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This communication introduces the concept of plasma-wall self-organization (PWSO) in magnetic fusion. The basic idea is the existence of a time delay in the feedback loop relating radiation and impurity production on divertor plates. Both a zero and a one-dimensional description of PWSO are provided. They lead to an iterative equation whose equilibrium fixed point is unstable above some threshold. This threshold corresponds to a radiative density limit, which can be reached for a ratio of total radiated power to total input power as low as 1/2. When detachment develops and physical sputtering dominates, this limit is progressively pushed to very high values if the radiation of non-plate impurities stays low. Therefore, PWSO comes with two basins for this organization: the usual one with a density limit, and a new one with density freedom, in particular for machines using high-Z materials. Two basins of attraction of PWSO are shown to exist for the tokamak during start-up, with a high density one leading to this freedom. This basin might be reached by a proper tailoring of ECRH assisted ohmic start-up in present middle-size tokamaks, mimicking present stellarator start-up. In view of the impressive tokamak DEMO wall load challenge, it is worth considering and checking this possibility, which comes with that of more margins for ITER and of smaller reactors. Important facts and results:The L-mode density limit increases with rising heating power P like P^{0.4} It is shown with a data base of 5 tokamaks that a scaling like (IP/a^4)^{4/9}, with a the small radius and I the total current, organizes much better the data than Greenwald's one in I/a^2; especially device per device. This scaling is a part of those derived in earlier works, which are in much better agreement with the tokamak and RFP databases. They apply to the stellarator too. They describe the density limit as a radiative one, and therefore include naturally a clear explicit dependence on P. A large part of the radiative density limit comes from the radiation of impurities. Their amount is governed by plasma-wall interaction. We provide a self-consistent description of this interaction and introduce the concept of PWSO. Both zero and one-dimensional descriptions lead to a delay equation whose simplest expression is R+ = \alfa (P-R), where P is the total input power in the plasma, R is the total radiated power, and R+ is its delayed value. This makes the plasma-wall system unstable for \alfa >1. Since \alfa is proportional to the density below detachment, this threshold defines a density limit. It can be reached for a ratio of total radiated power to total input power as low as 1/2. When detachment develops, the plasma temperature at the plates decreases, which makes \alfa to vanish. This pushes the radiative density limit to very high values when physical sputtering dominates, in particular for tungsten. Hence density freedom. The 0D and 1D models of PWSO apply to the stellarator and to the reversed field pinch as well.