Numerical simulations of sheath-interchange turbulence at the boundary of magnetically confined plasmas

Abstract

Controlled thermonuclear fusion holds great potential as an abundant, safe and environmentally friendly source of electrical energy. One of the most promising approach to harness fusion energy is trough the use of tokamak, a machine with a strong toroidal magnetic field. However the intrinsic curvature of the tokamak leads to an interchange instability, akin to the Rayleigh Taylor instability, in regions with unfavorable curvature. This eventually leads the plasma to become turbulent, resulting in enhanced cross-field transport to the material surfaces of the reactor. In the Scrape-Off Layer (SOL) the magnetic field lines intersect material walls, leading to the formation of sheaths, which influence the underlying turbulent fluctuations. The interaction between the sheaths and the interchange motion is whats studied in this thesis. Parameterizing the dynamics along the field lines leads to a set of two 2D coupled advection governing the evolution of the particle density and the electric drift vorticity in the drift-plane.

In this thesis the model equations describing the sheath-interchange instability is derived from first principals using drift-ordering. A linear stability analysis pursuit, followed by the theory behind the code developed in Julia alongside this thesis. The code is thoroughly validated, with one of the test focusing on the velocity and evolution of isolated blob structures. All this, leading up to gradient-driven sheath-interchange turbulence simulations, in which statistical properties are investigated. To conduct the statistical analysis long timeseries are required, hence there has been a focus in this thesis on developing efficient code. The code is also developed with the intent of being modular such that it can be used in the future.

Controlled thermonuclear fusion holds great potential as an abundant, safe and environmentally friendly source of electrical energy. One of the most promising approach to harness fusion energy is trough the use of tokamak, a machine with a strong toroidal magnetic field. However the intrinsic curvature of the tokamak leads to an interchange instability, akin to the Rayleigh Taylor instability, in regions with unfavorable curvature. This eventually leads the plasma to become turbulent, resulting in enhanced cross-field transport to the material surfaces of the reactor. In the Scrape-Off Layer (SOL) the magnetic field lines intersect material walls, leading to the formation of sheaths, which influence the underlying turbulent fluctuations. The interaction between the sheaths and the interchange motion is whats studied in this thesis. Parameterizing the dynamics along the field lines leads to a set of two 2D coupled advection governing the evolution of the particle density and the electric drift vorticity in the drift-plane.

In this thesis the model equations describing the sheath-interchange instability is derived from first principals using drift-ordering. A linear stability analysis pursuit, followed by the theory behind the code developed in Julia alongside this thesis. The code is thoroughly validated, with one of the test focusing on the velocity and evolution of isolated blob structures. All this, leading up to gradient-driven sheath-interchange turbulence simulations, in which statistical properties are investigated. To conduct the statistical analysis long timeseries are required, hence there has been a focus in this thesis on developing efficient code. The code is also developed with the intent of being modular such that it can be used in the future.