Plasma-based accelerators have achieved tremendous progress in the past few decades, thanks to the advances of high power lasers and the availability of high-energy and relativistic particle beams. However, the electrons (or positrons) accelerated in the plasma wakefields are subject to radiation losses, which generally suppress the final energy gains of the beams. In this paper, radiation reaction in plasma-based high-energy accelerators is investigated using test particle approach. Energy-frontier TeV colliders based on a multiple stage laser-driven plasma wakefield accelerator and a single-staged proton-driven plasma wakefield accelerator are studied in detail. The results show that the higher axial and transverse field gradients seen by an off-axis injected witness beam result in a stronger damping force on the accelerated particles. Proton-driven plasma wakefield accelerated electrons are shown to lose less energy compared to those accelerated in a multi-staged laser-driven plasma wakefield accelerator.
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