Synchronization and stochastic behavior of electrons in a Penning trap

Recent work has described the collective behavior of a large number of parametrically pumped electron oscillators as well as the behavior of a single electron in a Penning trap. The excitation of a single particle oscillator is well described by the classical Mathieu equation with interesting nonlinear dynamics appearing with increasing numbers of electrons. The plasma is extremely sensitive to the net heat in the system, particularly cooling from transverse electromagnetic modes of the cylindrical Penning trap cavity. Under certain conditions the plasma can be sufficiently cooled so that it acts like a rigid ball of charge. The goal of the current work is to bridge the single particle and many particle regimes by studying the collective behavior of "countable" numbers of electrons (i.e. 2,3,4), thereby building a plasma one electron at a time.