  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.
