Secular resonant dressed orbital diffusion – I. Method and WKB limit for tepid discs

The equation describing the secular diffusion of a self-gravitating collisionless system induced by an exterior perturbation is derived while assuming that the time-scale corresponding to secular evolution is much larger than that corresponding to the natural frequencies of the system. Its two-dimensional formulation for a tepid galactic disc is also derived using the epicyclic approximation. Its Wentzel-Kramers-Brillouin (WKB) limit is found while assuming that only tightly wound transient spirals are sustained by the disc. It yields a simple quadrature for the diffusion coefficients which provides a straightforward understanding of the loci of maximal diffusion within the disc.