Fusion Enginee ing and Design 192 (2023) 113833
A ailable online 28 May 2023
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Fusion Enginee ing and Design
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P edic i e simula ions o plasma scena ios in he SMART okamak
A. Mancini a,b,∗, L. Vela de b,c, E. Viezze a, D.J. C uz-Zabala a, J.F. Ri e o-Rod iguez d,
M. Ga cia-Muñoz a, L. Sanchis e, A. Snicke e, J. Segado-Fe nandez b, J. Ga cia-Dominguez b,
J. Hidalgo-Sala e i b,c, P. Cano-Megias b,c, M. Toscano-Jimenez , he PSFT G oup
aDepa men o A omic, Molecula and Nuclea Physics, Uni e si y o Se ille, Se ille, Spain
bCen o Nacional de Acele ado es (U. Se illa, CSIC, J. de Andalucia), Se illa, Spain
cDepa men o Ene gy Enginee ing, Uni e si y o Se ille, 41092 Se ille, Spain
dUni ed Kingdom A omic Ene gy Au ho i y, Culham Cen e o Fusion Ene gy, Culham Science Cen e, Abingdon, Oxon, OX14 3DB, UK
eDepa men o Applied Physics, Aal o Uni e si y, Espoo, Finland
Depa men o Applied Physics III, Uni e si y o Se ille, Spain
ARTICLE INFO
Keywo ds:
SMART
ASTRA
ASCOT5
FIESTA
Plasma scena ios
ABSTRACT
The SMall Aspec Ra io Tokamak (SMART) is a new sphe ical machine ha is cu en ly being cons uc ed a he
Uni e si y o Se ille (Mancini e al., 2021; Ag edano-To es e al., 2021). The ope a ion o SMART will co e
h ee di e en phases eaching an induc i e plasma cu en (𝐼𝑃) o mo e han 500 kA, a o oidal magne ic
ield (𝐵𝑇) o 1 T and a pulse leng h o 500 ms (Mancini e al., 2021; Ag edano-To es e al., 2021). The
main goal o he SMART okamak is o s udy high plasma con inemen egimes in a b oad iangula i y ange
(-0.5≤𝛿≤0.5) (Doyle e al., 2021; Doyle e al., 2021). While in phase 1 he ohmic hea ing alone is expec ed o
p o ide enough powe o access he H-mode, in phase 2 and phase 3 he access o he H-mode will be ensu ed
by applying Neu al Beam Injec ion (NBI) as ex e nal hea ing sys em. The NBI will consis o one injec o a 25
keV and 1 MW o powe . The o e all design o he NBI, including injec ion geome y, ene gy and powe ha e
been op imized using he ASCOT5 code (Hi ijoki e al., 2021). The SMART scena ios ha e been de eloped
wi h he help o he ee bounda y equilib ium sol e code FIESTA (Cunningham, 2013) coupled o he linea
ime independen , igid plasma model RZIP (Laza us e al., 1990) o calcula e he a ge equilib ia o all
he di e en ope a ional phases. To assess he easibili y o hose scena ios, p edic i e modelling needs o be
included o e alua e p ope ly he e olu ion o he empe a u es, densi y p o iles o bo h elec ons and ions.
To his ex en , he 1.5D anspo code ASTRA (Pe e e ze and Yushmano , 2002) has been used including
models o he ohmic cu en , boo s ap cu en and cu en d i en by NBI. This con ibu ion discusses he
elec on and ion densi y and empe a u e p o iles ob ained o a ious scena ios o phase 1 and 2 and p esen s
he design s udy o he NBI.
1. In oduc ion
The SMall Aspec Ra io Tokamak (SMART) is a new sphe ical oka-
mak cu en ly being cons uc ed and assembled a he Uni e si y o
Se ille [1,2]. SMART will ope a e h ough h ee phases ha di e
in alue o he plasma cu en 𝐼𝑝up o mo e han 500 kA, o oidal
magne ic ield 𝐵𝑇up o 1 T and pulse leng h 𝜏up o 500 ms, see
Table 1. I s e sa ili y is he ope a ion in single and double null
con igu a ion, and wi h posi i e and nega i e iangula i y (−0.5≤𝛿≤
0.5[3,4]). By phase 2, SMART will also be equipped wi h a Neu al
Beam Injec o (NBI) wi h a maximum powe o 1 MW, o s udy he
e ec s o as -ion physics in high posi i e and nega i e iangula i y
scena ios. In his en i onmen , he p edic ion o plasma pe o mance
∗Co esponding au ho a : Depa men o A omic, Molecula and Nuclea Physics, Uni e si y o Se ille, Se ille, Spain.
E-mail add ess: [email p o ec ed] (A. Mancini).
o he machine is essen ial and can be achie ed by using p edic i e
modelling codes in o de o compu e he e olu ion o plasma p o iles,
such as empe a u e and densi y, o he h ee di e en phases. The
aim o he pape is he desc ip ion o he SMART pe o mances in he
i s wo phases and i is o ganized as ollows. Sec ion 2will p o ide
a gene al desc ip ion o he SMART okamak, while he equilib ium
ob ained wi h FIESTA [3–5] and he anspo model used in ASTRA [6]
will be de ailed in Sec ion 3. Phase 1 in i s baseline and posi i e
iangula i y scena ios will be add essed in Sec ion 4, while Phase 2 will
be discussed in Sec ion 5wi h densi y and empe a u e p o iles in 5.1
and he desc ip ion o he op imiza ion p ocess o he NBI in 5.2. This
wo k ocuses solely in phase 1 and phase 2 in posi i e iangula i y,
h ps://doi.o g/10.1016/j. usengdes.2023.113833
Recei ed 28 Oc obe 2022; Recei ed in e ised o m 31 Ma ch 2023; Accep ed 17 May 2023
Fusion Enginee ing and Design 192 (2023) 113833
2
A. Mancini e al.
Fig. 1. O e iew o he SMART okamak oge he wi h he Neu al Beam Injec o
(NBI).
Fig. 2. Phase 1 equilib ium om FIESTA. Baseline is depic ed on he le while he
posi i e iangula i y case is on he igh .
while nega i e iangula i y will be assessed in a sepa a e wo k. The
posi i e iangula i y scena ios ha e been compu ed in o de o assess
he pe o mance o he machine in e ms o o oidal be a 𝛽𝑡, poloidal
be a 𝛽𝑝, no malized be a 𝛽𝑁=𝛽𝑡∕(𝐼𝑝∕(𝑎𝐵𝑇)) and con inemen ime 𝜏𝐸.
In addi ion, he e alua ion o hose scena ios will cons i u e a solid
base o he design o many diagnos ics, and o MHD and gy okine ics
analysis, and hei alidi y will be p o en once he machine will come
in o ope a ion.
2. SMART okamak
The SMall Aspec Ra io Tokamak (SMART) is a compac sphe ical
machine cha ac e ized by an o e all heigh o 3 m and an o e all
diame e o 2 m. I is composed by an AISI 316 L s ainless s eel acuum
essel ha ing an inne wall diame e o 300 mm, ou e wall diame e
o 1600 mm and an inne heigh o 1600 mm. The acuum essel has
an o e all numbe o 44 ci cula po s and 2 ec angula po s mainly
aimed o diagnos ics and main enance pu poses. A se o wel e coppe
o oidal ield coils (4 numbe o u ns each) a e capable o p oducing
he desi ed o oidal magne ic ield (𝐵𝑇) a he majo adius (𝑅0) o he
plasma o all he ope a i e phases (see Table 1).
Fou poloidal ield coils (PF1 and PF2), wi h 23 numbe o u ns
each, a e needed o he e ical con ol and shaping o he plasma.
Table 1
Ope a i e s ages o he SMART okamak.
Phase 1 Phase 2 Phase 3
𝑅0[m] 0.4 0.4 0.4
𝑎[m] 0.25 0.25 0.25
𝜅≤1.95 ≤2.00 ≤2.30
𝛿±0.4 ±0.5 ±0.5
𝐼𝑃[kA] 100 200 > 500
𝐵𝑇[T] 0.1 0.4 1
𝜏[ms] 0.100 0.150 0.500
𝑃𝐸𝐶𝑅𝐻 [kW] 6 (2.45 GHz) 6 (7.5 GHz) 200
𝑃𝑁𝐵𝐼 [kW] – 1000 1000
Table 2
ASTRA inpu model da a.
Phase 1 Phase 2
base @𝛿𝑚𝑎𝑥 base @𝛿𝑚𝑎𝑥
𝛥𝑠[m] 0.059 0.067 0.035 0.032
𝐼𝑃[kA] 30 30 200 200
𝐵𝑇[T] 0.1 0.1 0.4 0.4
𝜅1.83 1.48 1.95 1.79
𝛿0.23 0.4 0.35 0.4
𝑆𝑝[m2] 5.081 5.12 6.80 6.31
𝑉𝑝[m3] 0.68 0.70 1.03 0.90
𝛽𝑡1.74 2.46 2.92 3.3
𝛽𝑝0.337 0.395 0.325 0.322
𝛽𝑛1.25 1.77 1.46 1.61
The PF1 coils a e placed ou side he essel while he PF2 a e placed
inside (see Fig. 1). Two pai s o di e o ield coils (DIV1 and DIV2 in
Fig. 1), all placed inside he machine, a e needed o each he desi ed
elonga ion 𝜅and o ope a e he machine in single o double null con ig-
u a ion and in posi i e and nega i e iangula i y [3,4]. The numbe o
u ns o hese coils di e s, being 35 o DIV1 and 23 o DIV2. A coppe
solenoid wi h 230 numbe o u ns comple es he magne ic sys em o
he machine. SMART will be equipped wi h ou acuum pumps: wo
d y pumps o 80 m3h−1 and wo u bomolecula pumps o 2300 l s−1
designed o ob ain he equi ed le el o acuum o 10−8 o wi h a
maximum leakage o 10−8mba ⋅l s−1. Addi ional hea ing sys ems such
as Elec on Cyclo on Resonance Hea ing (ECRH) and Neu al Beam
Injec o (NBI) will also be ins alled du ing he ope a ional phases o he
machine. The op imiza ion p ocess and he pa ame e s o he NBI a e
discussed in Sec ion 5.2. Addi ional in o ma ion a e de ailed in [1,2].
3. Plasma scena ios modelling
The de elopmen o he ope a i e scena ios assume an impo an
ole in he design o okamak de ices, as hey in luence he ope a ion
o he machine, he assessmen o he pe o mance bu also he design
o se e al diagnos ic sys ems which need an es ima ion o he p o iles o
elec on and ion densi y (𝑛𝑒,𝑛𝑖) oge he wi h hei empe a u e p o iles
(𝑇𝑒,𝑇𝑖). In he SMART design, he modelling o he plasma scena ios
ha e been compu ed using he ASTRA code, a 1.5 D anspo code
which combines 2D equilib ium equa ions wi h a se o 1D anspo
equa ions [6]. The inpu pa ame e s o he modelling a e he majo
adius 𝑅0, mino adius 𝑎, elonga ion 𝜅, iangula i y 𝛿, Sha ano shi
𝛥𝑠, plasma olume 𝑉𝑝and plasma su ace 𝑆𝑝, which ha e been com-
pu ed wi h he FIESTA code [5,7]. The equilib ium p o iles o phase
1 and phase 2 a e shown in Figs. 2 and 3wi h he main equilib ium
pa ame e s summa ized in Table 2. The di e en be a (𝛽𝑁, 𝛽𝑡and 𝛽𝑝)
included in Table 2 ha e been compu ed wi h FIESTA and e i ied wi h
ASTRA.
The anspo simula ions we e ca ied ou wi h ASTRA by consid-
e ing a hyd ogen plasma wi h 𝑍𝑒𝑓𝑓 equal o 2, a G eenwald ac ion
(𝑓𝐺𝑊 ) o 0.4 and a Gy oBohm model [8] o he anspo coe icien s:
𝜒𝑖=𝐶1
𝑎2𝑇3∕2
𝑒
𝐵2
𝑡𝑜𝑟𝜇2
∇𝑇𝑒
𝑇𝑒
(1)
Fusion Enginee ing and Design 192 (2023) 113833
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A. Mancini e al.
Fig. 3. Phase 2 equilib ium om FIESTA. Baseline is depic ed on he le while he
posi i e iangula i y case is on he igh .
𝜒𝑒= 2𝜒𝑖(2)
𝐷=𝐶2𝜒𝑒(3)
𝑣=𝐶3𝑣𝑝𝑉′−𝐷
𝑅0(0.2𝑅0
𝐿𝑇 𝑒
+ 0.1𝑠𝐶4)(4)
being 𝜒𝑖 he ion hea anspo coe icien , 𝜒𝑒 he elec on hea anspo
coe icien (assuming pu e Ion Tempe a u e G adien , ITG), 𝐷 he
di usion coe icien , 𝑣 he con ec i e eloci y, 𝑣𝑝=𝐸||∕𝐵𝑝 he pinch
eloci y indica ing wi h 𝐸|| he pa allel componen o he elec ic
ield and 𝐵𝑝 he poloidal componen o he magne ic ield. Finally
𝐿𝑇 𝑒 =𝑇𝑒∕∇𝑇𝑒is he elec on empe a u e g adien leng h scale and
𝑠 he shea . The coe icien s 𝐶1,𝐶2,𝐶3and 𝐶4ha e been chosen
equal o [0.4, 0.2, 0.1, 1] o ha e compa able anspo coe icien s o
machines wi h simila size/aspec a io o SMART (i.e. GLOBUS-M [9]
and Pegasus [10]) and o ake in o accoun also neoclassical e ec s.
Fo he simula ions in H-mode, 𝜒𝑖has been chosen equal o 4 m2s−1
wi h he edge anspo ba ie (ETB) placed a 𝜌𝑝𝑜𝑙 = 0.95 [9–11] and
lea ing he same app oxima ion o he Gy oBohm model o he o he
coe icien s (see Sec ion 5.1).
4. Phase 1 scena ios
In his sec ion he phase 1 scena ios will be discussed bo h in
he baseline and posi i e iangula i y case. Simula ions o phase 1
equilib ia ha e been un wi h he pa ame e s included in Table 2.
Figs. 4 and 5show he densi y and empe a u e p o iles as a unc ion
o he no malized adius 𝜌𝑝𝑜𝑙 =√(𝜓−𝜓𝑏)∕(𝜓𝑏−𝜓0), being 𝜓𝑏and
𝜓0 he alue o he poloidal lux a he sepa a ix and in he cen e
espec i ely.
The densi y inc eases wi h he iangula i y bo h o ions and elec-
ons. The co e elec on densi y 𝑛𝑒0inc eases om 0.865 × 1019 m−3
o 1.01 × 1019 m−3, while he co e ion densi y 𝑛𝑖0inc eases om o
0.7 × 1019 m−3 o 0.8 × 1019 m−3. Tempe a u e p o iles show he same
end, wi h a maximum o 0.171 keV and 0.08 keV espec i ely o 𝑇𝑒
and 𝑇𝑖in he co e. The bene i s o inc easing he iangula i y is also
mani es ed in he educ ion o he anspo coe icien s 𝜒𝑖,𝜒𝑒and 𝐷
as shown in Fig. 6.
In phase 1, no addi ional sou ce o ene gy is used o hea he plasma
apa om he in insically ohmic hea ing. The ohmic powe , 𝑃𝑂𝐻 , can
be es ima ed as [12]:
𝑃𝑂𝐻 [MW] = 7 × 10−2 𝑍𝑒𝑓𝑓 𝐵2
𝑇𝑉𝑝
𝑞2
𝑎𝑅2
0𝑇3∕2
𝑒
(5)
Fig. 4. 𝑛𝑒and 𝑛𝑖p o iles o phase 1 in he baseline scena io and in he posi i e
iangula i y case.
Fig. 5. 𝑇𝑒and 𝑇𝑖p o iles o phase 1 in he baseline scena io and in he posi i e
iangula i y case.
Fig. 6. 𝜒𝑖,𝜒𝑒and 𝐷p o iles o phase 1 in he baseline scena io and in he posi i e
iangula i y case.
whe e 𝑞𝑎= 5𝜅𝑎2𝐵𝑇∕𝑅𝐼𝑝is he sa e y ac o a 𝑟=𝑎and 𝑇𝑒 he a e age
elec on empe a u e in keV. Using his simple 0-D app oxima ion, wi h
he pa ame e s included in Table 2, he ohmic powe 𝑃𝑂𝐻 is 47 kW,
simila o 50 kW es ima ed wi h ASTRA. The h eshold powe o he
ansi ion om L- o he H-mode (𝑃𝐿𝐻 ) can be e alua ed wi h he
ollowing exp ession [13,14]:
𝑃𝐿𝐻 [MW] = 0.0488𝑛0.717
20 𝐵0.803
𝑇𝑆0.941 (6)
whe e 𝑆= 4𝜋2𝑎𝑅√0.5(1 + 𝑘2)is he plasma su ace a ea and 𝑛20
he elec on a e age densi y exp essed in 1020 uni . Fo phase 1, he
Fusion Enginee ing and Design 192 (2023) 113833
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A. Mancini e al.
Fig. 7. Densi y p o iles o phase 2 wi h and wi hou NBI.
h eshold powe is app oxima ely 9 kW. The adia i e powe 𝑃𝑟𝑎𝑑 om
he plasma, app oxima ed by he sum o he B emss ahlung 𝑃𝐵𝑟 and
cyclo on 𝑃𝑐𝑦𝑐𝑙 losses, can be neglec ed as app oxima ely equal o 60 W.
𝑃𝐵𝑟 and 𝑃𝑐𝑦𝑐𝑙 ha e been es ima ed wi h he ollowingexp essions [15]:
𝑃𝐵𝑟[W] =
𝑍2
𝑒𝑓𝑓 𝑛𝑖𝑛𝑒𝑇0.5
𝑒
[7.69 × 1018]2𝑉𝑝(7)
𝑃𝑐𝑦𝑐𝑙[W] = 6.21 × 10−22𝐵2
𝑇𝑛𝑒𝑇𝑒𝑉𝑝(8)
which gi es esul s in acco dance wi h ASTRA simula ions. The e o e,
neglec ing he adia i e powe 𝑃𝑟𝑎𝑑 , i is expec ed ha in phase 1
SMART will achie e he ohmic H-mode (𝑃𝑂𝐻 ≫ 𝑃𝐿𝐻 ). The ene gy
con inemen ime has been app oxima ed wi h he ollowing scaling
law alid a low densi ies and o ohmic hea ing [16]:
𝜏𝐸[s] = 0.07𝑛20𝑎𝑅2
0𝑞𝑐𝑦𝑙 (9)
whe e 𝑞𝑐𝑦𝑙 = 5𝑎2𝐵𝑇∕𝐼𝑝𝑅 he cylind ical sa e y ac o . Fo phase 1,
an ene gy con inemen ime o 0.33 ms is expec ed while ASTRA
p edic s 0.22 ms, sligh ly lowe bu o he same o de o magni ude.
The boo s ap cu en ac ion 𝑓𝑏𝑠 is expec ed o inc ease wi h he
iangula i y 𝛿 om 14.3% o 15.1% as he e is a small inc ease in 𝛽𝑝,
see Table 2.
5. Phase 2 scena ios
5.1. ASTRA esul s
ASTRA simula ions ha e been ca ied ou in o de o de e mine
he p o iles o densi y and empe a u e in phase 2 wi h and wi hou
he NBI. The pa ame e s o he NBI used o he ASTRA simula ions
a e he injec ed powe (𝑃𝑁𝐵𝐼 ) o 1 MW and ene gy (𝐸0) o 25 keV
as desc ibed in Sec ion 5.2. Only he NBI hea ing has been included
in he simula ions. No ECRH hea ing has been conside ed as i will
only be used o p e-ioniza ion du ing he plasma s a -up. The baseline
case has been compa ed wi h he ex eme posi i e iangula i y, e en
hough he wo con igu a ions di e sligh ly (see Table 2). Figs. 7 and
8show he densi y and empe a u e p o iles in phase 2 whe e he
blue cu es ep esen s he scena ios wi hou NBI, and he ed ones
wi h he NBI. Do ed cu es in bo h cases ep esen he scena ios in
he highes posi i e iangula i y case. Wi h he NBI a ise in bo h
densi y and empe a u e is expec ed. 𝑛𝑒0and 𝑛𝑖0will inc ease up o 4.7×
1019 m−3 and 3.8 × 1019 m−3. No big di e ence is expec ed be ween he
baseline and he ex eme posi i e iangula i y case, as he di e ence
in iangula i y o hose wo cases is 0.1.
A la ge inc ease is expec ed in he elec on and ion empe a u e.
𝑇𝑒and 𝑇𝑖will inc ease up o 0.56 keV and 0.7 keV espec i ely in
Fig. 8. Tempe a u e p o iles o phase 2 wi h and wi hou NBI.
Fig. 9. T anspo coe icien s wi h he ETB loca ed a 𝜌𝑝𝑜𝑙 = 0.95.
he baseline case. In he case o ex eme posi i e iangula i y, he ion
empe a u e will be sligh ly highe up o 0.75 keV and he elec on
empe a u e up o 0.6 keV. Scena ios wi h NBI will enhance he 𝛽
pa ame e s. In he baseline case, he 𝛽𝑡will ise up o 8.23%, 𝛽𝑝up
o 0.7 and 𝛽𝑁up o 4.1, compa ed o he alues eached in phase 1
(see Table 2). In he ex eme posi i e case 𝛽𝑡will ise up o 9.1%, 𝛽𝑝o
0.69 and 𝛽𝑁up o 4.44. Mo eo e , ASTRA esul s o esee a boo s ap
cu en ac ion ha inc ease om 𝑓𝑏𝑠 ≈ 15% in phase 1 o 𝑓𝑏𝑠 ≈ 37%
in phase 2 (𝐼𝑏𝑠 ≈66 kA), wi h a cu en ac ion induced om he NBI
(𝑓𝐶𝐷) o almos 15% which co esponds o an induced cu en 𝐼𝐶𝐷 ≈
30 kA, in line wi h he esul s o GLOBUS-M [17].
ASTRA simula ions p edic ha he o al beam powe 𝑃𝐶𝐷 is app ox-
ima ely 0.7 MW high enough o o e come 𝑃𝐿𝐻 , see o mula (6), which
is app oxima ely 90 kW. The adia i e powe can be neglec ed as in
phase 1. In ac , using he o mulas (7) and (8), he adia i e powe
can be es ima ed o almos 2.2 kW. The e o e i is expec ed ha in
phase 2 wi h he NBI, SMART will achie e he H-mode as 𝑃𝐶𝐷 ≫ 𝑃𝐿𝐻 .
In addi ion wi hou he NBI, he ohmic powe (𝑃𝑂𝐻 ), e alua ed wi h
he o mula (5), is app oxima ely 0.22 MW simila o he 0.27 MW
ob ained wi h ASTRA. As he ohmic powe is highe han he h eshold
powe i is likely o expec ha SMART will achie e in a H-mode egime
also wi hou he NBI. This jus i ies he app oxima ion o using he
anspo coe icien s wi h he p o iles shown in Fig. 9 and desc ibed
in Sec ion 3.
Fusion Enginee ing and Design 192 (2023) 113833
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A. Mancini e al.
As he ope a ion will be in H-mode, he con inemen ime 𝜏𝐸can
be es ima ed wi h he ITER IPB(y,2) scaling law [18]:
𝜏𝐸[s] = 0.145 𝐼0.93
𝑃𝑅1.39
0𝑎0.58𝑘0.78𝑛0.41
20 𝐵0.15
𝑇𝑀0.19
𝑃0.69
𝐻
(10)
whe e 𝑃𝐻=𝑃𝑁𝐵𝐼 is he ex e nal hea ing powe . Fo phase 2 we
ge a con inemen ime o 6.5 ms sligh ly lowe bu o he same
o de o magni ude o he one compu ed by ASTRA, 10 ms. A be e
es ima ion o he con inemen ime 𝜏𝐸is ob ained when conside ing a
NSTX-Gy oBohm scaling law alid o sphe ical okamaks [19]:
𝜏𝐸[s] = 0.21
𝐼0.054
𝑝𝐵0.91
𝑇𝑅2.14
0
𝑛0.05
𝑒𝑃0.38
𝐻
(11)
which gi es a 𝜏𝐸o almos 9 ms, in line wi h he ASTRA esul s.
5.2. NBI design and op imiza ion
To ensu e H-mode in phase 2, 1 MW o Neu al Beam Injec ion (NBI)
will be applied o posi i e- iangula i y SMART plasmas. Beam heigh
and wid h ha e been de e mined scaling NBIs o simila machines
in size o SMART, such us Globus-M. The p elimina y dimensions o
he g id beams conside ed in he simula ions a e heigh and wid h
o 30 cm and 33 cm espec i ely. The main pa ame e s o he NBI
ha e been op imized h ough he Mon e-Ca lo o bi - ollowing code
ASCOT5 [20], using he wall geome y and he magne ic equilib ium
calcula ed wi h FIESTA (see Sec ion 3) and he empe a u e and densi y
p o iles ob ained wi h ASTRA wi hou ex e nal hea ing, see Sec ion 5.1.
The op imiza ion o he main NBI pa ame e s has been pe o med wi h
an i e a i e p ocess, analysing he con inemen o di e en pa icles
injec ed a he sepa a ix (𝑟= 0.75 m and 𝑧= 0 m) and ionized
inside he plasma. He e, he op imiza ion o he injec ion geome y is
p esen ed, pe o med se ing he NBI main beam ene gy, 𝐸0, o 25 keV.
This has been conside ed as he bes choice o phase 2 acco ding o
p e ious analysis, and ma ching he ene gy obse ed in o he simila
machines [9]. The ene gy o he beam is limi ed on one hand by he
gy o adius o he esul ing pa icles, ha inc eases wi h ene gy (𝑟𝐿=
𝑚𝑣⟂∕𝑞𝐵 ∝𝐸0∕𝐵), and by he o bi d i s, hus a ec ing as -ion losses.
On he o he hand, he highe he ene gy, he lowe he c oss-sec ion
o he global ioniza ion p ocesses be ween he injec ed neu als and he
he mal plasma [21], inc easing he shine- h ough (i.e., he pe cen age
o pa icles ha a el h ough he plasma wi hou ge ing ionized),
and hus, dec easing he o al e iciency. The e o e, he wo main
pa ame e s employed o op imize he NBI geome y and ene gy a e he
p omp losses (i.e., pa icles ha a e los be o e comple ing a o oidal
pe iod) and he shine- h ough. Mo eo e , a 25 keV injec ion ene gy
p o ides a supe -Al énic as -ion dis ibu ion, as he Al én eloci y
a 𝜌𝑝𝑜𝑙 = 0.5is 𝑣𝐴∼ 1.6 × 106m∕s, while he eloci y co esponding o
he main injec ion ene gy is 𝑣= 2.2 × 106m∕s, making i possible o
d i e uns able a wide a ie y o Al én Eigenmodes, enabling o s udy
hei beha iou as a unc ion o plasma shape and iangula i y. Highe
injec ion ene gies, up o 35 keV, will also be conside ed du ing he
op imiza ion p ocess.
In o de o op imize he injec ion con igu a ions, he as -ion bi h
dis ibu ion has been modelled wi h a se o 106ma ke s (high enough
o achie e good s a is ics, acco ding o p e ious analysis), whose o bi s
a e ollowed o 1 ms. The di e en se s o ma ke s ha e been gene a ed
wi h he BBNBI code [22], by a ying he angency adius o he beam
cen e line, as shown in Fig. 10. Then, by means o he ASCOT5 code,
he ionized pa icles ha e been ollowed in a collisionless and MHD-
quiescen en i onmen , in o de o calcula e he pe cen ages o p omp
losses (as men ioned, pa icles los be o e comple ing a o oidal pe iod,
and hus, no a ec ed by Coulomb collisions). The selec ed simula ion
ime is su icien o accoun o he p omp losses. The shine- h ough
has also been calcula ed o each o he 9 cases s udied, wi h he aim
o minimize he o al amoun o pa icles ha a e los .
Fig. 10. Ske ch o he o oidal iew o he SMART NBI con igu a ion. The black ci cles
ep esen he essel walls and he ed ones he o oidal sec ion o he sepa a ix. The
yellow line ep esen s he beamline. The pe pendicula dis ance om he beam o he
cen e o he de ice is ep esen ed by he blue ci cle and line, indica ing he angency
adius, 𝑅𝑡.
Fig. 11. NBI bi h dis ibu ion in he o oidal p ojec ion o he mos ex eme
con igu a ions, #1 (up) and #9 (down).
The esul s o he di e en con igu a ions s udied by a ying he
chosen op imiza ion pa ame e , 𝑅𝑡, a e shown in Fig. 12. As he plasma
inne and ou e adius is loca ed a 0.243 mand 0.747 m,𝑅𝑡has
been modi ied om 0.280 m o 0.735 m. The o oidal iew o he
bi h dis ibu ion o he pa icles gene a ed wi h hese wo ex eme
con igu a ions a e shown in Fig. 11.
The minimum o al amoun o losses is p o ided by con igu a ions
#3 and #4, see Fig. 12. The ise in he shine- h ough wi h 𝑅𝑡is
explained conside ing ha , as he angency adius is inc eased, he
beam a els a sho e pa h h ough he plasma, in a egion wi h lowe
densi y. On he con a y, inc easing he angency adius, he beam
aligns wi h he magne ic ield lines, dec easing he p omp losses o

Fusion Enginee ing and Design 192 (2023) 113833
6
A. Mancini e al.
Fig. 12. E olu ion o he esul ing losses o he di e en con igu a ions ( ed ci cles)
s udied o he NBI sys em.
Fig. 13. Slowing down dis ibu ion o he op imum con igu a ion, #4, in pi ch-ene gy.
a negligible le el. Hence, con igu a ions om #5 o #9 should be
disca ded, as he shine- h ough is oo high, as well as con igu a ions
#1 and #2, due o hei highe esul in p omp losses in compa ison
o he o he s.
As con igu a ions #3 and #4 show simila esul s, he shine- h ough
and he p omp losses ha e been compu ed a highe injec ion ene gies,
up o 35 keV, o bo h geome ies. This c i e ia has been chosen in
o de o assess hei pe o mance in he possible case o an inc ease in
he ene gy o he beam in he u u e [23], which would be pe o med
wi hou changing he injec ion geome y o he NBI. 35 keV is se
as he maximum pe mi ed injec ion ene gy, as i allows main aining
he shine- h ough below 10% wi h he cu en plasma p o iles. The
esul s in Table 3 show ha , as he ene gy inc eases, he p omp losses
in con igu a ion #3 ise apidly. The shine- h ough, on he con a y,
inc eases o bo h con igu a ions, and i s absolu e alue is compa able.
This e olu ion o he p omp losses wi h he ene gy has led o
choose con igu a ion #4 as he op imum one, showing ha he in-
jec ion ene gy o he NBI sys em could be inc eased in he u u e i
desi ed, and he p omp losses would s ay in an admissible ange,
while p ese ing an accep able e olu ion o he shine- h ough ac ion,
always kep below 10%.
The slowing down dis ibu ion o con igu a ion #4 and a 25 keV in-
jec ion ene gy has also been analysed. Fo his simula ion, he injec ed
pa icles a e allowed o in e ac wi h he bulk plasma ia Coulomb
collisions o 1 s, which is ound su icien o mos o he as -ion
dis ibu ion o he malize. The ma ke s a e s opped when hey each
ei he he selec ed he mal limi o 1 keV, o he maximum simula ion
Fig. 14. Bi h dis ibu ion o he pa icles gene a ed wi h he op imized con igu a ion
(#4). To oidal (up) and poloidal (down) p ojec ions. The la e includes a ypical
con ined o bi .
Table 3
Resul ing losses o con igu a ions #3 and #4, and di e en injec ion ene gies.
ID Ene gy Shine- h ough P omp losses To al losses
25 keV 4.9% 0.1% 5.0%
3 30 keV 6.9% 0.4% 7.3%
35 keV 9.0% 1.1% 10.1%
25 keV 5.3% 0.0 % 5.3%
4 30 keV 7.4% 0.1 % 7.5%
35 keV 9.6% 0.5 % 10.1%
ime. As shown in Fig. 13, mos o he pa icles ha e a pi ch angle abo e
0.9, meaning ha hey will desc ibe passing o bi s. This is desi able in
o de o educe possible losses due o he d i o apped o bi s, and
esul s in a be e con inemen o he beam pa icles. Hence, he bi h
dis ibu ion o he selec ed con igu a ion (#4) is shown in Fig. 14,
whe e an example o a passing o bi has been plo ed in he poloidal
p ojec ion o he dis ibu ion.
6. Conclusions
Re e ence scena ios o he SMART okamak ha e been compu ed
wi h he 1.5D anspo code ASTRA coupled wi h FIESTA o p edic he
densi y and empe a u e p o iles needed p ima ily o he assessmen
o he pe o mances o he machine. Only he baseline and maximum
posi i e iangula i y scena ios ha e been conside ed o phase 1 and
phase 2. In phase 1 he pa ame e s chosen he e sugges ha he ma-
chine will access he H-mode wi h a maximum 𝑛𝑒0and 𝑛𝑖0o 1×1019 m−3
and 0.8×1019 m−3. Maximum empe a u e 𝑇𝑒0and 𝑇𝑖0o 0.171 keV and
0.080 keV will be achie ed wi h a maximum con inemen ene gy ime
𝜏𝐸o 0.2 ms, lowe han he one es ima ed wi h he con inemen scaling
law o ohmic hea ing bu o he same o de o magni ude. Phase 2
will be equipped wi h a Neu al Beam Injec o whose cha ac e is ics
ha e been p esen ed oge he wi h he op imiza ion o i s pa ame e s,
Fusion Enginee ing and Design 192 (2023) 113833
7
A. Mancini e al.
in pa icula ene gy and injec ion geome y. The bes con igu a ion
has been de e mined, opening he possibili y o inc easing he NBI
ene gy wi hou changing he injec ion geome y in he u u e. ASTRA
simula ions o phase 2 p edic ha SMART will access H-mode wi h
and wi hou NBI as bo h he Ohmic Powe (𝑃𝑂𝐻 ) and he NBI coupled
powe (𝑃𝐶𝐷) a e su icien ly highe han he h eshold powe (𝑃𝐿𝐻 ) as
long as he expe imen s will con i m ha he adia i e powe losses
will be negligible. Co e densi ies up o 4.65 × 1019 m−3 will be eached
wi h a co e empe a u e o 0.75 keV. Be a no malized 𝛽𝑁will inc ease
up o 4.4 wi h a o oidal 𝛽𝑡up o 9%. A boo s ap cu en ac ion o 𝑓𝑏𝑠
o 37% will be eached and a NBI cu en d i e ac ion 𝑓𝐶𝐷 o 15% is
expec ed. Nega i e iangula i y p o iles will be assessed in a sepa a e
wo k, explo ing also he phase 3 scena io.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing inan-
cial in e es s o pe sonal ela ionships ha could ha e appea ed o
in luence he wo k epo ed in his pape .
Da a a ailabili y
Da a will be made a ailable on eques
Acknowledgemen s
This wo k ecei ed unding om he Fondo Eu opeo de Desa ollo
Regional (FEDER) by he Eu opean Commission unde g an ag eemen
numbe s IE17-5670 and US-15570. The au ho s g a e ully acknowledge
he inancial suppo o he Eu opean Resea ch Council (ERC) unde he
Eu opean Union’s Ho izon 2020 esea ch and inno a ion p og amme
(g an ag eemen No. 805162).
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