  It is known that a plasma in a magnetic field, conceived microscopically as a
system of point charges, can exist in a magnetized state, and thus remain
confined, inasmuch as it is in an ordered state of motion, with the charged
particles performing gyrational motions transverse to the field. Here we give
an estimate of a threshold, beyond which transverse motion become chaotic, the
electrons being unable to perform even one gyration, so that a breakdown should
occur, with complete loss of confinement. The estimate is obtained by the
methods of perturbation theory, taking as perturbing force acting on each
electron that due to the so--called microfield, i.e., the electric field
produced by all the other charges. We first obtain a general relation for the
threshold, which involves the fluctuations of the microfield. Then, taking for
such fluctuations the fomula given by Iglesias, Lebowitz and MacGowan for the
model of a one component plasma with neutralizing background, we obtain a
definite formula for the threshold, which corresponds to a density limit
increasing as the square of the imposed magnetic field. Such a theoretical
density limit is found to fit pretty well the empirical data for collapses of
fusion machines.
