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Iterative addition of finite Larmor radius effects to finite element models using wavelet decomposition
KTH, School of Electrical Engineering and Computer Science (EECS), Electrical Engineering, Fusion Plasma Physics.ORCID iD: 0000-0003-4343-6325
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Modeling the propagation and damping of electromagnetic waves in a hot magnetized plasma is difficult due to spatial dispersion. In such media, the dielectric response becomes non-local and the wave equation an integro-differential equation. In the application of RF heating and current drive in tokamak plasmas, the finite Larmor radius (FLR) causes spatial dispersion, which gives rise to physical phenomena such as higher harmonic ion cyclotron damping and mode conversion to electrostatic waves. In this paper, a new numerical method based on an iterative wavelet finite element scheme is presented, which is suitable for adding non-local effects to the wave equation by iterations. To verify the method, we apply it to a case of one-dimensional fast wave heating at the second harmonic ion cyclotron resonance, and study mode conversion to ion Bernstein waves in a toroidal plasma. Comparison with a local (truncated FLR) model showed good agreement in general. The observed difference is in the damping of the ion Bernstein wave, where the proposed method predicts stronger damping on the ion Bernstein wave.

Keywords [en]
Morlet wavelets, finite element method, ion cyclotron resonance heating, mode conversion, ion-Bernstein waves
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-265018OAI: oai:DiVA.org:kth-265018DiVA, id: diva2:1377057
Available from: 2020-02-03 Created: 2019-12-10 Last updated: 2019-12-18Bibliographically approved
In thesis
1. Modeling RF waves in hot plasmas using the finite element method and wavelet decomposition: Theory and applications for ion cyclotron resonance heating in toroidal plasmas
Open this publication in new window or tab >>Modeling RF waves in hot plasmas using the finite element method and wavelet decomposition: Theory and applications for ion cyclotron resonance heating in toroidal plasmas
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Fusion energy has the potential to provide a sustainable solution for generating large quantities of clean energy for human societies. The tokamak fusion reactor is a toroidal device where the hot ionized fuel (plasma) is confined by magnetic fields. Several heating systems are used in order to reach fusion relevant temperatures. Ion cyclotron resonance heating (ICRH) is one of these systems, where the plasma is heated by injecting radio frequency (RF) waves from an antenna located outside the plasma.

This thesis concerns modeling of RF wave propagation and damping in hot tokamak plasmas. However, solving the wave equation is complicated because of spatial dispersion. This effect makes the wave equation an integro-differential equation that is difficult to solve using common numerical tools. The objective of this thesis is to develop numerical methods that can handle spatial dispersion and account for the geometric complexity outside the core plasma, such as the antenna and low-density regions (or SOL). The main results of this work is the development of the FEMIC code and the so-called iterative wavelet finite element scheme.

FEMIC is a 2D axisymmetric code based on the finite element method. Its main feature is the integration of the core plasma with the SOL and antenna regions, where arbitrary geometric complexity is allowed. Moreover, FEMIC can apply a dielectric response in the SOL and in the region between the SOL and the core plasma (i.e. the pedestal). The code can account for perpendicular spatial dispersion (or FLR effects) for the fast wave only, which is sufficient for modeling harmonic cyclotron damping and transit time magnetic pumping. FEMIC was used for studying the effect of poloidal phasing on the ICRH power deposition on JET and ITER, and was benchmarked against other ICRH modeling codes in the fusion community successfully.

The iterative wavelet finite element scheme was developed in order to account for spatial dispersion in a rigorous way. The method adds spatial dispersion effects to the wave equation by using a fixed point iteration scheme. Spatial dispersion effects are evaluated using a novel method based on Morlet wavelet decomposition. The method has been tested successfully for parallel and perpendicular spatial dispersion in one-dimensional models. The FEMIC1D code was developed in order to model ICRH and to study the properties of the numerical scheme. FEMIC1D was used to study second harmonic heating and mode conversion to ion-Bernstein waves (IBW), including a model for the SOL and pedestal. By studying the propagation and damping of the IBW, we verified that the scheme can account for FLR effects.

Abstract [sv]

Fusionsenergi har potentialen att erbjuda en hållbar lösning för storskalig energiproduktion för mänskligheten. Fördelarna med fusionsenergi inkluderar inga utsläpp av växthusgaser, inget långlivat radioaktivt avfall, pålitlig energiproduktion, hög säkerhet och stora bränslereserver på jorden.

Tokamaken är en fusionsreaktor med ringformad geometri, där det heta bränslet (eller plasmat) innesluts med starka magnetfält för att det inte ska få kontakt med t.ex. väggar och antenn. För att uppnå fusionsrelevanta temperaturer (ca. 100 miljoner grader) har tokamaker flera uppvärmningssystem. Joncyklotronresonansuppvärmning (ICRH) är ett system där plasmat värms upp med hjälp av radiovågor. ICRH kommer att ha en viktig roll på ITER, vilket är nästa generations tokamakexperiment som beräknas vara operativ mot slutet av 2020-talet.

Denna avhandling handlar om modellering och beräkningar av radiovågor i tokamakplasman för ICRH. Beräkningar av radiovågor görs genom att lösa Maxwells ekvationer. Att lösa Maxwells ekvationer är svårt p.g.a. fenomenet rumslig dispersion som finns i heta plasman. Denna effekt resulterar i integraloperatorer som är svåra att hantera med numeriska verktyg. Målet med detta arbete är att utveckla numeriska verktyg som kan hantera rumslig dispersion i Maxwells ekvationer och kunna hantera den geometriska komplexitet som finns utanför plasmat, t.ex. antennen och regionerna med låg plasmatäthet (SOL). Huvudresultaten av detta arbete är utvecklingen av den tvådimensionella FEMIC-koden och den så kallade "iterativa wavelet finita element" algoritmen.

En av FEMIC-kodens viktigaste egenskaper är att den kan beskriva vågfysiken både i det heta inre plasmat och det omgivande SOL-området, där godtycklig geometrisk komplexitet är tillåten för att beskriva SOL, väggar och antenn. Dessutom tillämpar FEMIC en dielektricitetsmodell i SOL-området och i området mellan plasmat och SOL (som kallas för pedestalen). Koden kan beskriva vinkelrät rumslig dispersion (FLR-effekter) för den snabba vågen enbart, vilket är tillräckligt för att beskriva viktiga mekanismer som t.ex. harmonisk dämpning och magnetisk pumpning. FEMIC har används för att studera effekten av poloidal fasning i tokamakerna JET och ITER, samt validerats emot andra ICRH-koder framgångsrikt.

Den iterativa wavelet finita element algoritmen utvecklades för att behandla rumsligt dispersiva effekter på ett rigoröst sätt. I denna algoritm adderas rumsligt dispersiva effekter till vågekvationen med hjälp av iterationer. För att evaluera rumslig dispersion har en ny metod baserad på Morlet wavelets tillämpats. Algoritmen har testats framgångsrikt för vinkelrät och parallell dispersion i endimensionella modeller. Koden FEMIC1D utvecklades för att studera algoritmens egenskaper och för att simulera ICRH, inklusive FLR-effekter. Koden har tillämpats på ett fall för att studera harmonisk dämpning och modkonvertering till så kallade jon-Bernsteinvågor. I denna studie verifierades att algoritmen kan ta hänsyn till FLR-effekter genom att studera jon-Bernsteinvågens egenskaper.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2019. p. 77
Series
TRITA-EECS-AVL ; 2020:4
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-265016 (URN)978-91-7873-397-2 (ISBN)
Public defence
2020-01-17, F3, Lindstedtsvägen 26, Stockholm, 14:00 (English)
Opponent
Supervisors
Note

QC 20191211

Available from: 2019-12-11 Created: 2019-12-10 Last updated: 2019-12-19Bibliographically approved

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Citation style
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