We measure the field transmission matrix t for microwave radiation propagating through random waveguides in the crossover to Anderson localization. From these measurements, we determine the dimensionless conductance g and the individual eigenvalues τn of the transmission matrix tt † whose sum equals g. In diffusive samples, the highest eigenvalue, τ1, is close to unity corresponding to a transmission of nearly 100%, while for localized waves, the average of τ1, is nearly equal to g. We find that the spacing between average values of ln τn is constant and demonstrate that when surface interactions are taken into account it is equal to the inverse of the bare conductance.

In this paper, recent progress on experimental analysis and theoretical models for non-local transport (non-Fickian fluxes in real space) is reviewed. The non-locality in the heat and momentum transport observed in the plasma, the departures from linear flux-gradient proportionality, and externally triggered non-local transport phenomena are described in both L-mode and improved-mode plasmas. Ongoing evaluation of 'fast front' and 'intrinsically non-local' models, and their success in comparisons with experimental data, are discussed

The absolute rate of nonlinear energy transfer among broadband turbulence, low-frequency zonal flows (ZFs) and geodesic acoustic modes (GAMs) was measured for the first time in fusion-grade plasmas using two independent methods across a range of heating powers. The results show that turbulent kinetic energy from intermediate frequencies (20-80 kHz) was transferred into ZFs and GAMs, as well as into fluctuations at higher frequencies (>80  kHz). As the heating power was increased, the energy transfer from turbulence into GAMs and the GAM amplitudes increased, peaked and then decreased, while the energy transfer into the ZFs and the ZFs themselves increased monotonically with heating power. Thus there exists a competition between ZFs and GAMs for the transfer of turbulent energy, and the transfer into ZFs becomes dominant as the heating power is increased. The poloidal-radial Reynolds stress and the mean radial electric field profiles were also measured at different heating powers and found to be consistent with the energy transfer measurement. The results suggest that ZFs play an important role in the low-to-high (L-H) plasma confinement transition.

As the desire to explore opaque materials is ordinarily frustrated by multiple scattering of waves, attention has focused on the transmission matrix of the wave field. This matrix gives the fullest account of transmission and conductance and enables the control of the transmitted flux; however, it cannot address the fundamental issue of the spatial profile of eigenchannels of the transmission matrix inside the sample. Here we obtain a universal expression for the average disposition of energy of transmission eigenchannels within random diffusive systems in terms of auxiliary localization lengths determined by the corresponding transmission eigenvalues. The spatial profile of each eigenchannel is shown to be a solution of a generalized diffusion equation. These results reveal the rich structure of transmission eigenchannels and enable the control of the energy distribution inside random media.