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A fundamental problem in astrophysics is the interaction between magneticturbulence and charged particles. It is now possible to use \emph{Ramaty HighEnergy Solar Spectroscopic Imager (RHESSI)} observations of hard X-rays (HXR)emitted by electrons to identify the presence of turbulence and to estimate themagnitude of the magnetic field line diffusion coefficient at least in densecoronal flaring loops.} {We discuss the various possible regimes of cross-fieldtransport of non-thermal electrons resulting from broadband magnetic turbulencein coronal loops. The importance of the Kubo number $K$ as a governingparameter is emphasized and results applicable in both the large and small Kubonumber limits are collected.} {Generic models, based on concepts and insightsdeveloped in the statistical theory of transport, are applied to the coronalloops and to the interpretation of hard X-ray imaging data in solar flares. Therole of trapping effects, which become important in the non-linear regime oftransport, is taken into account in the interpretation of the data.} For thisflaring solar loop, we constrain the ranges of parallel and perpendicularcorrelation lengths of turbulent magnetic fields and possible Kubo numbers. Weshow that a substantial amount of magnetic fluctuations with energy $\sim 1%$(or more) of the background field can be inferred from the measurements of themagnetic diffusion coefficient inside thick-target coronal loops.

Turbulent cross-field transport of non-thermal electrons in coronal loops: theory and observations