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

## TL;DR

This paper derives a new nonlinear perpendicular diffusion coefficient for cosmic rays in non-uniform magnetic fields, showing how adiabatic focusing influences particle diffusion in astrophysical plasmas.

## Contribution

It introduces a novel formula for the perpendicular diffusion coefficient considering adiabatic focusing effects, extending previous models with a second-order approximation.

## Key findings

- Perpendicular diffusion coefficient is modified by along-field adiabatic focusing.
- In the weak focusing limit, the coefficient is independent of focusing sign.
- The second-order correction's sign depends on particle energy.

## Abstract

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.