Electron beam dynamics and self-cooling up to PeV level due to betatron radiation in plasma-based accelerators

In plasma-based accelerators, electrons are accelerated by ultrahigh gradient of $1--100\text{ }\text{ }\mathrm{GV}/\mathrm{m}$ and undergo the focusing force with the same order as the accelerating force. Heated electrons are injected in a plasma wake and exhibit the betatron oscillation that generates synchrotron radiation. Intense betatron radiation from laser-plasma accelerators is attractive x-ray/gamma-ray sources, while it produces radiation loss and significant effects on energy spread and transverse emittance via the radiation reaction force. In this article, electron beam dynamics on transverse emittance and energy spread with considering radiation reaction effects are studied numerically. It is found that the emittance growth and the energy spread damping initially dominate and balance with radiative damping due to the betatron radiation. Afterward the emittance turns to decrease at a constant rate and leads to the equilibrium at a nanometer radian level with growth due to Coulomb scattering at PeV-level energies. A constant radiation loss rate ${R}_{T}=2/3$ is found without regard to the electron beam and plasma conditions. Self-cooling of electron beams due to betatron radiation may guarantee TeV-range linear colliders and give hints on astrophysical ultrahigh-energy phenomena.