The Behaviour of a Large Number of Electrons Oscillating between the Plates of a Condenser†

Abstract

The transient and long-term behaviour of a cloud of electrons bound by a simple harmonic restoring force, which, for generality, depends oil the particular electron, to a position midway between the plates of is parallel-plats condenser, is investigated in tin approximation in which space charge is neglected. Collective behaviour, including instability and damping of the Landau type, is derived, as is the noisy spectrum resulting from the decay of a transient, The rate of damping of thermal motion when the external circuit contains resistance is calculated in order of magnitude