The role of the sheath in magnetized plasma turbulence and flows

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

Existence of subsonic plasma sheaths

The location of the plasma sheath edge, where quasineutrality is broken, is rigorously derived by using a kinetic description of the plasma. It is shown that sheaths can exist with arbitrarily small ion velocity at the sheath edge, thus violating the Bohm criterion, Vi = cs at the sheath edge. Bohm’s criterion is recovered in the case of large enough ion current through the wall, and it is found to be a reasonable approximation in floating potential conditions. However, in the case of a predominant electron current through the wall, Bohm’s criterion is not able to describe the sheath-edge transition. The analytical results are supported by numerical simulations performed with a fully kinetic particle-in-cell code modeling a source-driven, weakly collisional plasma, bound between two absorbing walls

Boundary conditions for plasma fluid models at the magnetic presheath entrance

For the first time, a rigorous definition of the magnetic presheath entrance (MPSE) is provided, as the location where the drift-reduced approximation breaks down. We consider a weakly collisional electrostatic plasma with cold ions in contact with an absorbing wall in the presence of ExB drifts. We provide expressions at the MPSE for the parallel ion and electron velocities, the gradients of plasma density and potential, and the vorticity. In particular, we show that the plasma potential with respect to the wall increases when the angle of incidence of the magnetic field is smaller. A fully kinetic PIC code simulating the plasma wall transition has been developed to validate these local relations, showing an excellent agreement with the theory. This work represents a first step towards a complete formulation of the boundary conditions for fluid codes used to simulate the edge of magnetic confinement devices

A comparison between a refined two-point model for the limited tokamak SOL and self-consistent plasma turbulence simulations

A refined two-point model is derived from the drift-reduced Braginskii equations for the limited tokamak scrape-off layer (SOL) by balancing the parallel and perpendicular transport of plasma and heat and taking into account the plasma–neutral interaction. The model estimates the electron temperature drop along a field line, from a region far from the limiter to the limiter plates. Self-consistent first-principles turbulence simulations of the SOL plasma including its interaction with neutral atoms are performed with the GBS code and compared to the refined two-point model. The refined two-point model is shown to be in very good agreement with the turbulence simulation results

Structure of pressure-gradient-driven current singularity in ideal magnetohydrodynamic equilibrium

Singular currents typically appear on rational surfaces in non-axisymmetric ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces and a continuous rotational transform. These currents have two components: a surface current (Dirac $\delta$-function in flux surface labeling) that prevents the formation of magnetic islands and an algebraically divergent Pfirsch--Schl\"uter current density when a pressure gradient is present across the rational surface. At flux surfaces adjacent to the rational surface, the traditional treatment gives the Pfirsch--Schl\"uter current density scaling as $J\sim1/\Delta\iota$, where $\Delta\iota$ is the difference of the rotational transform relative to the rational surface. If the distance $s$ between flux surfaces is proportional to $\Delta\iota$, the scaling relation $J\sim1/\Delta\iota\sim1/s$ will lead to a paradox that the Pfirsch--Schl\"uter current is not integrable. In this work, we investigate this issue by considering the pressure-gradient-driven singular current in the Hahm\textendash Kulsrud\textendash Taylor problem, which is a prototype for singular currents arising from resonant magnetic perturbations. We show that not only the Pfirsch--Schl\"uter current density but also the diamagnetic current density are divergent as $\sim1/\Delta\iota$. However, due to the formation of a Dirac $\delta$-function current sheet at the rational surface, the neighboring flux surfaces are strongly packed with $s\sim(\Delta\iota)^{2}$. Consequently, the singular current density $J\sim1/\sqrt{s}$, making the total current finite, thus resolving the paradox

Convective cells and blob control in a simple magnetized plasma

Blob control by creating convective cells using biased electrodes is demonstrated in simple magnetized toroidal plasmas. A two-dimensional array of electrodes is installed on a metal limiter to obtain different biasing schemes. Detailed two-dimensional measurements across the magnetic field reveal the formation of a convective cell, which shows a high degree of uniformity along the magnetic field. Depending on the biasing scheme, radial and vertical blob velocities can be varied significantly. A high level of cross-field currents limits the achievable potential variations to values well below the applied bias voltage. Furthermore, the strongest potential variations are not induced along the biased flux tube, but at a position shifted in the direction of plasma flows

Convective cells and blob control in a simple magnetized torus

In view of controlling wall and divertor heat loads in magnetic fusion devices, we investigate the possibility of creating convective cells by means of biased electrodes for turbulence and blob control in the simple magnetized toroidal plasmas of TORPEX. A two-dimensional array of 24 electrodes is installed on a metal limiter to test different biasing schemes. This allows influencing significantly the frequency of the dominant mode as well as radial and vertical velocities of blobs. Detailed measurements along and across the magnetic field provide a rather clear picture of the effect of the biasing. The biased electrodes produce perturbations of the plasma potential and density profiles that are fairly uniform along the magnetic field. Background flows influence the location where potential variations are induced. The magnitude of the achievable potential variations in the plasma is strongly limited by cross-field currents. A quantitative discussion on the origin of these currents is presented

Sheath boundary conditions for plasma fluid models

A new definition of the sheath edge is rigorously derived taking into account the kinetic properties of the plasma, and a consistent set of local sheath edge conditions is presented for the case of a magnetic field perpendicular to the wall. These local boundary conditions give explicit expressions for the ion velocity, the electron velocity, and the electron heat flux at the sheath edge, which can be easily implemented in a fluid code. It is shown that in the case of positive current to the wall, the commonly used Bohm's relations well aproximate the proposed boundary conditions, while large discrepancies are observed for negative currents. A fully kinetic PIC code simulating the plasma wall transition has been developed to validate these local relations, showing an excellent agreement with the theory. This work represents a first step towards a complete formulation of the sheath edge local boundary conditions for a general magnetic geometry

Intrinsic toroidal plasma rotation in the scrape-off-layer

The origin and nature of intrinsic toroidal plasma rotation in the scrape-off-layer are theoretically investigated. We discuss and analytically estimate three mechanisms that give rise to SOL toroidal rotation: turbulent momentum transport associated with electrostatic instabilities, pressure gradients along the poloidal direction, and deviation of the plasma velocity at the sheath entrance with respect to the Bohm's value. The results of three-dimensional global fluid simulations of tokamak scrape-off-layer in a limiter configuration are shown and compared