Cooling intense high-energy hadron beams remains a major challenge in modern accelerator physics. Synchrotron radiation of such beams is too feeble to provide significant cooling: even in the Large Hadron Collider (LHC) with 7 TeV protons, the longitudinal damping time is about thirteen hours. Decrements of traditional electron cooling decrease rapidly as the high power of beam energy, and an effective electron cooling of protons or antiprotons at energies above 100 GeV seems unlikely. Traditional stochastic cooling still cannot catch up with the challenge of cooling high-intensity bunched proton beams--to be effective, its bandwidth must be increased by about two orders-of-magnitude. Two techniques offering the potential to cool high-energy hadron beams are optical stochastic cooling (OSC) and coherent electron cooling (CEC)--the latter is the focus of this paper. In the early 1980s, CEC was suggested as a possibility for using various instabilities in an electron beam to enhance its interaction with hadrons (i.e., cooling them). The capabilities of present-day accelerator technology, Energy Recovery Linacs (ERLs), and high-gain Free-Electron Lasers (FELs), finally caught up with the idea and provided the all necessary ingredients for realizing such a process. In this paper, we discuss the principles, and the main limitations of the CEC process based on a high-gain FEL driven by an ERL. We also present, and summarize in Table 1, some numerical examples of CEC for ions and protons in RHIC and the LHC
