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Abstract: Gyrokinetics is a rich and rewarding playground to study some of themysteries of modern physics. In this thesis I present work, motivated by thequest for fusion energy, which seeks to uncover some of the inner workings ofturbulence in magnetized plasmas.I begin with the fundamental theory of gyrokinetics, and a novel formulationof its extension to the equations for mean-scale transport - the equationswhich must be solved to determine the performance of magnetically confinedfusion devices. The second project presents gyrokinetic secondary instabilitytheory as a mechanism to bring about saturation of the basic instabilities thatdrive gyrokinetic turbulence. Emphasis is put on the ability for this analytictheory to predict basic properties of the nonlinear state, which can be appliedto a mixing length phenomenology of transport. The final project is anapplication of the methods from inertial range understanding of fluidturbulence, to describe the stationary state of fully developed two-dimensionalgyrokinetic turbulence. This work explores the relatively new idea of aphase-space cascade, whereby fine scales are nonlinearly generated in bothposition space and velocity space, and ultimately smoothed by collisionalentropy production. This process constitutes the thermodynamic balance whichoccurs in the true steady state of a turbulent plasma, including those found infusion devices.

Autor: Gabriel G. Plunk


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