Modelling of divertor target plate heat fluxes during intense plasma transients in tokamaks

Vasileska, Ivona (author), Kos, Leon (mentor), Pitts, Richard A. (comentor)

One of the most essential tools for predicting and researching the tokamak scrape-off layer (SOL) is numerical simulation. One of the greatest threats, which can lead to serious, unwanted consequences in next-generation fusion reactors such as ITER, are the transient heat loads on the plasma-facing components (PFCs) due to magnetohydrodynamic plasma relaxations, known as Edge-Localised Modes (ELMs). These loads represent a important threat to the PFCs' lifetimes, especially on the divertor targets and can lead to the need to replace them with a frequency that has a major impact on the execution of the ITER Research Plan. The first step towards solving this research problem is understanding and characterising the underlying ELM physics, corresponding to the demanding discharge scenarios, such as mutual charge and neutral particles with fields and material-surface interactions that take place in tokamak devices. The work is based on the hypothesis that the understanding and describing of uncontrolled ELMs, i.e., spontaneous spatial-temporal evolution, will provide sufficient knowledge for the future establishment of fully controlled ELMs-suppressed regimes. This thesis investigates the advantage and effectiveness of the fluid plasma and the divertor modelling including the time-dependent ELM phenomena. It aims to predict the impact of such large transient heat loads through modelling, using the fluid plasma boundary modelling codes, such as SOLPS-ITER, which is a combination of the fluid (B2.5)-neutral Monte-Carlo (EIRENE) codes and is one of the most complex tools of this type. In SOLPS-ITER the ELM is crudely approximated as a fixed, large (but limited in time) increase in the anomalous cross-field transport coefficients for particles and heat to mimic a specified total ELM energy loss. However, one problem with this approach is that the boundary conditions at the target sheath's entrance are expected to vary strongly over time through the ELM transient, while fixed kinetic target sheath heat-transmission factors, and more generally, constant heat-flux limiters, are typically applied in the fluid codes. Resolving the spontaneous appearance and dynamics has to be done via the analytic-numerical approach combined with a numerical fluid simulation. The input data which are either an improved analytic formulation or improved raw-data arrays containing the spatial--temporal kinetic factors (limiters and boundary conditions) will be obtained by combining the kinetic simulation for ITER scenarios, with the experimental data extrapolated to ITER from existing tokamaks (for example JET). This contribution describes the first results of ELMs issues for ITER simulations under high-performance conditions using the 1D3V electrostatic parallel Particle-in-Cell (PIC) code BIT1. This code simulates the kinetic effects, from which the time-dependent kinetic target sheath heat-transmission factors can be provided. In the second step of the work, these are used in the formulation of fluid boundary conditions for calculations of the ELM target heat loads using the SOLPS-ITER code. Besides theoretical methods (attempting semi-analytic results) the particular kinetic and fluid algorithms for the plasma simulation (BIT1 and SOLPS-ITER) are updated and/or upgraded and applied. The BIT1-SOLPS-ITER coupling allows us to investigate the kinetic effects on the targets, by comparing power and particle fluxes from time-dependent simulations of ITER Type-I ELMs. A key element in this thesis is to create a kind of simulations that could fit in both codes. The approach is first to perform a plasma steady state on BIT1 to seek the boundary conditions and flux limiters and then to use them in the fluid code, SOLPS-ITER as a key to controlling the heat loads that occur on the tokamak divertor. Due to the complexity of ELM during the event, there exists no complete theoretical description. In SOLPS-ITER, the simplest method to simulate the ELMs is the following: Before starting the Type-I ELM, it is first necessary to simulate the plasma without ELM (ELM-free phase) during a brief time interval, then to simulate Type-I ELM and at the end to switch off the ELM and to see what is happening with the plasma after the ELM (post-ELM). Before using this method for ITER, it was tested on JET. In this work we present not only the ITER results, but also the JET results, using the same method to investigate and control the ELM over time, performing fully time-dependent simulations. A key characteristic of ELM boundary physics is the energy deposition asymmetries observed at the targets. The ELM is a absolute plasma instability from the pedestal to the SOL region. This hypothesis has been used here and for the first time has been coupled to the BIT1 and SOLPS-ITER simulating the ITER case. Based on this research, to obtain a whole ELM investigation would require further study.

• Language: English
• Keywords: fusion, tokamak, JET, ITER, SOL, ELMs, plasma wall transition, plasma sheath, divertor, numerical simulations, BCs, kinetic factors, kinetic modelling, fluid modelling, SOLPS-ITER, BIT1
• Work type: Doctoral dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2021
• PID: 20.500.12556/RUL-134107
• COBISS.SI-ID: 90644483
• Publication date in RUL: 23.12.2021

Secondary language

• Language: Slovenian
• Title: Modeliranje toplotnih tokov na divertorski plošči med intenzivnimi tranzienti plazme v tokamakih

Abstract

Eno izmed najbolj pomembnih orodij za napovedi in raziskave robne plazme (SOL) so numerične simulacije. Ena največjih groženj, ki lahko privede do resnih neželenih posledic na fuzijskih reaktorjih naslednje generacije, kot je ITER, so prehodne toplotne obremenitve na plazmi izpostavljenih komponentah (PFC) zaradi magnetohidrodinamičnih relaksacij plazme, znanih kot robni lokalizirani pojavov (ELM). Te obremenitve predstavljajo pomembno grožnjo za življenjsko dobo PFC-jev, zlasti za divertorske tarče, in bodo lahko vzrok za za njihovo pogosto zamenjavo, kar ima velik vpliv na izvajanje raziskovalnega načrta ITER. Prvi korak k reševanju tega raziskovalnega problema je razumevanje in karakterizacija osnovne fizike ELM-a, ki ustreza zahtevnim scenarijem praznjenja naboja, kot so vzajemno nabiti in nevtralni delci s polji in interakcija material-površina, ki potekajo v tokamakih. Delo temelji na hipotezi, da bo razumevanje in opis nenadzorovanih ELM-ov, tj. spontanega prostorsko-časovnega razvoja, zagotovil zadostno znanje za prihodnjo vzpostavitev popolnoma nadzorovanih režimov zadrževanih ELM-ov. V tej nalogi se raziskuje prednosti in učinkovitost plazme ter modeliranje divertorja, vključno s časovno odvisnimi pojavi ELM-a. Glavni namen je z modeliranjem napovedati vpliv tako velikih prehodnih toplotnih obremenitev in sicer z uporabo kod za modeliranje robne tekočinske plazme, kot je SOLPS-ITER, ki je kombinacija tekočinskih (B2.5) -nevtralnih Monte-Carlo (EIRENE) kod in je eno najbolj kompleksnih orodij te vrste. V SOLPS-ITER je ELM grobo aproksimiran kot fiksno velik (vendar časovno omejen) prirastek transportnih koeficientov za delce in toploto, ki posnemajo določeno skupno izgubo energije ELM-a. Vendar je ena od težav tega pristopa, da se za robne pogoje na vhodu v plašč tarče pričakuje, da se bodo časovno močno spreminjali v času ELM-ja, medtem ko se tipično v fluidnih kodah običajno uporabljajo fiksni kinetični faktorji prenosa toplote ciljnega plašča in v splošnem omejevalniki toplotnega toka. Razreševanje spontanih nastankov in dinamike je potrebno opraviti z analitično-numeričnim pristopom v kombinaciji s fluidno simulacijami. Vhodni podatki, bodisi izboljšana analitična formulacija ali izboljšani surovi nizi podatkov, ki vsebujejo prostorsko-časovne kinetične faktorje (omejevalniki in robni pogoji), bo pridobljeni s kombiniranjem kinetične simulacije scenarijev za ITER in eksperimentalnih podatkov, ekstrapoliranih na ITER iz obstoječih tokamakov (npr. JET). Ta prispevek opisuje prve rezultate rešavanja problemov ELM-ov v simulacije ITER v pogojih visokih zmogljivosti, in sicer z uporabo 1D3V elektrostatične paralelne kode delcev v celicah (PIC) BIT1. Ta koda se uporablja za preučevanje kinetičnih učinkov in za pridobivanje časovno odvisnih kinetičnih faktorjev prenosa toplote plašča tarče. V drugem delu te naloge se kinetični faktorji uporabljajo za formulacijo fluidnih robnih pogojev za izračun toplotne obremenitve tarče ELM-a z uporabo kode SOLPS-ITER. Poleg uporabe teoretičnih metod (poskus s semi-analitičnimi rezultati) je potrebno posodobiti in/ali nadgraditi ter uporabiti posebne kinetične in fluidne algoritme za simulacijo plazme (BIT1 in SOLPS-ITER). Sklopitev BIT1-SOLPS-ITER nam omogoča raziskovanje kinetičnih učinkov na tarče s primerjavo moči in tokov delcev iz časovno odvisnih simulacij Type-I ELM-ov. Ključni element te naloge je ustvariti takšne simulacije, ki bi ustrezale obema kodama. Pristop za to je najprej oblikovanje plazme v stanju dinamičnega ravnovesja na BIT1 s ciljem, da se poiščejo robni pogoji in omejevalniki toka, nato pa njihova uporaba v fluidni kodi SOLPS-ITER kot ključ za nadzor toplotnih obremenitev, ki nastanejo na divertorju tokamaka. Zaradi kompleksnosti ELM-a med dogodkom popolni teoretični opis za to ne obstaja. V SOLPS-ITER je najpreprostejša metoda za simulacijo ELM-a pred zagonom Type-I ELM-a sledeča: najprej za kratek časovni interval simulacija plazme brez ELM-a (faza ELM-free), nato se začne s simulacijo Type-I ELM-a in na koncu se izklopi ELM in opazuje, kaj se dogaja s plazmo po ELM-u (post-ELM). Pred uporabo te metode za ITER je bil narejen preizkus na JET. V tem delu niso prisotni le rezultati za ITER, ampak tudi rezultati za JET, za katerega se uporablja isto metodo za raziskave in nadzor ELM-a preko časovno odvisnih diagnostika. Ključna značilnost fizike robnih ELM-ov je odlaganja energije, opažene na tarčah. ELM je absolutna nestabilnost plazme od jedra do območja SOL. Na osnovi te hipoteze so bile prvič opravljene združene simulacije z BIT1 in SOLPS-ITER kodami na primeru ITER. Na podlagi tega dela bi za celotno raziskavo ELM-a bile potrebne dodatne študije.

• Keywords: fuzija, tokamak, JET, ITER, SOL, ELM-i, prehod plazme v steno, plazemski plašč, divertor, numerične simulacije, robni pogoji, kinetični faktorji, kinetično modeliranje, fluidno modeliranje, SOLPS-ITER, BIT1