Supernova remnant precursor width

1.Assuming that the line widths represent thermal broadening, an upper limit on the precursor width is obtained by requiring that it must be small enough to avoid complete ionization of neutral H before it enters the shock (Hester et al. 1994; Smith et al. 1994).

The limit on the diffusion coefficient is then $κ<v_S^2 /n_e q_i(T_e)$, where $n_e$ is the preshock electron density and $q_i(T_e)$ is the ionization rate coefficient at the preshock electron temperature $T_e$.

ref: https://www.aanda.org/articles/aa/pdf/2003/31/aah4405.pdf  sec. 4.4

2. simulations show that the magnetic field amplification expected to accompany efficient particle acceleration results in a very high thermal energy density, making the survival of neutrals directly in the acceleration region unlikely (Reville & Bell 2013).

“Bohm limit,” the smallest possible diffusion coefficient for isotropic turbulence is assumed.