Inverse-Compton Cooling

What you are seeing: the Thomson-limit IC cooling time $t_\text{cool} = 3 m_e c / (4 \sigma_T \gamma U_\text{ph})$ plotted versus electron Lorentz factor $\gamma$ , with the soft-photon energy density $U_\text{ph}$ set by a thermal bath of temperature $T$ . For CMB ( $T = 2.725$ K, $U_\text{CMB} \approx 4.2 \times 10^{-14}$ J/m $^3$ ), a $\gamma = 10^5$ electron cools in tens of Myr.

Cosmic ray electrons above $\gamma \sim 10^7$ ( $E \sim 5$ TeV) cool on Galactic-disk crossing times; this sets the local TeV electron population and the cosmic-ray "knee" near 1 PeV. The dashed line marks the Hubble time as a reference.

Figure 1. Inverse-Compton cooling time vs Lorentz factor for a thermal photon bath.

log10 T (K)0.435

log10 γ inj5.00

WHAT TO TRY

Raise the bath temperature: U_ph climbs as T to the fourth power, the whole t_cool curve drops, and the electrons cool visibly faster between reinjections.
Slide the injection energy: high-gamma electrons sit far right on the t_cool curve where the cooling time is shortest, so they crash down the axis almost at once. Low-gamma electrons barely move.
Watch the dashed marker track gamma_inj on the cooling curve and read its t_cool against the Hubble line: above the line, the photon bath cannot cool those electrons within the age of the Universe.