We study the enhanced damping of Trivelpiece-Gould modes in a nonneutral plasma column, due to application of a Debye-shielded cylindrically symmetric squeeze potential [phi]₁. Damping of these plasma modes is caused by additional Landau resonances at energies En for which the particle bounce frequency [omega]b(En) and the wave frequency [omega] satisfy [omega] = n[omega]b(En). In the first chapter we assume a smooth squeeze of finite width and find that additional resonances induced by the squeeze cause substantial damping, even in the large wave phase velocity compared to thermal velocity regime. For [omega]/ k >> (T /m) and [phi]₁ << T , the resonance damping rate has a I[phi]₁I² dependence. This dependence agrees with the simulations and experimental results. In chapter 2 a narrow partition-like squeeze is added to an unsqeezed 1D plasma and we evaluate the plasma heating, caused by cylindrically symmetric plasma modes. As in chapter 1, collisionless heating is enhanced by the squeeze, due to additional resonances, even when [omega]/k >> (T /m). Adding collisions to the theory broadens these resonances and also creates a boundary layer at the separatrix between trapped and passing particles. This further enhances the heating at [omega]/k vs < 1, where vs is the separatrix velocity. We study the nonlinear interaction of TG waves in chapter 3. We obtain corrections to the forms and frequencies of weakly nonlinear modes. Futhermore, we study the decay instability between a dominant axial mode m = 2 and a small amplitude mode m = 1, using both analytical and numerical techniques. In chapter 4, we study nonlinear interactions of the novel Electron Acoustic Waves in a 1D plasma. Here, we use a weakly nonlinear analysis of a 1D Vlasov-Poisson system, in a modified Maxwellian equilibrium, flattened at the phase velocity of the waves. Using numerical simulation of the 1D Vlasov-Poisson system, we study the unstable collapse of an EAW mode m = 2 to an EAW mode m = 1 and compare the numerically-obtained exponential growth rates to the analytically obtained results

This Rapid Communication sets forth the mechanism by which mesoscale staircase structures condense to form macroscopic states of enhanced confinement. Density, vorticity, and turbulent potential enstrophy are the variables for this model. Formation of the staircase structures is due to inhomogeneous mixing of (generalized) potential vorticity (PV). Such mixing results in the local sharpening of density and vorticity gradients. When PV gradients steepen, the density staircase structure develops into a lattice of mesoscale "jumps" and "steps," which are, respectively, regions of local gradient steepening and flattening. The jumps then merge and migrate in radius, leading to the emergence of a new macroscale profile structure, so indicating that profile self-organization is a global process, which may be described by a local, but nonlinear model. This work predicts and demonstrates how mesoscale condensation of staircases leads to global states of enhanced confinement.

This paper presents a theory for the formation and evolution of coupled density staircases and zonal shear profiles in a simple model of drift-wave turbulence. Density, vorticity, and fluctuation potential enstrophy are the fields evolved in this system. Formation of staircase structures is due to inhomogeneous mixing of generalized potential vorticity (PV), resulting in the sharpening of density and vorticity gradients in some regions, and weakening them in others. When the PV gradients steepen, the density staircase structure develops into a lattice of mesoscale “jumps,” and “steps,” which are, respectively, the regions of local gradient steepening and flattening. The jumps merge and migrate in radius, leading to the development of macroscale profile structures from mesoscale elements. The positive feedback process, which drives the staircase formation occurs via a Rhines scale dependent mixing length. We present extensive studies of bifurcation physics of the global state, including results on the global flux-gradient relations (flux landscapes) predicted by the model. Furthermore, we demonstrate that, depending on the sources and boundary conditions, either a region of enhanced confinement, or a region with strong turbulence can form at the edge. This suggests that the profile self-organization is a global process, though one which can be described by a local, but nonlinear model. This model is the first to demonstrate how the mesoscale condensation of staircases leads to global states of enhanced confinement.

The relationship between the physics of turbulent transport of particles and azimuthal momentum in a linear plasma device is investigated using a simple model with a background density gradient and zonal flows driven by turbulent stresses. Pure shear flow driven Kelvin-Helmholtz instabilities (k∥=0) relax the flow and drive an outward (down gradient) flux of particles. However, instabilities at finite k∥ with flow enhanced pumping can locally drive an inward particle pinch. The turbulent vorticity flux consists of a turbulent viscosity term, which acts to reduce the global vorticity gradient and the residual vorticity flux term, accelerating the zonal flows from rest. Moreover, we use the positivity of the production of fluctuation potential enstrophy to obtain a constraint relation, which tightly links the vorticity transport to the particle transport. This relation can be useful in explaining the experimentally observed correlation between the presence of E×B flow shear and the measured inward particle flux in various magnetically confined plasma devices.