Study of Magnetically Confined Plasma Dynamics with Cellular Automata

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dc.contributor.advisor Sánchez Fernández, Luis Raúl Fukuda León, Cristina Midori 2020-01-15T08:57:19Z 2020-01-15T08:57:19Z 2018-09 2018-10-09
dc.description.abstract Nuclear fusion has many chances to become the primary energy source of the future. The great energy density of fusion reactions, together with the environmental and safety benefits that it encloses makes it a powerful alternative to existing energy sources and a smart response to the increase in energy demand. Up to now, research has designated tokamaks as the best alternative to obtain fusion energy. However, their reliability has not yet been proved. To this matter, ITER, the most ambitious energy project in human history, is being built to demonstrate the viability of fusion energy by producing net positive energy in a giant tokamak. Fusion plasmas inside Tokamaks are known to be turbulent. The instabilities created in the plasma by the great gradients they are subjected to, turn the issue of their confinement into a difficult goal to achieve. Part of the plasma escapes from the confinement volume, reducing the density in its core and decreasing the efficiency of the fusion reaction as well as the energy obtained from it. As a consequence, the net fusion energy produced may not be sustainable. More energy is used in the process than the one that is extracted from it. If fusion reactors are meant to be a reliable source of energy in the future, effective solutions to mitigate the effects of turbulence are a critical necessity. Various confinement modes exist in a tokamak as the power of the heating source is increased. The most well-known one is the L-mode (Low confinement mode), but it is only the H-mode (High confinement mode) the one that brings some hope to the idea of industrial fusion processes. Still, there are many unknowns to the dynamic processes that take part in this last regime. In H-mode, a transport barrier created by the poloidal rotation of the plasma is known to appear at the edge of the tokamak section. The differences in radial velocities in this barrier, create zonal shear flows that shear apart turbulent eddies, reducing the transport of particles out of the tokamak. It is this mechanism that makes H-mode the most reasonable regime in which a fusion reactor would operate. Still, the transport dynamics of H-mode are not fully understood. In order to make effective predictions on confinement control strategies as well as the cost and size of a future fusion energy plant, the ultimate concepts on the interaction of shear with turbulence have to be clarified. It is a proved fact that the dynamics of transport in fusion plasmas is not diffusive. Instead, the transport regime operating in L-mode appears to be similar to ”SOC dynamics” (SOC = Self Organized Criticality), characterized by the existence of memory as well as the absence of characteristic scales or times. This absence makes the quest for an effective coefficient of diffusion a useless work. As a first step towards the understanding on how the relations between turbulence and shear change the transport dynamics in H-mode, the present project aims to create an abstract model of radial turbulent transport inside tokamaks. This model needs to be versatile enough to introduce and detect essential changes and fundamental relations in the transport dynamics of the system. With it, fundamental questions such as the search for a proper effective description of transport beyond usual diffusion could be investigated in the future. For this purpose, the running sandpile, a model that attempted to capture the basic dynamics of the plasma in L-mode introduced in the 1990’s, is used and modified by introducing in it a new variable, shear. By doing this an ”extended sandpile model” is created. In order to introduce the interactions of the shear with the other variables in the model in a way inspired by the actual physics in H-mode, new dynamic rules are implemented and included in a newly designed algorithm created with the software tool Matlab. This ”Extended sandpile model” has then been tested by analyzing data retrieved from its continued operation. The tool that has been used to examine the validity of this extended model is known as ”transfer entropy”, a tool capable of determining the direction and importance of causal flows between variables. Variables such as the instantaneous variance of the average shear, the instantaneous variance of the average gradient and the instantaneous number of unstable cells have been tested by this tool, revealing reverted relations in causality between the model with shear and the one without. Moreover, in the extended running sandpile the results show that shear can be made to become the most influential factor, something that was intended, since it is what actually happens in H-mode plasmas. As a conclusion for these results follow that the procedures here conducted have been able to produce a model that is able to capture the essence of near-marginal transport in the presence of shear in a few rules and parameters. Furthermore, transfer entropy has been proved to be able to detect these changes afterwards. As content of future research one could mention that a thorough exploration of the parameter space that defines the extended model should be carried out before selecting the operational point that would set the system closer to actual H-mode transport dynamics. Once done, this could serve as the starting point of investigations aiming at finding appropriate effective transport equations that, from previous experience with the usual running sandpile, would probably have to be based on the use of the integro-differential operators usually known as fractional derivatives.
dc.language.iso eng
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.subject.other Nuclear fusion
dc.subject.other Plasma
dc.subject.other Tokamak
dc.subject.other Sandpile
dc.subject.other Transfer entropy
dc.subject.other Shear
dc.subject.other Turbulence
dc.title Study of Magnetically Confined Plasma Dynamics with Cellular Automata
dc.type bachelorThesis
dc.subject.eciencia Física
dc.rights.accessRights openAccess Ingeniería Aeroespacial
dc.contributor.departamento Universidad Carlos III de Madrid. Departamento de Física
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