We study the transport of high-energy particles in pulsar wind nebulae ( PWN ) using three-dimensional MHD ( see ( ) for details ) and test-particle simulations , as well as a Fokker-Planck particle transport model .
The latter includes radiative and adiabatic losses , diffusion , and advection on the background flow of the simulated MHD nebula .
By combining the models , the spatial evolution of flux and photon index of the X-ray synchrotron emission is modelled for the three nebulae G21.5-0.9 , the inner regions of Vela , and 3C 58 , thereby allowing us to derive governing parameters : the magnetic field strength , average flow velocity and spatial diffusion coefficient .
For comparison , the nebulae are also modelled with the semi-analytic ( ) model but the ( ) model generally yields better fits to the observational data .

We find that high velocity fluctuations in the turbulent nebula ( downstream of the termination shock ) give rise to efficient diffusive transport of particles , with average Péclet number close to unity , indicating that both advection and diffusion play an important role in particle transport .
We find that the diffusive transport coefficient of the order of \sim 2 \times 10 ^ { 27 } ( L _ { s } / 0.42 Ly ) cm ^ { 2 } s ^ { -1 } ( L _ { s } is the size of the termination shock ) is independent of energy up to extreme particle Lorentz factors of \gamma _ { p } \sim 10 ^ { 10 } .