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Development of a lagrange-Monte-Carlo scheme for 3D plasma fluid simulation in fusion edge plasmas (本文)

巽, 瞭子 慶應義塾大学

2020.03.23

概要

Nuclear fusion is a promising candidate for a new energy resource. One issue for magnetic- confinement fusion reactors is enormous amount of particle and heat loads onto the machine inner-walls. In order to keep the loads in manageable level, plasma fluid simulation in edge region, so-called Scrape-Off-Layer (SOL), plays a key role. The simulation has mainly been done with two-dimensional (2D) plasma fluid codes, however, a three-dimensional (3D) plasma fluid code is required to simulate non-axisymmetric configurations of the machines. Extension of current numerical schemes in the 2D codes, such as a finite volume scheme (FV), is difficult due to the following unique characteristics of SOL plasma; 1) Different mechanism of the transport depending on the direction to the magnetic field, 2) Different dominant mechanism between the transport of particles, momentum and energy, and 3) Presence of sheath at the wall imposing complex boundary conditions. Therefore, the purpose of this study is to develop a new 3D simulation scheme for SOL/divertor plasma. By developing a Lagrange–Monte-Carlo scheme as the new scheme, the study has established a basis for 3D simulation of SOL plasma in fusion devices. The thesis is constructed as follows.

Chapter 1 describes the background and purpose of this study. Chapter 2 introduces basic equations for the plasma and neutral particles in the SOL.

Chapter 3 focuses on the Monte-Carlo scheme (MC). After describing basic theory of MC, two matters regarding MC are discussed. One is the ways to set boundary conditions. By solving a simple diffusion equation with MC, valid numerical treatments for Dirichlet and Neumann conditions have been clarified. The other one is the way to solve the energy equation, more specifically, the conduction equation. The raised issues are the effects of background density profiles, mixed weights of the pseudo fluid particles, and so on. Through some tests regarding each issue, validity of the algorithm solving the conduction equation has been confirmed under the use of fine-enough mesh.

Chapter 4 introduces the Lagrange scheme (LG). Since MC is originally for diffusive problems, its applicability to convective problems is unclear. Therefore, a pure-convective problem was calculated by MC and also by LG. As a result, MC obtained unphysical numerical solution while LG obtained the correct physical solution. Semi-implicit treatment of the pressure gradient term is the key factor of the success in LG.This was the starting point of LG and the last half of Chap. 4 describes further development and consideration on LG.

Chapter 5 describes numerical algorithm and results of the Lagrange–Monte-Carlo scheme (LG-MC). LG-MC integrates LG for the convective part and MC for the diffusive part. After coupling MC and LG, validity of LG-MC has been confirmed by a 1D benchmark test. Finally, by extending the LG-MC code to a 3D cylindrical geometry, applicability of LG-MC to 3D geometries has been confirmed.

Chapter 6 concludes the thesis, with giving future steps of this study.

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