Small edge resonant magnetic perturbations are used to control the pedestal transport and stability in low electron collisionality ( e * ), ITER relevant, poloidally diverted plasmas. The applied perturbations reduce the height of the density pedestal and increase its width while increasing the height of the electron pedestal temperature and its gradient.The effect of the perturbations on the pedestal gradients is controlled by the current in the perturbation coil, the poloidal mode spectrum of the coil, the neutral beam heating power and the divertor deuterium fueling rate. Large pedestal instabilities, referred to as edge as an array of higher frequency electromagnetic waves and turbulence [7]. Outside the plasma, sources such as field-errors from asymmetries in toroidal and poloidal magnetic field coils, magnetic materials, vacuum vessel image and return currents [8], external control coils used to stabilize plasma modes, and correction coils [9] used to minimize perturbations from known field-errors on low integer rational surfaces all contribute to the structure of the magnetic field in which the plasma resides. At the edge of the plasma where the safety factor [ q ( ) defined as the rate of change in toroidal magnetic flux with poloidal magnetic flux ] increases rapidly, all of these perturbations contribute to the creation of closely spaced resonant magnetic islands which may result in the formation of edge stochastic layers. In a poloidally diverted tokamak, the high magnetic shear q across the edge of the plasma results in an increased density of island states and a significantly higher probability of forming open stochastic layers that connect magnetic field lines to plasma facing material surfaces [10]. Thus, the edge plasma is immersed in a dynamically complex magnetic topology over the same region where substantial radial flows of mass and energy, driven by large gradients, compete with strong turbulent transport in highly sheared toroidal and poloidal plasma flow fields. Large radial gradients in the plasma pressure are often established by a strong reduction in turbulent 4 transport due to sheared plasma flow. The large edge gradients are a key factor in the establishment of good confinement levels that make the tokamak the leading candidate for fusion reactors. However, they also lead to the instabilities known as ELMs which drive impulsive energy losses that can be detrimental to plasma facing surfaces. It is easy to understand why the development of tools to control the pedestal transport and stability is a compelling issue for improving the performance and operational safety of high energy density tokamak based fusion confinement systems.A strong motivation for understanding the physics of edge stochastic layers is to enable the development of predictable and reliable tools for controlling key fusion plasma pedestal processes such as: the plasma temperature and pressure at the top of the pedestal, the size and frequency of ELMs, the energy and particle exhaust rate in steady-state cond...