An algorithmic unification of particle -in -cell and continuum methods and a wave -particle description for the electron temperature gradient (ETG) instability saturation

This thesis consists of two major parts. In the first part we detail a new numerical algorithm that encompasses both the delta f particle-in-cell (PIC) method and a continuum method. We describe this new algorithm and methods of interpolation. The issue of phase space convergence of this algorithm is also addressed. We analyze the induced numerical diffusion and compare between theory and simulation. We also create a simple test problem that shows this algorithm solves the so-called "growing weight" problem. The second part of the thesis presents a wave-particle description for the saturation of the electron temperature gradient (ETG) instability. It has been proposed that electron temperature gradient (ETG) driven turbulence is responsible for experimentally observed electron thermal transport in tokamak plasmas. Significant transport levels are possible by the creation of radially elongated vortices or "streamers", which are sustained by the nonlinear saturation of the instability and are not susceptible to shear flow destruction, as is the case with the ion temperature gradient (ITG) mode. We present a dynamical system to explore the dependence of saturation level due to E x B and E ∥ motion, as well as the effect of radial elongation. With this model, we can predict the nonlinear saturation level of the ETG streamers. We compare our theoretical predictions with a 2D shear-less slab gyrokinetic electron code that includes the E∥ nonlinearity.