  High energy emissions near particle accelerators provide unique windows to
probe the particle acceleration and ensuing escape process determined by local
medium properties, particularly the turbulence properties. It has been
demonstrated both theoretically and observationally that particle diffusion in
local environment can differ from the averaged values inferred from the CR
global propagation in the Galaxy determined by local medium, particularly
magnetic field and turbulence. A recent publication by Fornieri & Zhang (2022)
computed particle transport employing the formalism of fast modes scattering
calculation from Yan & Lazarian (2008) and the MHD modes composition results
from Makwana & Yan (2020) and Zhang et al. (2020). The authors claim that the
Cygnus X observations from HAWC and Ferm-LAT can be reproduced (Abeysekara et
al., 2021; Ackermann et al., 2011). We clarify in this paper that the particle
diffusion coefficients they obtained do not correspond to their adopted
turbulence and medium properties and are incorrect by an order of magnitude. We
also point out that the injection process also plays an indispensable role in
determining the high energy particle distribution and the resulting gamma-ray
emission.
