Cooling of relativistic electron beams in intense laser pulses

• The Lorentz force describes the motion of a charged particle in an external electromagnetic field, but as the particle accelerates it radiates energy and momentum. • Radiation reaction describes the effect of this radiative loss on the motion of the particle itself. This radiation reaction force is typically extremely small compared to the applied force, so can be safely neglected. • However... as the field becomes strong, the particle radiates more and more, and this correction can become significant: for example, at future high-intensity laser facilities such as ELI. • Furthermore, in strong fields the quantum nature of photon emission may also become important. • Lorentz–Abraham–Dirac equation Fully relativistic equation of motion for a classical point particle [1] ẍ = − q m F b ẋ b + τ∆b ... x b , (1) where τ = q/6πm ' 6× 10−24s is the characteristic time of the electron and ∆b = δ b + ẋẋb. . Jerk term leads to pathological solutions: → Runaway solutions (unphysical) or preaccelerations (violation of causality). . Overcome using the Landau–Lifshitz approach [2]: treat the radiation reaction as a small perturbation to the applied Lorentz force.