ic usion yield, coupled wi h limi ed cen al s ack
space, esul s in ele a ed neu on luence a es in he pol-
oidal ield coils. This deg ee o luence can po en ially damage
ma e ials and induce hea luxes incompa ible wi h he coils’
he momechanical in eg i y.
2. Scope
Fusion holds a unique posi ion in he ene gy u u e land-
scape, ma ked by ecen ad ancemen s in echnological
demons a ion and signi ican in es men , especially in p i a e
de elope s. Ye , he e is a no ewo hy absence o s a egic
planning conce ning i s comme cial applica ion and econom-
ics. The lack o s udies in he li e a u e add essing po en-
ial non-elec ic comme cial applica ions o usion, pa ic-
ula ly o STs, unde sco es he necessi y o his s udy. We
ou line h ee echno-economic scena ios, op imis ic, mode -
a e and conse a i e. Fo each one, he e a e a se o impo an
physics and enginee ing pa ame e s wi h a gi en alue, and a
co esponding capi al cos . These alues a e ca ied o wa d
and ed in o examina ions o powe blocks and elec olyse s.
No wi hs anding hese challenges, comme cial usion ia
STs emains a p omising, ye un ealised echnology, s ill in
he p o o yping phase o esea ch and de elopmen . To g asp
he echno-economic implica ions o an ST in hyb id elec-
ici y and hyd ogen p oduc ion, i is necessa y o en isage a
u u e con ex whe e usion echnology has been demons a ed
wi h an ope a ional Fi s o a Kind (FOAK) powe plan .
Consequen ly, ho ough concep ualisa ion o design speci ic-
a ions becomes pa amoun . This ensu es he op imisa ion o
ene gy p oduc ion and a deep unde s anding o plasma phys-
ics and enginee ing pa ame e s ha impac impo an echno-
economic indica o s, such as capi al cos . Le e aging sys-
ems codes can enable his app oach, acili a ing design op im-
isa ion. Howe e , concep ualising an un ealised echnology
means ha assump ions and unce ain ies ine i ably a ise in
hese powe plan s concep s.
The PROCESS sys ems code has been chosen o concep u-
alise he ST [27]. De eloped by UKAEA, PROCESS is able
o s udy he in e play be ween he enginee ing and physics
aspec s ha comp ise a usion powe plan . The code is gi en
a s udy space o med by he cons ain s se by he use . Then,
PROCESS can ob ain he op imum wo king poin ( o he
chosen igu e o me i ) using a se ies o 0D and 1D app ox-
ima ions ha model all subsys ems. The code achie es con-
e gence wi hin seconds, making i a aluable ool in cases o
explo a o y analysis aimed a es ablishing a design baseline
[28]. The low compu a ional cos o he code allows also o
unce ain y s udies o pinpoin he mos in luen ial pa ame e s
wi h espec o he chosen igu e o me i .
To add ess unce ain ies and assump ions su ounding
he ST concep , a wo- old sensi i i y analysis app oach
was used. Fi s , Mo is unce ain y analysis was applied
o educe dimensionali y and s eamline pa ame e selec-
ion (sec ion 3.1). Nex , an in-dep h Sobol analysis was pe -
o med (sec ion 3.2), e alua ing i s -o de (S1), second-o de
(S2), and o al in e ac ion e ec s (S o ). These me hods iden-
i ied key pa ame e s and hei in e ela ionships, imp o -
ing he unde s anding o ac o s in luencing capi al cos .
F om his analysis, h ee dis inc eac o scena ios-op imis ic,
mode a e, and conse a i e- we e iden i ied. These scena ios
in o med he subsequen he modynamic powe block mod-
elling (sec ion 4), elec olyse modelling o hyd ogen p o-
duc ion (sec ion 5), and economic modelling o le elised
cos o elec ici y and hyd ogen calcula ions (sec ion 6).
This app oach allows o explo ing di e se ope a ing condi-
ions and design pa ame e s, p o iding insigh s in o po en ial
ene gy gene a ion and hyd ogen p oduc ion capabili ies.
3
Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Sala e i e al
3. Sensi i i y me hods
In his sec ion, wo s a is ical me hods (Mo is and Sobol) will
be used o de e mine hei e ec on he capi al cos o a ST.
The me hodology he e p esen ed is simila o he ollowed in
[29], whe e PROCESS was used o de e mine he main capi al
cos d i e s o a DEMO-like usion powe plan . Thus, allow-
ing o he di ec compa ison o he cos d i e s ound o a
con en ional okamak and a sphe ical one. The iden i ica ion
o he cos d i e s allows o he de ini ion o h ee scena ios
(conse a i e, mode a e and op imis ic) in he nex sec ion
ha will be used o analyse hei he moeconomic beha iou
(powe block, elec olyse and hei espec i e cos s).
The s udied ST model he e p esen ed is modelled a e he
wo k p esen ed by Mena d e al in [14], ha was success ully
ep oduced in PROCESS by Muld ew e al [30]. Mena d’s
model, om now on e e ed as Mena d-2016 baseline, is an
ST pilo powe plan wi h a usion powe ou pu o 500 MW
and solenoid- ee ope a ion achie ed hanks o a high boo -
s ap cu en ac ion (∼70%–80%, consis en wi h he ac-
ions ob ained in o he modelling [31,32] and heo e ical
s udies [33]) and 50 MW o NBI powe . This has mo i a ed
esea ch lines on solenoid- ee s a up [34,35], solenoid- ee
ope a ion [18,31]. In Bock e al [36], an ad anced scen-
a io was expe imen ally explo ed in he con en ional okamak
ASDEX Upg ade whe e jus a small ac ion o he cu en
d i e was p o ided om induc i e means, while he es was
p o ided by a subs an ial boo s ap cu en and ex e nal means
(NBI, ECCD).
Fo his wo k, he elec ic ou pu o he eac o has been
cons ained o 500 MWe. This is in line wi h he DEMO
design p esen ed in [29] allowing o a mo e di ec compa -
ison. Table 1shows all he pa ame e s ha will be s udied in
his s a is ical s udy oge he wi h hei uppe and lowe limi s.
A ew o hese pa ame e s include he supe index max o min,
hese co espond o i e a ion a iables ha PROCESS a y
be ween some gi en limi s in o de o achie e he op imum
esul wi h he gi en cons ain s. Fo example, Bmax
Tmeans ha
PROCESS can a y BTup o his alue, bu he op imum scen-
a io may ea u e a lowe alue.
Se e al pa ame e s in he in es iga ion o e lap wi h hose
in Pea ce e al [29], while some ha e been in oduced o
emo ed in acco dance wi h hei ele ance o compac STs.
Pa ame e s like ρco e and Wa e wi hin he anges used in
Pea ce e al’s wo k. Adjus men s ha e been made o he lim-
i s o A o e lec hose seen in STs. Pa ame e s such as max
GW,
He, min
LH ,CBS,ηiso,q95, CD,Pmax
inj ,σmax
CS , and Bmax
Tsha e he
same ange wid hs as Pea ce e al bu a e cen ed a ound he
Mena d-2016 baseline. The es o he pa ame e s limi s a e
se a ound exis ing/p ojec ed echnophysical alues o limi s.
i.e. ∆Tin a ies be ween no mal powe plan empe a u e and
achie able u bine empe a u es in supe c i ical ca bon diox-
ide plan [37], o β ha a ies be ween he minimum con-
e ged alue ob ained in [14] and 20% ha is he maximum
s able and economically easible alue despi e la ge βo up
o 50% ha e been achie ed in START [38]. This lis does no
Figu e 1. Absolu e mean, µ∗, and a iance, σi, o he elemen a y
e ec s o sc een PROCESS pa ame e s. X in he uni s ep esen he
uni s o he a ied quan i y (i.e. M$ T−1 o Bmax
T). The e is a
signi ican accumula ion o unimpo an pa ame e s close o he
(0,0) posi ion, hese pa ame e s a e: ηiso,qmin
95 ,Pmax
inj ,σlimi
CS ,ηh p.
in end o collec all he possible pa ame e s and hei anges,
u u e con ibu ions should help expand his s udy o imp o e
he gene ali y o he indings.
The Mo is me hod was used i s as i is compu a ion-
ally mo e e icien han Sobol, making i ad an ageous in high
dimensionali y p oblems o il e ou less in luen ial a iables.
Howe e , he Mo is me hod p o ides less de ailed in o ma-
ion and does no cap u e he in e play be ween di e en a i-
ables as comp ehensi ely as he Sobol me hod.
3.1. Mo is me hod
The Mo is Me hod [39], also known as he me hod o ele-
men a y e ec s, is a sensi i i y analysis echnique used o
explo e he quali a i e beha iou o a model’s ou pu in
esponse o changes in inpu pa ame e s. Unlike adi ional
sensi i i y analyses ha ocus on quan i ying he impac o
each pa ame e indi idually, he Mo is Me hod assesses he
in luence and in e ac ions o mul iple pa ame e s simul an-
eously. I achie es his by sys ema ically a ying each pa a-
me e ac oss a ange o alues while keeping o he s cons an ,
allowing o he iden i ica ion o in luen ial ac o s and coup-
ling e ec s on he model’s ou pu . In he con ex o his s udy,
he Mo is Me hod was employed o analyse he sensi i i y o
capi al cos o changes in inpu pa ame e s, p o iding insigh s
in o he ela i e impo ance and in e dependencies o hese
pa ame e s in shaping he economic iabili y o he p oposed
usion powe plan design.
In igu e 1, a sca e plo o he absolu e mean and s and-
a d de ia ion o he elemen a y e ec s o each pa ame e is
p esen ed. The absolu e mean, µ∗, shown in equa ion (1) can
be seen as p o iding a anking o he e ec o such an inpu
on he capi al cos , and his allows o easy iden i ica ion o
negligible inpu s, whe eas he s anda d de ia ion σi, p o ides
an es ima ion o he linea i y o he inpu and i s in e ac ion
4
Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Sala e i e al
wi h o he a iables:
µ∗
i=1
N
N
X
j=1
|EEij|(1)
σi=
u
u
1
N−1
N
X
j=1
(|EEij| − µ∗
i)2(2)
whe e: µ∗is he calcula ed absolu e mean o pa ame e Xi.
σiis he s anda d de ia ion o he elemen a y e ec s o pa a-
me e Xi.Nis he o al numbe o samples. EEij is he j h ele-
men a y e ec o pa ame e Xi.
The EEij measu es he change in he ou pu o a model due
o a small, inc emen al change in one o i s inpu pa ame e s.
I is a sensi i i y measu e used in sensi i i y analysis o unde -
s and he in luence o indi idual pa ame e s on he model ou -
pu . The uni s o elemen a y e ec s depend on he uni s o
he model ou pu and he co esponding inpu pa ame e . Fo
example, o he model ou pu is capi al cos , (wi h uni s o
dolla s) and he inpu pa ame e is Bmax
T(wi h uni s o T), he
EEij will be in dolla s/T. The e o e, µ∗and σwill sha e he
same uni s.
Fusion pa ame e s in he uppe igh quad an (high µ∗
and high σi), such as β, indica e pa ame e s ha s ongly
e ec o he capi al cos , and a e s ongly co ela ed o o he
a iables. Conce ning β, i s in luence on capi al cos can
be a ibu ed o he necessi y o achie ing high plasma β,
which demands obus plasma con ol sys ems. Al e na i ely,
ins ead o achie ing high plasma β, he e is a solu ion ha
uses high- empe a u e supe conduc ing magne s (HTS mag-
ne s) o achie e a s onge magne ic ield, he eby mi iga -
ing he equi emen o high plasma β. In he case o ce ain
p oposed HTS apes, such as a e-ea h ba ium coppe oxide
(ReBCO), challenges eme ge due o he sca ci y o some con-
s i uen mine als in he Ea h’s c us . This sca ci y can lead o
ele a ed ma e ial cos s. Fu he mo e, he no el y o he ech-
nology inc eases inal p ices due o limi ed indus ial in a-
s uc u e o la ge-scale p oduc ion.
Da a poin s in he uppe le quad an (high σi, low µ∗),
such as Psep/R, ep esen pa ame e s wi h a no able a e age
e ec on he capi al cos bu ela i ely low in e -dependence.
These pa ame e s could consis en ly a ec he capi al cos ,
making hem impo an and s able con ibu o s. The usion
pa ame e Psep/Rimpac s he capi al cos o a usion machine
by indica ing he e iciency o plasma con inemen and powe
losses. A high Psep/Rsugges s less e icien con inemen and
inc eased powe losses due o plasma anspo . To mi iga e
hese losses and sus ain a iable usion eac ion, ad anced and
cos ly echnologies o supplemen a y hea ing ( o main ain
plasma empe a u e and hus sus ain usion eac ions), con-
inemen , plasma s abili y, and ma e ials a e equi ed. E icien
hea ing sys ems and cu en d i e me hods, such as neu al
beam injec o s employed in his ST concep play a c ucial
ole in con ibu ing o he capi al cos . O he me hods include
cyclo on esonance hea ing.
Da a poin s in he lowe igh quad an (low σiand high µ∗)
indica e pa ame e s ha exhibi subs an ial in e -dependency,
bu ha e a modes a e age e ec on he capi al cos . The
absence o usion pa ame e s in he lowe igh quad an (low
σiand high µ∗) is con ex -dependen and e lec s he unique
condi ions and pa ame e s in he s udy, a he han a limi a ion.
Da a poin s in he lowe le quad an (low µ∗and low σi) ep-
esen pa ame e s wi h bo h a low a e age e ec and low a i-
abili y, such as Pmax
inj , min
LH ,σmax
TF ,ηh p, and q95. These pa ame -
e s show minimal impac on he capi al cos and a e ela i ely
s able in hei beha iou . The same uppe and lowe limi s,
as shown in able 1, we e used, and he nine mos in luen ial
pa ame e s we e ca ied o wa d o a iance-based analysis
o Sobol indices. These we e: max
GW, W,Psep/R, CD,A,Bmax
T,
∆Tin,β, and ηNBI.
Compa ing Mo is sensi i i y analysis esul s wi h Pea ce
e al highligh s simila i ies and di e ences in pa ame e
impo ance [29]. Pa ame e s like CBS,Bmax
T, and Wexhibi
consis en high in luence. In con as , Psep/R, max
GW, and Ashow
dis inc a ia ions in in luence, wi h g ea e p ominence in his
s udy. Pa ame e s such as σmax
CS ,ρco e, and Pmax
inj exhibi educed
in luence and coupling compa ed o [29].
3.2. Sobol me hod
Sobol analysis, a a iance decomposi ion me hod, s ands apa
om he Mo is me hod in i s igo ous app oach o sensi i -
i y assessmen . While Mo is e alua es pa ame e impo ance
h ough di ec e alua ions, Sobol analysis del es deepe by
u ilising Sobol sampling me hods, unco e ing he indi idual
and in e ac i e con ibu ions o pa ame e s o o e all ou pu
a iance. This me hod o e s a mo e comp ehensi e pe spec -
i e on sensi i i y and in luen ial ac o s, especially bene icial
o models wi h nume ous inpu pa ame e s. Employing sens-
i i i y indices like S1( i s -o de sensi i i y index), Sobol ana-
lysis quan i ies he p opo ion o ou pu a iance a ibu ed o
each pa ame e indi idually, p o iding insigh s in o hei isol-
a ed e ec s on he ou pu a iabili y. Speci ically, S1answe s
he ques ion: ‘How much does changing his pa ame e alone
impac he a iabili y in he ou pu ?’ This index is calcula ed
as he a io o he a iance o he condi ional expec a ion o he
ou pu gi en he a ia ion in a single pa ame e o he o e all
ou pu a iance:
S1(Xi) = V[E(Y|Xi)]
V(Y)(3)
whe e: V[E(Y|Xi)] is he a iance o he condi ional expec -
a ion o Ygi en only Xi a ies. V(Y) is he a iance o he
ou pu Y.
Sobol analysis also ex ends o highe -o de sensi i i y
indices o p o ide a mo e de ailed unde s anding o pa ame e
in e ac ions. Second-o de sensi i i y indices (S2) assess he
join e ec s o pai s o pa ame e s. They e alua e how wo
5
Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Sala e i e al
Table 1. Pa ame e s p edic ed o impac powe plan economics, wi h hei co esponding uppe and lowe limi s.
Pa ame e Lowe limi Uppe limi
max
GW G eenwald ac ion 0.85 1.15
H98,y2Radia ion co ec ed H-Fac o 1.47 1.67
He Helium impu i y ac ion 0.085 0.115
WTungs en impu i y ac ion 1.00e−5 1.00e−4
Psep/R(MW m−1) 20.0 45.0
min
LH Lowe bound LH h eshold 0.85 1.15
CBS Boo s ap cu en ac ion 0.08 0.80
CD Cu en d i e e iciency [A W−1] 0.03 3.00
ηiso Isen opic e iciency o blanke coolan pumps 0.75 0.95
qmin
95 Sa e y ac o nea plasma edge 3.0 3.5
Pmax
inj Maximum allowable alue o injec ed powe (MW) 45.0 55.0
σlimi
CS Allowable hoop s ess in cen al solenoid s uc u e (MPa) 340 460
σlimi
TF Allowable maximum shea s ess in TF coil case
(T esca c i e ion) (MPa)
640 760
AAspec a io 1.8 2.0
Bmax
TTo oidal ield on axis (T) 3.5 4.5
ρco e No malised adius de ining he co e egion 0.45 0.75
∆Tin Tu bine inle empe a u e (◦C) 519.85 824.9
βTo al plasma be a 0.04 0.2
ηNBI NBI plug e iciency 0.2 0.6
ηh p Elec ic e iciency o p ima y pumps 0.75 0.95
pa ame e s, when a ied oge he , in luence he capi al cos
a iabili y beyond hei indi idual impac s. Thi d-o de and
highe -o de sensi i i y indices (S3,S4, and so on) u he
expand he analysis o conside he join e ec s o h ee o
mo e pa ame e s simul aneously. They help in unco e ing
in ica e ela ionships ha migh no be e iden when analys-
ing pa ame e s indi idually o in pai s.
In addi ion o lowe o de indices, S o ( o al-o de sensi i -
i y index) akes a b oade iew. This index quan i ies he en i e
in luence o a pa ame e on capi al cos a iabili y, encom-
passing i s di ec impac and i s collabo a i e e ec s wi h o he
inpu s. The o al-o de sensi i i y index S o is exp essed algeb-
aically as he sum o all he lowe -o de sensi i i y indices. In
essence, S o answe s he ques ion: ‘When conside ing all pos-
sible in e ac ions, how much does his pa ame e con ibu e o
he capi al cos a iabili y?’:
S o (Xi) = 1−V[E(Y|X∼i)]
V(Y)=1−
n
X
i=1
Si(4)
whe e: V[E(Y|X∼i)] is he a iance o he condi ional expec -
a ion o Ygi en all inpu pa ame e s excep Xi a y. V(Y) is
he a iance o he ou pu Y. He e, n ep esen s he o al num-
be o pa ame e s o ac o s being conside ed in he sensi i -
i y analysis. Non-ze o alues o all indices sugges ha he
pa ame e has bo h di ec in luence on he capi al cos and
con ibu es o he o e all a iabili y h ough in e ac ions wi h
o he pa ame e s.
In he equa ions p o ided, he a gumen s o Va e de ined as
ollows: V[E(Y|X∼i)]: This ep esen s he a iance o he con-
di ional expec a ion o he ou pu Y, gi en ha all inpu pa a-
me e s excep Xi a y. In o he wo ds, i quan i ies he a iab-
ili y in he expec ed alue o Ywhen all pa ame e s excep Xi
a e conside ed o a y. V(Y): his deno es he a iance o he
ou pu Y, which measu es he deg ee o dispe sion o sp ead
o he ou pu alues a ound hei mean.
CD,Bmax
T,β, and ηNBI ha e non-ze o S1indices, hus indic-
a ing ha he pa ame e s in ques ion ha e bo h indi idual and
in e ac ion e ec s on he capi al cos a iance. The colou map
in igu e 2(a) ep esen s he S2indices ob ained om he ana-
lysis. Posi i e alues in second-o de Sobol analysis indica e
he deg ee o which wo inpu a iables, in e ac wi h each
o he o in luence he capi al cos . A highe posi i e alue sug-
ges s a s onge in e ac ion be ween he wo ac o s, meaning
ha hey join ly explain a la ge po ion o he capi al cos a i-
ance. As shown, βshows s ong coupling wi h Bmax
T(0.15),
∆Tin (0.15) and ηNBI (0.16). Ze o alues imply ha he e is
no signi ican in e ac ion be ween he wo ac o s in explain-
ing he capi al cos a iance, as shown be ween Aand Bmax
T. In
o he wo ds, he di ec combina ion o hese wo pa ame e s
do no ha e an e ec on he capi al cos .
In his s udy β,A, and Bmax
Tha e he highes S o indices,
and he e o e demons a e ha hey in e ac s ongly wi h
o he pa ame e s, and ha e a s ong in luence on capi al cos .
max
GW,Psep/R,A, and ∆Tin exhibi ze o S1indices, bu no able
S o , see igu e 2(b). This indica es ha hese pa ame e s ha e
s ong in e ac ions and hei e ec s on he ou pu a iance a e
6
Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Sala e i e al
Figu e 2. (a) Second o de Sobol esul s. Each squa e shows how s ong is he in e play be ween wo a iables. Only he op hal is shown
as he ma ix is symme ic and he diagonal (each pa ame e o i sel ) is equi alen o S1(shown in (b)). (b) showing S1and S o indices o
sc eened PROCESS pa ame e s.
p edominan ly d i en by highe -o de in e ac ions a he han
hei indi idual con ibu ions.
High S o indices sugges ha hese pa ame e s, when com-
bined wi h o he inpu s, ha e a signi ican impac on he cap-
i al cos a iabili y. The in luence o Bmax
Ton capi al cos is
explained by i s s ong e ec on he usion powe : P usion ∝
B4
T. Whils high usion powe is desi able, i can also lead o
inc eased cos s, d i en by he need o ad anced echnologies,
ma e ials, sa e y measu es, and in as uc u e o suppo he
inc eased powe ou pu . The ∆Tin in luences he e iciency
o he he mal managemen sys em. A la ge empe a u e di -
e ence would equi e ad anced cooling sys ems and ma e -
ials o handle he hea load, he e o e impac ing he capi al
cos . max
GW is ela ed o he maximum allowable plasma dens-
i y. Achie ing and main aining high plasma densi y equi es
enhanced uelling and di e o sys ems and could be mo e
expensi e.
I is impo an o no e ha he cu en ly implemen ed model
o STs in PROCESS conside s δand κas a unc ion o he
aspec a io; hus, hey canno be con olled as independen
pa ame e s. This explains why hese wo pa ame e s, he op
con ibu o s o he capi al cos in he DEMO-like s udy p esen-
ed by Pea ce e al a e no conside ed in his s udy. The in lu-
ence o Aon he plasma’s inc eased p oximi y o he cen al
s ack oge he wi h i s con ol on δand κ esul s on he hi d
highes S o ac o o he s udied ST case.
3.3. Scena io iden i ica ion
Iden i ying he main cos d i e s o he p esen ed ST con-
igu a ion led o he design o h ee scena ios wi h inc eas-
ing echno-physical complexi y: conse a i e, mode a e, and
op imis ic. These scena ios, de ailed in able 2, we e de ined
using he pa ame e s s udied wi h he Sobol me hod. Figu e 3
p esen s a his og am o he capi al cos o all cases examined
Table 2. Inpu and ou pu pa ame e s ha compose he op imis ic,
mode a e and conse a i e scena ios.
Conse a i e Mode a e Op imis ic
Inpu s
W4.5·10−55·10−510−4
Psep/R[MW m−1] 25 33 42
max
GW 1.0 1.0 1.0
CD 0.8 1.0 0.8
A2.0 2.0 2.0
Bmax
T[T] 3.8 4.0 4.5
β0.081 0.11 0.18
ηNBI 0.3 0.4 0.5
∆Tin [◦C] 500 650 800
Ou pu s
Ip[MA] 18.5 15.3 13.9
R[m] 4.75 3.10 2.78
Capi al cos [1990 M$] 9827.76 5124.62 4551.47
Q eac o [MW ] 1916.9 1466.8 1231.5
Consump ions [MWe] 241.0 180.1 151.6
in he Sobol s udies. He e, he op imis ic case lies he bo om
10% o cases, mode a e a 50%, and conse a i e a 90%. The
Sobol analysis iden i ied he pa ame e βas highly in luen ial
on he capi al cos . E en small changes in βcan lead o sig-
ni ican luc ua ions in capi al cos , highligh ing he po en ial
o a ge ed e inemen s o subs an ially educe cos s wi hin
he scope o his s udy.
W, e ec i ely a p oxy o he plasma impu i ies, is play-
ing an in e es ing ole in hese scena ios. The i s o de e ec
o his pa ame e is ha he plasma adia ion inc eases which
dampe s he eac o e iciency. Bu a highe plasma adia ion
means a lowe hea lux on he di e o which is known o
7
Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Sala e i e al
Figu e 3. His og am wi h he dis ibu ion o all capi al cos alues
es ima ed by he Sobol analysis wi h op imis ic, mode a e and
conse a i e FOAK scena ios e e enced espec i ely.
be a bo leneck o STs. Fo he sho ange he e exp essed
a highe impu i y ac ion was ound o elax su icien ly he
di e o hea lux o allow o a cheape design as his limi was
me la e on he op imisa ion p ocess. None heless, i is clea
ha his endency will be o e u ned o a su icien ly la ge
impu i y ange. Fu u e con ibu ions should add ess his poin
by s udying wide anges unde di e en scena ios o unde -
s and he iable design space.
Th ough dis inc ion o he scena ios, pa ame e alues a e
able o be ca ied o wa d in o he echnological pa o he
echno-economic in es iga ion, as ou lined in he scope. The
u ilisa ion o hese pa ame e s in o m he modelling o he -
modynamic cycles, elec olyse pe o mance, and economic
assessmen s. In sec ion 4, he modynamic modelling will
inco po a e pa ame e s Q eac o ( he he mal powe ou pu by
he eac o ), ∆Tin ( he u bine inle empe a u e as de ined in
able 1) and Consump ions ( he o e all elec ical consump-
ions o he eac o ). In he inal sec ion 6, he ou pu a iable
Capi al cos will be analysed o de e mine he economic iab-
ili y o each scena io.
4. Powe blocks
In his sec ion, he in eg a ion o h ee powe blocks (namely
Rankine wa e cycle, B ay on helium cycle, and Fehe supe -
c i ical ca bon dioxide cycle) on he h ee scena ios p e iously
exposed will be p esen ed. This me hodology, hus, highligh s
he impo ance o knowing he main cos d i e s o a usion
powe plan be o e i s design as hey will end up de e mining
he main cha ac e is ics o he powe block.
As p e iously men ioned, he key pa ame e s o he powe
block selec ion a e Q eac o ,∆Tin, and he plan Consump ions
(see able 2). Mo e ad anced scena ios will ea u e lowe con-
sump ions and highe inle empe a u es, leading o highe
elec ic e iciencies o he cycle. The e o e, hese pa ame e s
a e pi o al in he selec ion p ocess. He e, he e iciency o he
cycle is de ined as:
ηcycle =˙
Welec, u bines −˙
Wcons, cycle −consump ions
˙
Q eac o
(5)
Whe e ˙
Welec, u bines ep esen s he elec ic powe gene a ed
in he u bines. ˙
Wcons, cycle deno es he inne consump ions
wi hin he cycle, such as pumps. Consump ions co espond o
he plan consump ions, as indica ed in able 2.˙
Q eac o signi-
ies he hea lux p oduced in he eac o , also sou ced om
able 2. He e, ˙
Q eac o comp ises he hea lux coming om he
blanke , di e o , shield and i s wall, hus, i is supposed ha
all o hem can each he same empe a u e le els.
4.1. Rankine s eam cycle
This cycle is based on he wo k de eloped in [3,40] and is
illus a ed in igu e 4. This is a layou wi h h ee s eam u -
bines whe e he high p essu e (HPT) and medium p essu e
(MPT) u bines ea u e wo bleedings o hea up he low p es-
su e s eam. The HPT ou le s eam is ehea ed wi h he eac o
hea o a oid he o ma ion o liquid wa e . This is a s and-
a d Rankine cycle, hus, he inle u bine empe a u e limi has
been se a 600 ◦C o no become supe c i ical. This ma ks a
limi o he mode a e and op imis ic scena ios ha could each
empe a u es o 650 ◦C and 800 ◦C espec i ely.
4.2. B ay on helium cycle
The p oposed cycle, shown in igu e 5, is based on [3,41].
Helium comp ession is an ene gy-in ensi e p ocess, o educe
i s powe consump ion, he comp ession p ocess has been
in e up ed by wo in e cooling s eps. A e he comp ession
(poin 9 in igu e 5), he cold s eam is hea ed wi h he u -
bine ou le s eam be o e passing h ough he eac o hea
exchange . As in [3], he comp ession ela ion in bo h com-
p esso s is de ined by equa ion (6):
ci =n
q c /Σ( c /Σ(1−∆Picj)(6)
whe e ci is he comp ession ela ion in each comp esso ; n,
he numbe o comp ession s ages; c , he o al comp ession
ela ion, and ∆Picj is he p essu e jump.
4.3. Fehe supe -c i ical-CO2cycle
Supe -c i ical-CO2cycles a e enowned o hei excep ional
egene a i e capabili ies, achie ed by e aining ele a ed em-
pe a u es a he u bine ou le . Addi ionally, hese cycles
exhibi a high comp essibili y close o he c i ical poin allow-
ing an inexpensi e comp ession o he luid. The chosen layou
is a modi ied e sion (shown in igu e 6) o he HLC.LDS e -
sion o [37]. This layou ea u es wo egene a o s, a high em-
pe a u e one o ake ad an age o he high- empe a u e a he
u bine ou le and an mass-unbalanced low- empe a u e hea
exchange o con ol he pi ch poin inside he egene a o . Fo
u he explana ion e e o [37].
8
Nucl. Fusion 65 (2025) 036027 J. Hidalgo-Sala e i e al
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