  The influence of adiabatic focusing on particle diffusion is an important
topic in astrophysics and plasma physics. In the past several authors have
explored the influence of along-field adiabatic focusing on parallel diffusion
of charged energetic particles. In this paper by using the Unified NonLinear
Transport (UNLT) theory developed by Shalchi (SH2010) and the method of He and
Schlickeiser (HS2014) we derive a new nonlinear perpendicular diffusion
coefficient for non-uniform background magnetic field. This formula
demonstrates that particle perpendicular diffusion coefficient is modified by
along-field adiabatic focusing. For isotropic pitch-angle scattering and weak
adiabatic focusing limit the derived perpendicular diffusion coefficient is
independent of the sign of adiabatic focusing characteristic length. For
two-component model we simplify the perpendicular diffusion coefficient up to
second 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 of
the second one is determined by the energy of particles.
