Reabsorption and Density Limit in Magnetized Plasmas Through a First-Principles Toy Model

In the physics of magnetized plasmas there are problems of principle that apparently still miss a microscopic explanation. A typical case is the reabsorption of cyclotron emission by gyrational electron motions in a magnetic field. On the other hand, it seems that a microscopic explanation of reabsorption is contained in the 1945 paper of Wheeler and Feynman that, however, strangely enough, to our knowledge is never mentioned in this connection. Here we introduce a simple toy model that, on the one hand, contains all the features of the Wheeler-Feynman electrodynamics (which in fact is just the standard electrodynamics, as they repeatedly point out) and, on the other hand, presents such a simple kinematics as to allow for an analytic treatment. In such way reabsorption is proven. As a byproduct, a density limit for magnetic confinement due to a microscopic instability is also deduced.