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The influence of adiabatic focusing on particle diffusion is an importanttopic in astrophysics and plasma physics. In the past several authors haveexplored the influence of along-field adiabatic focusing on parallel diffusionof charged energetic particles. In this paper by using the Unified NonLinearTransport (UNLT) theory developed by Shalchi (SH2010) and the method of He andSchlickeiser (HS2014) we derive a new nonlinear perpendicular diffusioncoefficient for non-uniform background magnetic field. This formulademonstrates that particle perpendicular diffusion coefficient is modified byalong-field adiabatic focusing. For isotropic pitch-angle scattering and weakadiabatic focusing limit the derived perpendicular diffusion coefficient isindependent of the sign of adiabatic focusing characteristic length. Fortwo-component model we simplify the perpendicular diffusion coefficient up tosecond order of the power series of adiabatic focusing characteristic quantity.We find that the first order modifying factor is equal to zero and the sign ofthe second one is determined by the energy of particles.

Perpendicular diffusion coefficient of cosmic rays in the presence of weak adiabatic focusing