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Drift-reduced plasma fluid models are commonly used in plasma physics for analytics and simulations; however, the validity of such models must be verified for the regions of parameter space in which tokamak plasmas exist. By looking at the…
This paper presents eigensolution and non-modal analyses for immersed boundary methods (IBMs) based on volume penalization for the linear advection equation. This approach is used to analyze the behavior of flux reconstruction (FR)…
We present a novel direct transcription method to solve optimization problems subject to nonlinear differential and inequality constraints. We prove convergence of our numerical method under reasonably mild assumptions: boundedness and…
Plasma turbulence is the dominant transport mechanism for heat and particles in magnetized plasmas in linear devices and tokamaks, so the study of turbulence is important in limiting and controlling this transport. Linear devices provide an…
Despite the significant role of turbomachinery in fluid-based energy transfer, precise simulation of rotating solid objects with complex geometry is a challenging task. In the present study, the volume penalization method (VPM) is combined…
We present a convergence analysis of the penalty method applied to unilateral contact problems in two and three space dimensions. We first consider, under various regularity assumptions on the exact solution to the unilateral contact…
The edge plasma turbulence and transport dynamics, as well as the divertor power loads during the thermal quench phase of tokamak disruptions are numerically investigated with BOUT++'s flux-driven, six-field electromagnetic turbulence…
We study an optimal control problem for the heat equation with a prescribed terminal state. To circumvent the difficulty of enforcing a hard terminal constraint, we analyze a penalized formulation and prove that the corresponding optimal…
Advanced tokamak scenarios often feature equilibriums with zero and reversed magnetic shear. To isolate and investigate their impacts on the resistive wall mode (RWM) instability analytically, we construct a series of cylindrical limiter…
During a tokamak discharge, the plasma can vary between different confinement regimes: Low (L), High (H) and, in some cases, a temporary (intermediate state), called Dithering (D). In addition, while the plasma is in H mode, Edge Localized…
A strongly interacting plasma of linearly dispersing electron and hole excitations in two spatial dimensions (2D), also known as a Dirac fluid, can be captured by relativistic hydrodynamics and shares many universal features with other…
This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are…
In this work, a Model Predictive Controller (MPC) is proposed to control the plasma shape in the Tokamak \`a Configuration Variable (TCV). The proposed controller relies on models obtained by coupling linearized plasma response models,…
We consider minimization problems with structured objective function and smooth constraints, and present a flexible framework that combines the beneficial regularization effects of (exact) penalty and interior-point methods. In the fully…
Energy transport and confinement in tokamak fusion plasmas is usually determined by the coupled nonlinear interactions of small-scale drift turbulence and larger scale coherent nonlinear structures, such as zonal flows, together with free…
Chaotic transport is a subject of paramount importance in a variety of problems in plasma physics, specially those related to anomalous transport and turbulence. On the other hand, a great deal of information on chaotic transport can be…
Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of…
Barriers have been identified in magnetically confined plasmas reducing the particle transport and improving the confinement. One of them, the primary shearless barriers are associated to extrema of non-monotonic plasma profiles.…
This paper presents a general convergence theory of penalty based numerical methods for elliptic constrained inequality problems, including variational inequalities, hemivariational inequalities, and variational-hemivariational…
The effect of flow shear on turbulent transport in tokamaks is studied numerically in the experimentally relevant limit of zero magnetic shear. It is found that the plasma is linearly stable for all non-zero flow shear values, but that…