Plasma Physics and
Con olled Fusion
PAPER • OPEN ACCESS
The ole o SOL plasma in he con inemen o NBI
as ions in W7-X
To ci e his a icle: T P Ki iniemi
e al
2025
Plasma Phys. Con ol. Fusion
67 025034
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Plasma Physics and Con olled Fusion
Plasma Phys. Con ol. Fusion 67 (2025) 025034 (12pp) h ps://doi.o g/10.1088/1361-6587/adaa14
The ole o SOL plasma in he
con inemen o NBI as ions in W7-X
T P Ki iniemi1,∗, T Ku ki-Suonio1, S Laze son2,4, S Äkäslompolo1, P Ollus1,
L Sanchis3, D Kulla4and he W7-X Team4
1Aal o Uni e si y, Espoo, Finland
2Gauss Fusion, 85748 Ga ching bei München, Ge many
3Uni e si y o Se ille, Se illa, Spain
4Max-Planck-Ins i u ü Plasmaphysik, 17491 G ei swald, Ge many
E-mail: imo.ki[email p o ec ed]
Recei ed 2 Oc obe 2024, e ised 12 Decembe 2024
Accep ed o publica ion 14 Janua y 2025
Published 30 Janua y 2025
Abs ac
The impac o he sc ape-o laye (SOL) plasma on deposi ion, con inemen and losses o
neu al beam injec ed as ions was in es iga ed in W7-X plasma. The e ec o SOL wid h,
densi y, empe a u e p o iles, adial elec ic ield, and cha ge–exchange eac ions (CX) was
explo ed. Ioniza ion and slowing down pa ly coun e balance each o he , as slowing down in
cold SOL plasma compensa es o ioniza ion e ec s in adially decaying model p o iles.
Howe e , he e ec o SOL plasma on mo e ulne able s eel componen s is mi iga ed o e a
wide ange o di e en p o iles, because o hose componen s he collisionali y e ec o e ules
he e ec o SOL on ioniza ion. The e ec o he adial elec ic ield is mi iga ed o s eel
componen s in he expe imen ally obse ed di ec ion o he ield. The e ec o CX eac ions is
shown o lead o a widely sp ead low powe load dis ibu ion wi h no clea e ec on peak load.
S a is ical challenges caused by hugely a ying iangle sizes in he disc e iza ion o walls a e
discussed.
Keywo ds: NBI, as ions, Wendels ein 7-X, s ella a o , ASCOT
1. In oduc ion
Losses o neu al beam injec ed (NBI) as ions can pose a
signi ican challenge o s ella a o i s walls. Highly local-
ized hea luxes can cause sublima ion o ca bon and mel -
ing o s eel componen s when peak loads a e o he o de o
10 MW m−2o mo e [1]. In Wendels ein 7-X (W7-X) his
is especially ue, whe e he o e hea ing o he s eel plasma
acing componen s (PFCs) om los as ions can esul in
signi ican damage. In p e ious simula ions o neu al beams
∗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.
in W7-X, he ioniza ion p obabili y has adi ionally been
e alua ed only a e he beam neu als ha e c ossed he las
closed lux su ace (LCFS). Howe e , expe imen al e idence
o edge-bo n as ions exis s [2]. Simila ly, when a beam ion
exi s he plasma and en e s he sc ape-o laye (SOL), i is
assumed o be collisionless. While sophis ica ed wall model-
ing has been conduc ed o di e en magne ic con igu a ions
(e.g. [3] whe e eigh con igu a ions, including he s anda d
con igu a ion, we e in es iga ed), he e ec o SOL plasma
and cha ge–exchange eac ions ha e no been conside ed in
hose s udies.
In he p esen s udy, we add ess his limi a ion by in odu-
cing a ini e plasma a ini e empe a u e in he W7-X SOL o
he s anda d con igu a ion. The goal is o assess he impac o
pa ially ionized SOL plasma on he beam deposi ion, beam
ion con inemen , and losses o beam ions when he plasma
ex ends beyond he LCFS. This is possible using BBNBI5 [5]
o he beam deposi ion and ASCOT5 [4] o he collisional
1 © 2025 The Au ho (s). Published by IOP Publishing L d
Plasma Phys. Con ol. Fusion 67 (2025) 025034 T P Ki iniemi e al
p ocesses, including cha ge exchange (CX) eac ions, o he
beam ions. In he wo s -case scena io, he SOL plasma can
lead o a signi ican inc ease in powe loads ia p ema u e
beam ioniza ion and/o CX eac ions. On he o he hand, since
SOL plasma p o ides an addi ional egion o he beam o slow
down, i could mi iga e he powe loads. De e mining he ne
e ec o SOL plasma can only be achie ed h ough me iculous
simula ion. In he p esen wo k, we concen a e on in es iga -
ing he in eg a ed e ec s due o di e en physical phenomena.
In addi ion, he s a is ical challenges due o he disc e e 3D
wall s uc u e when es ima ing he peak loads a e discussed
and means o a oid nume ical anomalies a e p oposed.
The ASCOT sui e o codes is a comp ehensi e and well-
es ablished ool o as ion s udies in bo h cu en and u u e
okamaks. I s ini ial applica ion in 3D s ella a o geome y
was o p edic beam powe loads o sensi i e PFCs in he
i s ope a ing phase o W7-X. The simula ion esul s p o ed
o be o immense alue, leading o imp o ed sa e y o he
i s wall [3]. Subsequen ly, ASCOT has also been employed
o in es iga e he impac o W7-X magne ic con igu a ion on
neu on p oduc ion a es [6] and he e ec o NBI ion powe
load on he ICRH an enna [7]. The p esen s udy on powe
loads is an ex ension o he OP2 phase, which no only in ol es
highe hea ing powe bu , mo e impo an ly, includes he phys-
ical p ocesses p e iously o e looked.
In addi ion o collisional p ocesses, he e ec o a SOL
adial elec ic ield is also included. To da e, he e ec o a
adial elec ic ield on as pa icle con inemen in W7-X has
only been s udied in he egion inside he LCFS [8]. He e he
as pa icle con inemen is ound o be signi ican ly imp o ed
by he associa ed E×Bd i . In okamaks, he SOL E has
been ound o ha e a clea impac on he as ion powe
load dis ibu ion [9]. In dedica ed expe imen s on W7-X, local
powe loads due o bulk plasma we e measu ed by a sys em
o in a ed (IR) ideo came as and e ealed asymme ies ha
could no be explained o he han by assuming a SOL adial
elec ic ield wi h he associa ed E×Bd i [10]. This e ec
should hus also be s udied o beam ions. In he absence o
adequa e measu ed da a, we es he po en ial e ec o SOL E
on beam powe load dis ibu ion using model p o iles.
Beam ion powe loads in W7-X we e ecen ly s udied
expe imen ally wi h he mog aphic measu emen s and simu-
la ed using BEAMS3D and ASCOT5 codes [11]. This wo k
explici ly poin ed ou he lack o SOL physics in he simula-
ions, a si ua ion which we now wish o emedy. The e o e,
e en cha ge exchange (CX) eac ions a e included he e: he
new a omic eac ion module in ASCOT5 enables he inco po -
a ion o CX eac ions in he SOL plasma [12,13]. The model
has been applied o TJ-II s ella a o plasma in [14].
This a icle is o ganized as ollows. The ele an ea u es
o he ASCOT5 and BBNBI5 simula ion codes and W7-X
se up a e desc ibed in sec ion 2. In sec ion 3, he e ec s o
bo h slowing down and ioniza ion on beam powe loads a e
in es iga ed. The ele ance o he SOL wid h is also es ed. Ad
hoc SOL adial elec ic ields a e included in he simula ions
in sec ion 4, and he e ec o cha ge exchange in sec ion 5.
Finally, he conclusions a e p esen ed in sec ion 6.
2. Tools and me hods
2.1. ASCOT5 and BBNBI5
In his wo k, he main ools a e ASCOT5 and BBNBI5.
ASCOT5 [4] is he la es de elopmen e sion o ASCOT,
which is a Mon e Ca lo code o simula ing ma ke s in a mag-
ne ically con ined plasma, including collisional p ocesses wi h
a ixed backg ound plasma. The code has wo di e en op ions
o o bi - ollowing:
(i) gy o o bi me hod, whe e he ma ke s ollow he ajec -
o ies o physical pa icles in elec ic and magne ic ields
Eand B, espec i ely. The equa ions o mo ion, de i ed
om he Hamil onian dynamics:
˙
x=p
γm
˙
p=q(E+˙
x×B)
a e sol ed using he olume-p ese ing algo i hm [15],
which can be hough o as a ela i is ic a ian o he Bo is
scheme. He e, xand pa e he posi ion and momen um
o he pa icle wi h mass m, and γ=√1−(p/mc)2is
he Lo en z ac o . In SOL, he gy o o bi s a e always
ollowed.
(ii) he guiding cen e me hod, which is as e bu mo e
inaccu a e in e alua ing powe loads. The guiding-cen e
equa ions o mo ion can be sol ed wi h ei he ou h-o de
Runge–Ku a me hod ( ixed ime s ep) o Cash–Ka p [16]
(adap i e ime-s ep). These me hods do no conse e he
ma ke ene gy, bu by choosing a su icien ly small ime-
s ep he esul ing e o emains insigni ican .
In he p esen wo k, mos o he simula ions a e ca ied
ou using he so-called hyb id me hod in which he guiding-
cen e app oach is used inside he LCFS, while gy o o bi s a e
ollowed once he ma ke has c ossed he LCFS. The hyb id
me hod is cos -e icien o e alua ing powe loads since he
ole o he slowing-down simula ions inside he LCFS is only
o iden i y he ma ke s eaching he LCFS. A no able excep-
ion o his is a simula ion including he CX eac ions since,
in he p esen code e sion, he CX model is only applicable
o ull o bi simula ions ( o an example o he guiding-cen e
app oach on CX eac ions see, e.g. [17]).
The CX eac ion be ween a as hyd ogen ion H+
and a
hyd ogen neu al H(simila ly o o he iso opes) is based on
he equa ion H+
+H→H +H+, which, in he Mon e Ca lo
simula ion, is modeled assuming neu aliza ion p obabili y
Pn=1−e−R∆ , wi h he eac ion a e R=n0⟨σCX ⟩. He e,
n0is he neu al densi y, ⟨σCX ⟩is he CX eac ion a e coe -
icien and ∆ is he ime s ep. In [12], his as -ion CX model
using a omic eac ion da a om he ADAS da abase [18,19]
was implemen ed in ASCOT and e i ied by es ima ing he
eac ion mean ee pa hs. Subsequen ly, he model has been
used in simula ions o beam-ion con inemen in he MAST
Upg ade [13].
2
Plasma Phys. Con ol. Fusion 67 (2025) 025034 T P Ki iniemi e al
The magne ic con igu a ion and plasma p o iles a e used
o gene a e he beam ion bi h p o ile wi h BBNBI5. The ime
e olu ion o he ensemble o beam ion ma ke s is hen modeled
wi h he ASCOT5 code un il hey ei he collide wi h he 3D
wall o a e slowed down close o he local he mal ene gy. The
ene gy and pi ch collisions wi h he s a ic hyd ogen-elec on
plasma backg ound, de ined by he inpu p o iles, a e modeled
wi h Mon e Ca lo collision ope a o s.
BBNBI [5] gene a es he ions om beam neu als o
ASCOT simula ions. BBNBI5 is an ASCOT5 na i e imple-
men a ion o BBNBI wi h iden ical physics. He e, he ioniz-
a ion c oss-sec ions o he Suzuki model [20] a e used. The
NBI beam is modeled as ealis ic, injec o -speci ic beamle s
o ma ke s. Beam neu als a e ad anced un il hei ioniza-
ion p obabili y exceeds a andom h eshold λ, a e which he
exac ioniza ion loca ion is calcula ed and a new beam ion is
eco ded.
2.2. W7-X se up
W7-X will be equipped wi h wo NBI Boxes ( o balanced
injec ion), each wi h ou sou ces [21]. Hal o he sou ces
ha e no ye been included in he OP2 campaign bu , in his
wo k, all planned sou ces a e included. In BBNBI5 simula-
ions, hese eigh NBI sou ces a e se o injec hyd ogen wi h
a nominal powe o 1.7 MW. BBNBI5 uses a de ailed model
o he NBI injec o s, wi h 774 beamle s pe sou ce, each wi h
a gi en di e gence alue o 0.0125 ad. The maximum pa icle
ene gy o hyd ogen injec ion is 55 keV, and ealis ic ac ions
o 1/2 and 1/3 ene gy pa icles a e 39% and 28%, espec i ely.
The equilib ium, co esponding o he W7-X discha ge
20180920.17, was econs uc ed using he equilib ium sol e
STELLOPT [22,23] which is in e aced o he VMEC 3D
equilib ium sol e . This was an ECRH discha ge in he s and-
a d magne ic con igu a ion wi h added NBI [24]. Equilib ium
magne ic ields and lux su ace coo dina es we e hen placed
on o he cylind ical ASCOT5 backg ound g ids using he
BEAMS3D code [25]. The boo s ap cu en and he adial
elec ic ield inside he equilib ium bounda y we e ob ained
using he NEOTRANSP [26,27] anspo sol e .
As VMEC is an in e se code, only ields inside he VMEC
domain can be in e pola ed om he VMEC lux-aligned g id
o he cylind ical g id. Ou side he VMEC domain, he same
me hods we e used o ex apola e he lux su ace coo dina es
in o he SOL, and he magne ic ields we e ob ained by Bio –
Sa a in eg a ion o e he W7-X coils se , wi h a i ual cas-
ing p inciple o he plasma esponse [28]. The SOL plasma
p o iles can hen be speci ied as a unc ion o he ex apola ed
lux su ace coo dina e only. In igu e 1, he ex apola ed adial
g id, VMEC equilib ia, acuum Poinca é, and wall s uc u e
a e plo ed in he egion o he NI21 neu al beam line. A solid
blue line is used o deno e he ρ=1.1 and 1.2 su aces which
de ine he maximum ex en o ou p o iles.
The de ailed 3D wall is acqui ed om CAD models by
expo ing hem as iangula su ace meshes wi h oughly 7.8
million iangles [29]. In his wo k, we mainly ocus on he
o al load a i ing a di e en wall componen s consis ing o
Figu e 1. Plo o he a ious adial g id quan i ies o he W7-X
s anda d magne ic con igu a ion. The colo map shows he adial
g idding used in his wo k (ex apola ed ou side he VMEC
domain). Whi e solid lines depic he VMEC lux su aces wi h he
magne ic axis deno ed by a whi e c oss. A acuum Poinca é plo is
included showing he edge island s uc u e (no conside ed in adial
g idding). Solid blue lines a e d awn a he ρ=1.1 and 1.2 su aces
o e e ence o he edge p o iles conside ed. A c oss sec ion o he
i s wall s uc u es is depic ed in black.
Figu e 2. A iew o he W7-X in e nal wall as seen by ASCOT.
Wall componen s ele an o his wo k a e colo coded.
hese iangles. Such componen s, as seen by ASCOT ma ke s,
a e illus a ed in igu e 2. Since he beam ion weigh s co es-
pond o a sou ce, hey a e in uni s o s-1, and he powe load
(in Wa s) is calcula ed simply by summing up he ene gy con-
ibu ion o all ma ke s a i ing a a pa icula wall compon-
en / iangle. The powe loads can hen be ob ained by di id-
ing he powe by he su ace a ea. As shown in igu e 3 i-
angle sizes a y a lo which, oge he wi h a ini e numbe
o ma ke s, causes s a is ical p oblems o he smalles i-
angles as discussed la e in sec ion 3. In igu e 4 he ex apol-
a ed ρ- alues o wall componen s a e shown. This alue indic-
a es how close o he co e plasma and LCFS he componen s
a e.
Due o he ad hoc na u e o much o he SOL inpu da a,
hese simula ions do no aim a quan i a i e es ima es o he
3
Plasma Phys. Con ol. Fusion 67 (2025) 025034 T P Ki iniemi e al
Figu e 3. Numbe o wall iangles as a unc ion o iangle size.
Small iangle sizes a e equi ed a some pa s o he wall o
accu a ely disc e ize he wall bu his also causes challenges in
s a is ics o he simula ion.
Figu e 4. The ex apola ed ρ- alues o wall s uc u e show ha he
ca bon componen s ge ing mos o he load a e much close o he
co e plasma when compa ed o s eel componen s.
peak powe bu , a he , a ob aining a quali a i e unde s and-
ing o he ela i e ole o di e en SOL mechanisms a ec -
ing he beam ion con inemen and powe loads. Consequen ly,
1.2 million ma ke s is conside ed su icien in all add essed
cases.
The inpu p o iles o densi y n(ρ)and empe a u e T(ρ),
oge he wi h he adial elec ic ield E and he beam ion
bi h p o ile, calcula ed om he densi y and empe a u e al-
ues, a e shown in igu e 5. The inpu p o iles a e based on
a s e eo ypical W7-X s anda d magne ic con igu a ion dis-
cha ge wi h mixed ECRH and NBI [24]. The elec on dens-
i y p o ile and elec on empe a u e p o iles a e based on i s
o Thomson da a [30], while he ion empe a u e is based on
XICS measu emen s [31] (inside o ρ=1). The adial elec ic
ield is de i ed om neoclassical es ima es based on hese p o-
iles and magne ic con igu a ion. No edge anspo modeling
Figu e 5. Plasma backg ound used in he simula ions: (a) densi y,
(b) empe a u e, and (c) adial elec ic ield. In (d), he NBI sou ce
dis ibu ion, calcula ed wi h BBNBI5 using hese p o iles, is shown.
No ice ha he SOL p o iles a e a ied along he s udy in an a emp
o de e mine he impo ance o di e en physical p ocesses.
was conside ed in his wo k, ins ead edge p o ile shapes we e
chosen o help scope he e ec o including such p o iles in
he u u e.
3. The e ec o slowing down and ioniza ion in SOL
In his sec ion, he e ec o slowing down and ioniza ion due
o he SOL plasma a e s udied. The p o iles inside LCFS a e
kep in ac h oughou his s udy, while we expe imen wi h
he SOL p o iles o ob ain a quali a i e unde s anding o he
ela i e impo ance o di e en p ocesses.
The elec on empe a u e a LCFS is abou 150 eV, which
implies ha he c i ical ene gy (Ec i ≈14.8·Te) in he SOL
will be app oxima ely equal o o less han 2 keV. The e o e,
pi ch sca e ing will play no ole in SOL and, consequen ly, we
e e o collisional p ocesses in SOL as slowing down only.
Fi s , we use cons an SOL densi y and empe a u e p o iles
o examine i he SOL wid h plays an impo an ole. This is
ollowed by in es iga ions wi h mo e ealis ic p o iles.
3.1. Cons an p o iles and SOL wid h
We s a ou wo k on he e ec o SOL plasma wi h sani y
checks ha also add ess he signi icance o he SOL wid h.
Since he magne ic islands in he s anda d con igu a ion can
4
Plasma Phys. Con ol. Fusion 67 (2025) 025034 T P Ki iniemi e al
Table 1. Change in he numbe o ions los o he wall (∆pa s) and
in he powe load (∆P), caused by in oducing a SOL plasma.
Numbe s w i en in i alics co espond o cases whe e cons an SOL
densi y o nLCFS and cons an empe a u e a wo di e en alues
(TLCFS/10 and TLCFS/3) we e assumed, while numbe s w i en in
bold ha e linea ly decaying SOL p o iles. The wo bo om lines
co espond o cases whe e ei he densi y o empe a u e was kep
cons an a he gi en alue, while he o he decayed linea ly (‘linea
n’, ‘linea T’). Bo h slowing down (SD) and ioniza ion p ocesses in
SOL a e included unless o he wise s a ed.
Case ∆pa s ∆P
no SOL base base
T/3 (ρmax =1.2), SD only −12.0% −30.0%
T/10 (ρmax =1.1), SD only −37.3% −60.2%
T/10 (ρmax =1.2), SD only −40.7% −66.3%
T/10 (ρmax =1.2)−16.4% −27.6%
linea n&T, SD only −1.5% −9.4%
linea n&T, Ioniza ion only +9.9% +19.8%
linea n&T+8.3% +8.5 %
linea n,T=TLCFS +8.7% +9.5%
linea T,n=nLCFS +15% +9.3%
be 10 cm wide and he e ec i e mino adius o W7-X is
o he o de o 50 cm, as a p elimina y check we compa e
plasmas ex ending o di e en adii: ρmax =1.0 (i.e. no SOL
plasma), 1.1, and 1.2. He e, ρs ands o he ex apola ed adial
coo dina e, wi h ρ=1.0 co esponding o he LCFS. Fo cla -
i y, hese es s we e done assuming a cons an SOL plasma
wi h nSOL =nLCFS and TSOL =TLCFS/10. These alues p ob-
ably o e es ima e SOL collisionali y so he a ionali y o hese
simula ions is o explo e he uppe limi o slowing down
e ec s.
The esul s, collec ed o able 1, show ha he e is e y
li le di e ence be ween he plasmas ex ending o ρmax =1.1
and ρmax =1.2, indica ing ha he main slowing down e ec s
o SOL a e coming om he egion be ween ρ=1.0–1.1.
Ex ending he SOL u he does no change he esul s, which
is due o he di e o pla es being close o he plasma (as shown
la e in igu e 4). Ano he in e es ing obse a ion om his
simple simula ion se is ha he powe load d ops mo e signi-
ican ly han he numbe o wall pa icles. Fo he ρmax =1.2
case, he SOL plasma educes he powe load by oughly 66%
, while he numbe o wall pa icles d ops by only 41% . This
means ha no only is he numbe o pa icles eaching he wall
educed, bu hose eaching he wall a e less ene ge ic due o
he slowing down e ec .
The simula ions we e epea ed o highe SOL empe a -
u e, TSOL =TLCFS/3, bu keeping he same densi y. As expec-
ed, due o he in e se empe a u e dependence o he collision
equency, his leads o a mo e modes slowing down e ec ,
i.e. he powe load was educed only by 30%, and he numbe
o wall pa icles d opped by a me e 12%.
The T/10, ρmax =1.2-case was hen epea ed including he
e ec o SOL also on ioniza ion. Beam neu als can be ionized
al eady in he SOL which, o he wall loads, has an e ec
opposi e o he slowing down. The powe load, in pa icula ,
can be expec ed o e en inc ease since he ions bo n in SOL do
no necessa ily slow down be o e eaching he wall. Indeed,
bo h he educ ion in he numbe o los pa icles (−16.4%)
and he powe load educ ion (−27.6%) a e oughly a ac o 2
smalle han wi h jus pu e slowing down.
I can hus be concluded ha , as a as wall loads a e con-
ce ned, he bene icial e ec o he slowing down in he SOL
plasma can be la gely educed by he p ema u e ioniza ion o
he beam ions. Nex we shall u he in es iga e he ela i e
impo ance o slowing down and ioniza ion using mo e eal-
is ic, decaying plasma p o iles in he SOL.
3.2. Ioniza ion and slowing down wi h expe imen ally
mo i a ed SOL plasma p o iles
Since he NBI ioniza ion p o ile, in pa icula , depends
s ongly on he densi y bu only weakly on he plasma empe -
a u e, we now ake a close look a he ela i e signi icance o
ioniza ion and slowing down using mo e ealis ic model p o-
iles. We le ne,iand Te,id op om hei alues a LCFS lin-
ea ly o ze o a ρ=1.15. Fo hese p o iles, he ioniza ion in
SOL is abou 3% o he o al injec ed pa icles, see igu e 5(d)
ha shows he adial ioniza ion p o ile wi h and wi hou he
SOL plasma.
Table 1also lis s he esul s o a se o simula ions whe e he
di e en p ocesses we e ac i a ed one a a ime. I is immedi-
a ely no iced ha , compa ed o he cons an p o iles, he e ec
o decaying SOL p o iles is de imen al—e en in he absence
o beam ions bo n in SOL, he slowing down e ec on powe
loads is now only abou a 10% dec ease (compa ed o 66%
wi h he cons an p o iles). In all o he cases, he minus signs
change o plus signs. Compa ed o he no-SOL case, ioniza-
ion alone is ound o inc ease he powe load by almos 20%.
Including SOL slowing down educes his o below 10%.
Howe e , be o e d awing any conclusions on he se e -
i y o hese obse a ions, i is impo an o no ice ha he
W7-X wall consis s o s eel and ca bon componen s, wi h
he s eel componen s being signi ican ly mo e ulne able o
powe loads. Table 2lis s he powe ecei ed by a ious
wall componen s, wi h ed co esponding o s eel compon-
en s and blue o ca bon ones (see igu e 2 o he mean-
ing o he componen s). Cases wi h and wi hou SOL plasma
a e p esen ed, and o he SOL plasma, di e en p ocesses
we e ac i a ed one a a ime. Acco ding o he able, p e-
ma u e beam ioniza ion in SOL mos ly inc eases he a ge
load, wi h a no iceable e ec also on he ba le and shield.
All h ee a e ca bon componen s, designed o ecei e signi-
ican loads, and including he slowing down p ocess pa ly
compensa es o he inc ease. Fo he s eel componen s includ-
ing he SOL plasma ei he sligh ly educed he a i ing powe
o did no ha e a no iceable e ec . The e o e, he ne e ec
on powe loads does no appea signi ican . In igu e 4 he
ρ- alues o load posi ions a e shown. E en hough we do
no expec he ex apola ion o ρbe accu a e up o ρ=1.5,
he alues clea ly indica e ha he a ge in he igu e show-
ing ρ- alues o ρ≈1.1 is much close o he co e plasma
compa ed o he panel and o he s eel componen s in he
igu e.
5
Plasma Phys. Con ol. Fusion 67 (2025) 025034 T P Ki iniemi e al
Table 2. Beam ion powe loads (kW) on selec ed wall componen s
wi h di e en physical mechanisms included: no SOL, SOL e ec
on beam ioniza ion only, SOL e ec on slowing down only, and
e ec o SOL on bo h. Ca bon componen s a e indica ed in i alics.
O he componen s a e s eel componen s.
case No SOL Ioniz. Slow.down Bo h
Closu e: 9 10 7 8
Closu eside 82 85 75 77
Panel: 184 190 165 171
Sli s: 2 3 3 2
Vessel: 3 3 3 3
Ba le: 309 353 289 326
Shield: 224 244 205 220
Ta ge : 662 882 592 791
To me al: 281 291 252 261
To ca bon: 1196 1479 1085 1337
Also, he ela i e impo ance o he densi y and empe a u e
p o iles was es ed and is epo ed a he bo om o able 1: i s
he SOL empe a u e was kep cons an a i s LCFS alue while
he densi y d opped linea ly, which is he lowes SOL colli-
sionali y case conside ed. The simula ion was hen epea ed
wi h p o iles o he opposi e beha io : he densi y was kep a
i s high LCFS alue while he empe a u e d opped linea ly. In
hese simula ions, he e ec o he SOL plasma on bo h ioniz-
a ion and collisional p ocesses was included.
Compa ing he numbe s, i is seen ha wi h cons an em-
pe a u e bu dec easing densi y p o ile we ob ain esul s e y
simila o he case whe e bo h he densi y and empe a u e
decay owa d he wall. As expec ed, he case wi h cons an ,
high densi y b ings he la ges changes in he numbe o los
ions due o inc eased ioniza ion, bu he change in powe load
is modes due o he s onge slowing down wi h he decaying
empe a u e p o ile.
The in o ma ion in ables 1and 2is combined in igu e 6
o isual inspec ion. The e ec o collisionali y clea ly has
highe ela i e impo ance o he loads on s eel componen s.
This is p obably due o he ac ha , on a e age, he dis ance o
hese componen s is la ge , which enhances he e ec o colli-
sions. In all cases whe e slowing-down is aken in o accoun ,
he powe load o s eel componen s is lowe han in he absence
o SOL. Thus i can be concluded ha he e ec o SOL plasma
in mos cases (o e a wide ange o di e en p o iles) is o
mi iga e he powe load on s eel componen s e en i i would
inc ease he o al load.
Figu e 7shows a his og am o he ρ-dis ibu ion o he
powe load o he di e en physics cases. This dis ibu ion
gi es an indica ion o he dis ance a which he beam ions each
he wall componen . The wo di e o pla es (in each o he
i e segmen s, he e summed o e ) a e clea ly isible as wo
humps a a ound ρ=1.07 and ρ=1.11, wi h he one close
o he plasma ecei ing a la ge powe load. I is also a hese
componen s ha he di e ence be ween he assumed physics
cases becomes no iceable: only wi h ioniza ion included do we
ge enhancemen in powe loads.
Figu e 6. Powe loads on s eel ( ed) and ca bon (blue illed
ma ke s) componen s. He e, i s ou cases a e no SOL; linea ly
decaying SOL p o iles; linea ly decaying n, cons an T=TLCFS;
cons an n=nLCFS, linea ly decaying T. All cases included bo h
ioniza ion and slowing down e ec s in SOL. Las wo cases bo h
ha e linea ly decaying p o iles bu educed SOL physics i.e. only
slowing down o only ioniza ion.
3.3. S a is ics o ho spo s
Mos o he analysis in his wo k is done o in eg a ed wall
loads, which is su icien o gi e insigh in o he ela i e
impo ance o he e ec s o di e en physics p ocesses on wall
loads. Thus, he la ge numbe o small iangles, as shown in
igu e 3, does no play a signi ican ole as esul s a e weigh ed
by hei small a ea. We ha e nume ically es ed ha lea ing ou
small iangles (<2 mm2) can be up o 2% o closu e sides,
bu o o he elemen s i is <1% being negligible o a ge s
and ba le.
Also, in 3D isualiza ions, all he iangles a e included bu
possible high peak loads caused only by pu e s a is ics in small
iangles na u ally ge he weigh hey dese e as small i-
angles a e di icul o see by eye. Howe e , in machine sa e y
6
Plasma Phys. Con ol. Fusion 67 (2025) 025034 T P Ki iniemi e al
Figu e 7. Numbe o ma ke s each he wall as a unc ion o he
adial coo dina e ρ o he di e en cases: no SOL, only SOL
slowing down, only SOL beam ioniza ion, and including SOL
mechanisms. The wo di e o pla es show up as dis inc humps.
Figu e 8. Tes on s a is ical signi icance o small wall elemen s: he
numbe o wall iangles ecei ing a gi en peak powe load, in
MW m−2, including all elemen s o lea ing ou hose ecei ing only
one, wo o h ee ma ke s. The dis ibu ion is ound o con e ge
a e lea ing ou iangles ecei ing only wo ma ke s.
he highly localized peak loads a e o special in e es , so we
he e ake a close look a he s a is ical challenges in e alua -
ing hem, al hough his is no he main scope o he p esen
pape . In o de o iden i y possible ho spo s, i is necessa y
o look a he powe densi ies, in uni s o MW m−2. He e, he
disc e e na u e o ou app oach becomes an issue: no only
do we ha e a ini e numbe o ma ke s, ep esen ing he beam
ions, bu also deciding he size o he su ace a ea o be used
in he calcula ion ma e s: a e y small su ace a ea ecei ing
a single ma ke can esul in an excessi e, a i icial peak load.
To a oid such anomalies, we calcula ed he powe densi ies
on each wall iangle keeping ack o cases whe e he iangle
ecei es only one, wo o h ee ma ke s. The esul s o his ana-
lysis a e p esen ed in igu e 8, illus a ing ha he high-end o
Table 3. Resul s om he s a is ical es . The numbe o wall
iangles ecei ing mo e han 2 MW m−2o 10 MW m−2( o al
numbe o iangles almos 8 million). Top: no iangles excluded.
Bo om: iangles ecei ing only one o wo ma ke s excluded.
>2 MW m−2>10 MW m−2
No sol e ec s 4237 1445
Ioniza ion in SOL 4454 1526
Slowing down in SOL 4035 1352
Bo h e ec s in SOL 4268 1384
>2 MW m−2>10 MW m−2
No sol e ec s 667 126
Ioniza ion in SOL 694 134
Slowing down in SOL 606 117
Bo h e ec s in SOL 641 109
he powe densi y dis ibu ion is indeed s ongly a ec ed by
his il e ing. This is an indica ion o he sugges ed anomaly
and is con i med by he ac ha i we do he il e ing based
on he size o he iangles ins ead o he numbe o ma ke s
ecei ed, i.e. by excluding iangles wi h a size o less han
2×10−6m2, we ge e y simila esul s. Fu he mo e, when
looking a he e ec o he chosen selec ion c i e ia on di e -
en mechanisms, i u ns ou ha he indi idual hi s on andom,
iny elemen s a e due o he slowing down p ocess, while he
ioniza ion p ocess is qui e insensi i e o i .
Figu e 8shows ha he esul s seem o con e ge when
iangles ecei ing only wo ma ke s a e excluded, so in
able 3we summa ize he cases whe e ei he 2 MW m−2o
10 MW m−2is exceeded. The numbe o such iangles is
ound o be qui e limi ed and is expec ed o ge e en smal-
le i he CX eac ions, o be in es iga ed in sec ion 5, a e also
included. Howe e , a he p esen le el o unce ain ies in all
SOL pa ame e s, a mo e ex ensi e s udy is no meaning ul bu
will ha e o wai un il expe imen al da a is a ailable. The me i
o he p esen wo k is me ely o iden i y he impo ance o di -
e en SOL p ocesses.
4. E ec o SOL elec ic ield
In his sec ion, he e ec o a adial elec ic ield is es ed. In
he absence o accu a e da a o he SOL po en ial and keeping
in mind ha e en he alues o he lux su ace coo dina e ρ
a e ex apola ed, he pu pose o his sec ion is only o gi e a
quali a i e pic u e o possible e ec s o he SOL ields. O he
SOL e ec s, such as beam ioniza ion o slowing-down, a e no
included he e.
In expe imen s, o good co e con inemen , he adial elec-
ic ield E can be ei he nega i e (ion- oo ) o posi i e
(elec on- oo ) inside ρ=0.5. A he edge (inside he LCFS),
nega i e E is always obse ed, and a shea low laye a he
LCFS has been clea ly measu ed, implying ha he SOL adial
elec ic ield is always posi i e. This is also in ui i e: he elec-
on empe a u e ypically d ops when mo ing deepe in he
SOL, as is he co esponding elec ic po en ial. Based on hese
obse a ions we cons uc ed simplis ic E p o iles in he egion
7
Plasma Phys. Con ol. Fusion 67 (2025) 025034 T P Ki iniemi e al
Figu e 9. Model p o iles o E = (−dΦ/dρ)/amino used o
es ing he e ec o adial elec ic ield in SOL.
ρ=1–1.15. The a ia ion o he ield s eng h is piece-wise
linea , wi h a ying peak alues o E ,max =0, ±15, ±30 and
±60 kV m−1as illus a ed in igu e 9. The p o iles depic ed
wi h solid lines in a e hus in quali a i e ag eemen wi h expe -
imen s, and ou co e E co esponds o he ion- oo . The neg-
a i e ield alues, shown wi h dashed lines, a e included ou o
cu iosi y since hese simula ions could shed ligh on he si u-
a ion when he magne ic ield di ec ion is e e sed.
In he ASCOT simula ions, we assume ha he elec os a ic
scala po en ial Φis cons an on a lux su ace and plo he
esul s as a unc ion o E (ρ)=(−dΦ/dρ)/amino which, wi h
his simpli ica ion, is also only a unc ion o he ex apola ed
adial coo dina e. He e, amino is he e ec i e mino adius.
P e-shea h o shea h (o any o he E∥) elec ic ields which
could accele a e he ions nea a ge s a e no aken in o accoun
in he p esen s udy.
The o e all e ec o a SOL adial elec ic ield is summa -
ized in igu e 10, sepa a ely o ca bon (blue) and s eel ( ed)
componen s. A non-ze o adial elec ic ield is ound o lowe
he powe load on he s eel componen s, pa icula ly he panel,
wi h he e ec being signi ican ly la ge o he posi i e E ,max
and emo es he ho spo s obse ed on he panel o he s and-
a d con igu a ion in [3]. On he con a y, he powe los on
ca bon componen s has a s ong dependence on he di ec ion
o he adial elec ic ield: a posi i e E ,max inc eases he powe
load, he e ec being mos d ama ic o he a ge . A nega i e
E ,max, on he o he hand, has a mi iga ing e ec on all bu he
load on he a ge . This kind o change o a ge load asym-
me y due o SOL E×B-d i is a well-known phenomenon
in okamaks (see e.g. [9,35,36]). Howe e , his has no been
Figu e 10. E ec o a adial elec ic ield on s eel ( ed) s ca bon
(blue) componen s. He e, ‘s eel o he ’ includes loads on closu e,
sli s and essel which a e no ele an o he ealis ic di ec ion o
SOL E .
Figu e 11. A 3D illus a ion o he e ec o SOL adial elec ic ield
on peak powe load nea he AEF20 po , panels (a) and (b), and
a ound he lowe a ge , panels (c) and (d). In (a) and (c),
E ,max =−30 kV m−1, while in (b) and (d) E ,max = +30 kV m−1,
which is he mo e ealis ic di ec ion.
g ea ly s udied in s ella a o s. The p esen wo k sugges s ha
simila phenomena also exis in s ella a o s bu should be u -
he e i ied wi h a 3D po en ial backg ound, e.g. om EMC3-
EIRENE. The main e ec he e is ha d i s lead he pa icles
ca ying he hea load o he a ge s and o he ca bon com-
ponen s which a e close o he co e plasma compa ed o s eel
componen s as shown in igu e 4.
Figu e 11 shows syn he ic came a iews o he powe load
wi h E ,max =±30 kV m−1 o wo speci ic loca ions: a ound
he po AEF20, which hos s some imme sion ubes (no
included in his simula ion), and he a ge . A posi i e E ,max
is ound o inc ease he load on he a ge al hough he peak
loads seen in he igu e a e lowe . Nea he AEF20 po he
load is highe wi h posi i e E ,max. In igu e 12, we show he
8
