  A gyrokinetic Coulomb collision operator is derived, which is particularly
useful to describe the plasma dynamics at the periphery region of magnetic
confinement fusion devices. The derived operator is able to describe collisions
occurring in distribution functions arbitrarily far from equilibrium with
variations on spatial scales at and below the particle Larmor radius. A
multipole expansion of the Rosenbluth potentials is used in order to derive the
dependence of the full Coulomb collision operator on the particle gyroangle.
The full Coulomb collision operator is then expressed in gyrocentre phase-space
coordinates, and a closed formula for its gyroaverage in terms of the moments
of the gyrocenter distribution function in a form ready to be numerically
implemented is provided. Furthermore, the collision operator is projected onto
a Hermite-Laguerre velocity space polynomial basis and expansions in the small
electron-to-ion mass ratio are provided.
