Undergraduate Honors Theses

Thesis Defended

Spring 2016

Document Type


Type of Thesis

Departmental Honors



First Advisor

Scott Parker

Second Advisor

Jamie Nagle

Third Advisor

Harvey Segur


Tokamak magnetic confinement experiments are the most researched prospect for controlled thermonuclear fusion energy production. The quasi-toroidal geometry along with the large, twisting toroidal magnetic field pose great engineering and physics challenges. Plasma physicists use large-scale simulations of Tokamak plasmas in order to further understand their physics and inform experimental design to strive towards the goal of reliable fusion energy [20]. One type of simulation uses a gyrokinetic formulation to study plasmas in strong magnetic fields. A fundamental concept in gyrokinetic plasma physics is that of the guiding center drifts, which influence the motion of the guiding center of a gyrating charged particle in electric and magnetic fields. Previously, the significant toroidal and poloidal equilibrium flows of a tokamak plasma were not fully included in simulation models. Experiments have suggested that these flows have noticeable effects on tokamak physics [5][17]. In this thesis, we discuss the formulation of a gyrokinetic model that includes these flows by shifting velocity space to the frame moving with the plasma flow [18]. Many of the previous calculations can be used with relatively small modifications of the standard lab frame model. However, in this new frame, the centrifugal and Coriolis forces, which are well established physics concepts in rotating reference frames, manifest themselves as new drift terms in the drift gyrokinetic equation [2]. In this thesis, we will step through the calculation of these terms in cylindrical coordinates starting with the Sugama-Horton model for drift velocity [18] to obtain the established result from the literature. We will also use the guiding center Hamiltonian formulation [15] in a tokamak plasma by explaining the previous work on this topic from a few references in detail to obtain an equivalent result [17][9]. The original work of this thesis is the implementation of the new drift terms in the simulation's magnetic field-following coordinate system in a usable way for the purposes of large-scale tokamak simulations. We will examine the effect of the equilibrium flow by visualizing results for the simple test case of a linear eigenmode in a tokamak. We find that the fundamental structure of the mode is unchanged, but the ExB drift connected to the flow results in a tilt of the poloidal mode structure in accordance with our expectations. Finally, future work using the gyrokinetic model that includes large equilibrium flows is discussed.