Quasilinear Theory Approximations

Abstract

If the instability increases exponentially without any limitation, evidently, this does not reflect the reality and it is therefore necessary to identify a mechanism responsible for the saturation of this instability. The aim of this work is to add such a capability, the first step is to let vary slowly (compared to the wave period) over time. The quasilinear theory has been precisely introduced to describe such an evolution. It is clear that when collisions are neglected, we are in the presence of diffusion equation. In fact, in its Fokker-Planck form, the collision operator is splitting into a transport and diffusive terms. The resulting phenomenon is known as the quasilinear diffusion: under the conjugate effects of the wave on one hand and collisions on the other hand, the variation of the distribution function has a diffusive nature.