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Fusion research on magnetic confinement is confronted with a severe problemconcerning the electron densities ne to be used in fusion devices. Indeed, highdensities are mandatory for obtaining large efficiencies, whereas it isempirically found that catastrophic disruptive events occur for densitiesexceeding a maximal one n^M_e. On the other hand, despite the large theoreticalwork there is no widely accepted, first principles model for the density limit(see [1], abstract). Here, we propose a simple microscopic model of amagnetized plasma suited for a tokamak, for which the existence of a densitylimit is proven. This property turns out to be a general collective feature ofelectrodynamics of point charges, which is lost in the continuum approximation.The law we find is n^M_e = 1.74 1/(me c^2) B^2/ \mu_0, (1), where \mu_0 is thevacuum permeability, c the speed of light, me the electron mass, and B themagnetic field. As shown in Fig. 1, the theoretical limit (big circles) is inrather good agreement with the empirical data, actually a surprisingly good onefor a model based on first principles, with no adjustable parameter.

A first principles explanation for the density limit in magnetized plasmas