The effect of collisions on the transverse plasma oscillations has been studied by using a relaxation model for the collision term. With the Fourier-Laplace transform method, a general dispersion relation for the oscillations of an infinite uniform plasma has been derived. We obtain and where ω is the frequency of oscillations, ωp is the plasma electron frequency, k is the wave propagation vector, v is the damping due to collisions, vcoll is a phenomenological collision frequency, and ν0 is the mean thermal velocity. The real part (a) is consistent with the results of earlier authors and the imaginary part (b) gives the damping of the oscillations by the collisions.
Plasma Oscillations: II. Kinetic theory of waves in plasmas