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Publication# A phase-contrast-imaging core fluctuation diagnostic and first-principles turbulence modeling for JT-60SA

Stephan Brunner, Stefano Coda, Aylwin Iantchenko, Kenji Tanaka, Matthieu Toussaint

2021

Journal paper

2021

Journal paper

Abstract

A core fluctuation diagnostic based on the phase-contrast imaging (PCI) technique has been designed for the JT-60SA tokamak, with the assistance of a synthetic diagnostic coupled to a gyrokinetic code. Using a tangentially viewing geometry, this system would be able to resolve small-scale microturbulence as well as macroscopic fluctuations, with good spatial and temporal resolution, throughout the plasma cross-section and in all plasma regimes. The spatial resolution will be optimal (

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Tokamak

A tokamak (ˈtoʊkəmæk; токамáк) is a device which uses a powerful magnetic field to confine plasma in the shape of a torus. The tokamak is one of several types of magnetic confinement devices being

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Plasma () is one of four fundamental states of matter, characterized by the presence of a significant portion of charged particles in any combination of ions or electrons. It is the most abundant form

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Nuclear fusion is a reaction in which two or more atomic nuclei, usually deuterium and tritium (hydrogen variants), are combined to form one atomic nuclei and subatomic particles (neutrons or prot

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The present work takes place within the general context of research related to the development of nuclear fusion energy. More specifically, this thesis is mainly a numerical and physical contribution to the understanding of turbulence and associated transport phenomena occuring in tokamak plasmas, the most advanced and promising form of magnetically confined plasmas. The complexity of tokamak plasma phenomena and related physical models, either fluid or kinetic, requires the development of numerical codes to perform simulations of the plasma behaviour under given conditions defined by the magnetic geometry as well as density and temperature profiles. The studies presented in this work are based on electrostatic kinetic simulations, taking advantage of a reduced kinetic model (the gyrokinetic model) which is particularly suitable for studying turbulent transport in magnetically confined plasmas, in effect solving an approximate form of the Vlasov equation for the distribution function of each species (electrons, ions) along with a reduced form of the Poisson equation providing the self-consistent electric fields. The main tool of this work, the gyrokinetic ORB5 code making use of numerical particles according to the Particle-In-Cell (PIC) method, has been upgraded during this thesis with different linearized collision operators related to both ions and electrons. The BIRDIE code, enabling to study collisional effects on the evolution of Langmuir waves in an unmagnetized plasma, has been written in order to serve as a test-bed for the collision operators ultimately implemented in ORB5. Some essential algorithms related to collisional simulations have been jointly implemented, such as the two-weight scheme which is extensively described in this work. The collision operators in ORB5 have been further carefully tested through neoclassical simu- lations and benchmarked against other codes, providing reliable levels of collisional transport. Together with different procedures controlling the numerical noise, the collision operators have then been applied to the study of collisional turbulent transport in two different regimes, the Ion-Temperature-Gradient (ITG) regime and the Trapped-Electron-Mode (TEM) regime re- quiring a trapped electron kinetic response. Although not dominant in core tokamak plasmas, collisional effects nevertheless lead to interesting modifications in the turbulence behaviour which are not captured by the often considered collisionless gyrokinetic models. The so-called coarse-graining procedure, a noise-control algorithm which is suitable for collisional gyrokinetic simulations with particles, is shown to enable carrying out relevant simulations over many col- lision times. Consequently, reliable conclusions regarding turbulent transport in the presence of collisions could be drawn in this thesis. Namely, the turbulent transport in the ITG regime is found to be enhanced by ion collisions through interactions with so-called zonal flows as- sociated to axisymmetric modes, while it is reduced by electron collisions in the TEM regime through electron detrapping processes. The zonal flow dynamics in collisionless and collisional ITG turbulence simulations is studied, emphasizing the limitation of the zonal flow level due to Kelvin-Helmoltz-type instabilities. Additionally, some purely collisionless issues related to tokamak physics are discussed, such as the finite plasma size effects in TEM-dominated regime which are found to be important in non-linear simulations but unimportant in linear simu- lations. The role of zonal flows in temperature-gradient-driven TEM turbulence saturation is confirmed to be weak, in agreement with previous studies. Finally, a realistic global gy- rokinetic simulation, accounting for a proper TCV tokamak magnetic equilibrium and related experimental profiles, has been successfully carried out thus demonstrating the relevance of the ORB5 code for predictions related to physics of real tokamaks. A good agreement with GAM experimental measurements is indeed obtained.

Controlled nuclear fusion could provide our society with a clean,
safe, and virtually inexhaustible source of electric power production.
The tokamak has proven to be capable of producing large amounts of
fusion reactions by confining magnetically the fusion fuel at
sufficiently high density and temperature, thus in the plasma state.
Because of turbulence, however, high temperature plasma reaches the
outermost region of the tokamak, the Scrape-Off Layer (SOL), which
features open magnetic field lines that channel particles and heat
into a dedicated region of the vacuum vessel. The plasma dynamics in
the SOL is crucial in determining the performance of tokamak devices,
and constitutes one of the greatest uncertainties in the success of
the fusion program. In the last few years, the development of
numerical codes based on reduced fluid models has provided a tool to
study turbulence in open field line configurations. In particular, the
GBS (Global Braginskii Solver) code has been developed at CRPP and is
used to perform global, three-dimensional, full-n, flux-driven
simulations of plasma turbulence in open field lines.
Reaching predictive capabilities is an outstanding challenge that
involves a proper treatment of the plasma-wall interactions at the end
of the field lines, to well describe the particle and energy losses.
This involves the study of plasma sheaths, namely the layers forming
at the interface between plasmas and solid surfaces, where the drift
and quasineutrality approximations break down. This is an
investigation of general interest, as sheaths are present in all
laboratory plasmas.
This thesis presents progress in the understanding of plasma sheaths
and their coupling with the turbulence in the main plasma. A kinetic
code is developed to study the magnetized plasma-wall transition
region and derive a complete set of analytical boundary conditions
that supply the sheath physics to fluid codes. These boundary
conditions are implemented in the GBS code and simulations of SOL
turbulence are carried out to investigate the importance of the sheath
in determining the equilibrium electric fields, intrinsic toroidal
rotation, and SOL width, in different limited configurations. For each
study carried out in this thesis, simple analytical models are
developed to interpret the simulation results and reveal the
fundamental mechanisms underlying the system dynamics. The
electrostatic potential appears to be determined by a combined effect
of sheath physics and electron adiabaticity. Intrinsic flows are
driven by the sheath, while turbulence provides the mechanism for
radial momentum transport. The position of the limiter can modify the
turbulence properties in the SOL, thus playing an important role in
setting the SOL width.

The goal of thermonuclear fusion research is to provide power plants, that will be able to produce one gigawatt of electricity. Among the different ways to achieve fusion, the tokamak, based on magnetic confinement, is the most promising one. A gas is heated up to hundreds of millions of degrees and becomes a plasma, which is maintained – or confined – in a toroidal vessel by helical magnetic field lines. Then, deuterium and tritium are injected and fuse to create an α particle and an energetic neutron. In order to have a favorable power balance, the power produced by fusion reactions must exceed the power needed to heat the plasma and the power losses. This can be cast in a very simple expression which stipulates that the product of the density, the temperature and the energy confinement time must exceed some given value. Unfortunately, present-days tokamaks are not able to reach this condition, mostly due to plasma turbulence. The latter phenomenon enhances the heat losses and degrades the energy confinement time, which cannot be predicted by analytical theories such as the so-called neoclassical theory in which the heat losses are caused by Coulomb collisions. Therefore, numerical simulations are being developed to model plasma turbulence, mainly caused by the Ion and Electron Temperature-Gradient and the Trapped-Electron-Mode instabilities. The plasma is described by a distribution function which evolves according to the Vlasov equation. The electromagnetic fields created by the particles are self-consistently obtained through Maxwell's equations. The resulting Vlasov-Maxwell system is greatly simplified by using the gyrokinetic theory, which consists, through an appropriate ordering, of eliminating the fast gyromotion (compared to the typical frequency of instabilities). Nevertheless, it is still extremely difficult to solve this system numerically due to the large range of time and spatial scales to be resolved. In this thesis, the Vlasov-Maxwell system is solved in the electrostatic and collisionless limit with the Particle-In-Cell (PIC) ORB5 code in global tokamak geometry. This Monte-Carlo approach suffers from statistical noise which unavoidably degrades the quality of the simulation. Consequently, the first part of this work has been devoted to the optimization of the code with a view to reduce the numerical noise. The code has been rewritten in a new coordinate system which takes advantage of the anisotropy of turbulence, which is mostly aligned with the magnetic field lines. The overall result of the optimization is that for a given accuracy, the CPU time has been decreased by a factor two thousand, the total memory has been decreased by a factor ten and the numerical noise has been reduced by a factor two hundred. In addition, the scaling of the code with respect to plasma size is presently optimal, suggesting that ORB5 could compute heat transport for future fusion devices such as ITER. The second part of this thesis presents the validation of the code with numerical convergence tests, linear (including dispersion relations) and nonlinear benchmarks. Furthermore, the code has been applied to important issues in gyrokinetic theory. It is shown for the first time that a 5D global delta-f PIC code can achieve a thermodynamic steady state on the condition that some dissipation is present. This is a fundamental result as the main criticism against delta-f PIC codes is their inability to deal with long time simulations. Next, the role of the parallel nonlinearity is studied and it is demonstrated in this work that this term has no real influence on turbulence, provided the numerical noise is sufficiently low. This result should put an end to the controversy that recently occurred, in which gyrokinetic simulations using different numerical approaches yielded contradictory results. Finally, thanks to the optimization of the code, the gyrokinetic model has been extended to include the kinetic response of trapped-electrons, in place to the usual adiabatic (Boltzmann) approximation. For the first time, global TEM nonlinear simulations are presented, and the role of the zonal flow on heat transport is analyzed. This study will help in acquiring some knowledge on the less-known TEM turbulence (as compared to ITG). In conclusion, this thesis is one of the main steps of the development of ORB5, which is now a state-of-the-art gyrokinetic code for collisionless ITG and TEM turbulence, and has brought several contributions to the understanding of these phenomena.