= Isotropic inverse-Compton drag
{title2=$P=(4/3)\sigma_Tcu_{\rm ph}\beta^2\gamma^2$}
An isotropic photon bath with total <radiation energy density> $u_{\rm ph}$ exerts this drag on an electron in the <Thomson scattering> regime. Its <stress-energy tensor> has spatial diagonal entries $u_{\rm ph}/3$. A boost to the electron frame gives radiation <energy flux> $S'_\parallel=-(4/3)c\gamma^2\beta u_{\rm ph}$; multiplying its radiation force $\sigma_TS'_\parallel/c$ by the laboratory speed gives the electron's energy loss. This is net energy transferred, not all scattered photon energy. If only the magnetic wave-energy density is used, it is half of $u_{\rm ph}$ and the numerical coefficient doubles.
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