Analysis of a generalized nonlinear diffusion equation in fusion plasma physics

Abstract

Using similarity methods, an investigation is made of a generalized nonlinear diffusion equation arising in plasma physics in connexion with several recently proposed models for turbulent plasma energy transport and particle diffusion.In almost every field of physics, diffusion or transport equations of the form Ψt = Δ. (DΔΨ) play an important role. The theory of linear diffusion equations, where the diffusion constant D is independent of Ψ, has been developed to a high degree of sophistication (e.g. Carsiaw & Jaeger 1959).