Predictive simulations for plasma scenarios in the SMART tokamak

Fusion Enginee ing and Design 192 (2023) 113833 A ailable online 28 May 2023 0920-3796/© 2023 The Au ho (s). Published by Else ie B.V. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by- nc-nd/4.0/). Con en s lis s a ailable a ScienceDi ec Fusion Enginee ing and Design jou nal homepage: www.else ie .com/loca e/ usengdes 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 3 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 4 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 5 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). Re e ences [1] A. Mancini, e al., Mechanical and elec omagne ic design o he acuum essel o he SMART okamak, Fusion Eng. Des. 171 (2021). [2] M. Ag edano-To es, J.L. Ga cia-Sanchez, A. Mancini, e al., Coils and powe supplies design o he SMART okamak, Fusion Eng. Des. 168 (2021). [3] S.J. Doyle, D. Lopez-Ai es, A. Mancini, e al., Magne ic equilib ium design o he SMART okamak, Fusion Eng. Des. 171 (2021). [4] S.J. Doyle, A. Mancini, e al., Single and double null equilib ia in he SMART okamak, Plasma Res. Exp ess 3 (2021). [5] G. 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