Analytical solution of the diffusion equation in a cylindrical medium with step-like diffusivity

The exact analytical solution of the one-dimensional diffusion equation in a cylinder has been found, for a medium characterized by a diffusion coefficient with step-like and/or monomial variations, in addition to a constant damping term. This type of equation has important applications in the field of magnetically confined plasmas, in the presence of a transport barrier. A sharp variation of the heat diffusivity can also result from the microturbulence that develops whenever the temperature gradient exceeds a critical value. This analytical solution can be used to model the evolution, in space and time, of the electron temperature of a plasma heated up by an external source, the step in the heat diffusion coefficient being related to the space location of the critical temperature gradient. The general properties of the solution and its application to the analysis of perturbative electron heating experiments are discussed