LANDAU DAMPING.

The classic treatments by Landau and by Van Kampen of the initial value problem of the linearized Vlasov equation are raecapitulated, with special reference to the Landau Damping. It is emphasized that the time dependence of the potential, or the density is jointly determined by 1 the form of the unperturbed velocity distributtion F sub 0 u and 2 the nature of the initial velocity distribution fx, u, 0. This latter dependence is more explicitly brought out in the Van Kampen treatment in which the velocity distribution is expressed in terms of the normal modes of the plasma, which in general can be described as involving a collective motion arising from the Coulomb interactions and the streaming motions of the particles. It is the superposition of the streaming motion of the particles on the collective motion the plasma oscillations that causes the spatial uniformization o the potential, or the density, which is represented by the Landau damping. The Landau damping constant gamma for the case of Maxwellian F sub 0 u has been calculated from the classical limit of the quantum mechanical transition probability with which an electron having a velocity u omegak exchanges energy with the collective motion. Author