Effect of Weak Collisions on Ion Waves

The linearized Fokker-Planck equation is solved by an iteration method which assumes the collision term is one order higher than the other terms. It is solved (1) for the case of ion wave instabilities, where the unperturbed situation consists of a constant electric field, electrons with the Spitzer-Härm distribution, and ions with a Maxwellian distribution of much lower temperature. The effect of collisions on the critical current for instability is determined, and it is found that the electron-ion collisions predominate and lower the critical current. An attempt is made to justify the use of the Fokker-Planck equation when the distribution functions are nearly unstable. The linearized Fokker-Planck equation is also solved for (2) the case of ion waves in a cesium plasma. Here the electrons are taken as an isothermal fluid. The propagation and time damping constants are obtained as a function of collision rate. Also, the first root of the dispersion relation is applied to the space damping of ion waves in order to make a comparison with the experiment of Motley and Wong.