We compute the one-point probability distribution for the stationary KPZ equation (i.e. initial data H(0, X) = B(X), for B(X) a two-sided standard Brownian motion) and show that as time T goes to infinity, the fluctuations of the height function H(T , X) grow like T 1/3 and converge to those previously encountered in (2015) 18: 20 the study of the stationary totally asymmetric simple exclusion process, polynuclear growth model and last passage percolation. The starting point for this work is our derivation of a Fredholm determinant formula for Macdonald processes which degenerates to a corresponding formula for Whittaker processes. We relate this to a polymer model which mixes the semi-discrete and log-gamma random polymers. A special case of this model has a limit to the KPZ equation with initial data given by a two-sided Brownian motion with drift β to the left of the origin and b to the right of the origin. The Fredholm determinant has a limit for β > b, and the case where β = b (corresponding to the stationary initial data) follows from an analytic continuation argument.

Two aspects of edge turbulence and transport in Alcator C-Mod are explored. The quasi-coherent mode (QCM), an edge fluctuation present in Enhanced Dα H-mode plasmas, is examined with regard to its role in the enhanced particle transport found in these plasmas, its in/out asymmetry, its poloidal wave number and its radial width and location. It is shown to play a dominant role in the perpendicular particle transport. The QCM is not observed at the inboard midplane, indicating that its amplitude there is significantly smaller than on the outboard side. The peak amplitude of the QCM is found just inside the separatrix, with a radial width 5 mm, leading to a non-zero amplitude outside the separatrix and qualitatively consistent with its transport enhancement. Also examined are the characteristics of the intermittent convective transport, associated with the larger scale turbulent structures, also called blobs, and typically occurring in the scrape-off-layer (SOL). These turbulent structures are qualitatively similar in Land H-mode. When their perpendicular extent, occurrence frequencies and magnitudes are compared, it is found that their size is somewhat smaller in ELMfree H-Mode, while their frequency is similar. A clear difference is seen in the magnitude of these turbulent fluctuations in the far SOL, with ELMfree H-mode showing a smaller perturbation there than L-mode. As the Greenwald density limit is approached (n/n GW 0.7), blobs are seen inside the separatrix consistent with the observation that the high cross-field transport region, normally found in the far SOL, penetrates the closed flux surfaces at high n/n GW .