= Shear-only photon diffusion damping
{title2=$k_D^{-2}=\frac2{15}\int\tau_c\,d\tau$}
For the simplified quadrupole equation $\sigma_\gamma'+4k^2\theta_\gamma/15=-\sigma_\gamma/\tau_c$, neglecting its time derivative and gravitational driving gives $\sigma_\gamma=-\tau_c\delta_\gamma'/5$. A radiation-dominated inertia then obeys $\delta_\gamma''+4\tau_ck^2\delta_\gamma'/15+k^2\delta_\gamma/3=0$. On slowly varying subhorizon scales the amplitude is damped by $\exp[-(2/15)k^2\int\tau_cd\tau]$. This coefficient belongs to that truncated collision model, rather than the polarization-inclusive <Silk damping> equation.
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