Linear Oscillations of a Collisionless Plasma

In ordinary neutral gas theory, one uses the Boltzmann equation to determine the oscillations occurring in a gas. This equation assumes that particles suffer binary collisions only, and that in between these collisions they move freely under the influence of external forces only. An extremely useful additional approximation is to assume that the collision terms are very large in magnitude compared to the ''streaming'' terms. In this case the distribution function is very close to a Maxwell-Boltzmann and one can take moments of the Boltzmann equation and obtain the considerably more convenient hydrodynamic equations. A hot, fully ionized plasma does not allow us these luxuries. Because of the long range nature of the coulomb force, the assumption of binary collisions is clearly inadequate. Even more important, the collision terms are now considerably smaller than the ''streaming'' terms. To compare these quantities, we now calculate the approximate oscillation frequency of a plasma (since this is a measure of the ''streaming'' terms) and the corresponding collision frequency. (author)