Landau’s calculation of electron plasma oscillations demonstrated the phenomenon now known as Landau damping.1 The calculation used a Fourier-Laplace transform and regarded the electron velocity as complex in order to properly locate the pole in the complex frequency plane that gives the dispersion relation containing the wave damping. Here, the same subject is examined using real variables and straightforward algebra. The aim is to understand the damping and growth of plasma oscillations, shown by Landau to arise from particles with velocities close to that of the plasma wave. It is found that the physics underlying the damped oscillations is different from that in the case of growth.
