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A theoretical framework is developed to clarify the relation between theprofiles of density and temperature in the Scrape Off Layer (SOL) with thefluctuations (filaments) that generate them. The framework is based on thedynamics of independent filaments and on their statistical behaviour and can beused to rigorously understand the mechanisms that lead to the non-exponentialnature of the radial SOL profiles as well as the increase of the relativefluctuation amplitude in the far SOL. Several models for the dynamics of thefilaments, which can be applied to the framework, are derived and discussed forthe purpose of identifying how different assumptions lead to the emergence offeatures in the profiles. It is found that multiple alternative models canexplain the observations, thus motivating more stringent and focusedexperimental analysis. In particular, radially accelerating filaments, lessefficient parallel exhaust and also a statistical distribution of the velocityof the filaments can all contribute to induce flatter profiles in the far SOL.A quite general result is the resiliency of the non-exponential nature of theprofiles. At the same time, several of the models discussed can also capturethe increase of the relative fluctuation amplitude observed in the far SOL. Itis also shown that several scenarios are compatible with the broadening of theSOL, which could be caused by charge exchange interactions with neutralparticles or by a significant radial acceleration of the filaments.

On the relation between non-exponential Scrape Off Layer profiles and the dynamics of filaments