Density limit in a first principles model of a magnetized plasma in the Debye--H\"uckel approximation

A crucial problem concerning a large variety of fusion devices is that the confinement due to an external magnetic field is lost above a critical density, while a widely accepted first principles explanation of such a fact is apparently lacking. In the present paper, making use of standard methods of statistical mechanics in the Debye--H\"uckel approximation, we give indications that for a plasma there exists a density threshold corresponding to a transition from order to chaos, the ordered motions being those in which the confining Lorentz force on a single electron prevails over the diffusive effect of the Coulomb forces. The density limit, which is proportional to the square of the magnetic field, turns out to fit not too badly the empirical data for plasma collapses in a large set of fusion devices.