  A fundamental problem in plasma physics, space science, and astrophysics is
the transport of energetic particles interacting with stochastic magnetic
fields. In particular the motion of particles across a large scale magnetic
field is difficult to describe analytically. However, progress has been
achieved in the recent years due to the development of the unified non-linear
transport theory which can be used to describe magnetic field line diffusion as
well as perpendicular diffusion of energetic particles. The latter theory
agrees very well with different independently performed test-particle
simulations. However, the theory is still based on different approximations and
assumptions. In the current article we extend the theory by taking into account
the finite gyroradius of the particle motion and calculate corrections in
different asymptotic limits. We consider different turbulence models as
examples such as the slab model, noisy slab turbulence, and the two-dimensional
model. Whereas there are no finite gyroradius corrections for slab turbulence,
the perpendicular diffusion coefficient is reduced in the other two cases. The
matter investigated in this article is also related to the parameter a^2
occurring in non-linear diffusion theories.
