Inverse Compton scattering

Inverse Compton scattering transfers energy from an energetic electron to a photon in a Compton scattering event. Transforming into the electron's rest frame blueshifts an approaching photon; scattering there and transforming back can produce a much more energetic outgoing photon.

For a head-on collision with an ultrarelativistic electron of Lorentz factor $\gamma$, the low-recoil limit gives an approximately forward maximum photon energy $E_{\gamma ,\max }\simeq 4{\gamma }^2ϵ$, where $ϵ$ is the incident photon energy. This requires $\gamma ϵ\ll m_e{c}^2$; recoil limits the increase outside that regime.

A laboratory source overlaps a laser beam with an electron beam and selects scattered photons within an angular acceptance. Electron energy spread, beam divergence and collection angle affect the emitted bandwidth, so one photon-energy value does not characterize every collected event. ^[ref]

A population of relativistic electrons emits synchrotron radiation and then scatters some of those same photons through inverse Compton scattering. The emitting region supplies both the scatterers and the seed radiation field. Comparing the two spectral components can constrain electron energies and the magnetic field, but source geometry and relativistic beaming affect the inference.

An isotropic photon bath with total radiation energy density $u_{\mathrm{ph}}$ exerts this drag on an electron in the Thomson scattering regime. Its stress-energy tensor has spatial diagonal entries $u_{\mathrm{ph}}/3$. A boost to the electron frame gives radiation energy flux $S_{\parallel }^{\prime }=-(4/3)c{\gamma }^2\beta u_{\mathrm{ph}}$; multiplying its radiation force ${\sigma }_T{S}_{\parallel }^{\prime }/c$ 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 $u_{\mathrm{ph}}$ and the numerical coefficient doubles.

For a head-on photon and massive-particle collision, boost into the initial particle rest frame, apply the Compton recoil formula for backward photon scattering, then boost the outgoing photon forward. For incident photon energy below the particle momentum times $c$, this backward-scattering endpoint is the maximal outgoing laboratory energy. The result in the title approaches $4{\gamma }^2\epsilon$ only when the particle is ultrarelativistic and its rest-frame incident photon energy is small compared with $m{c}^2$. Recoil limits amplification at larger incident energies and preserves the total-energy bound.