radiationreaction

Radiation reaction, also known as self-force, is the force that a charged particle experiences due to its own electromagnetic field when it accelerates and emits radiation. The emission carries away energy and momentum, so the particle must experience a recoil that alters its motion. Classical electrodynamics treats this self-interaction as a back-reaction term in the equation of motion.

In the nonrelativistic limit, the radiation reaction force is F_rad = (q^2 / (6π ε0 c^3)) da/dt, where a is the acceleration. The equation of motion becomes m a = F_ext + F_rad. The power radiated is given by the Larmor formula P = q^2 a^2 /(6π ε0 c^3).

Relativistically, the correct covariant generalization is the Abraham-Lorentz-Dirac equation, which adds a self-force term built from derivatives of the four-velocity. The theory explains energy-momentum loss but introduces conceptual difficulties: the third derivative of position yields solutions with pre-acceleration and, for some external forces, runaway motion.

To avoid these issues, the Landau-Lifshitz formulation provides a practical, causal approximation by expressing the radiation reaction in terms of the external field and lower derivatives. It is widely used in simulations of charged particles in strong fields, accelerators, and laser-plasma interactions.

In quantum electrodynamics, radiation reaction arises from discrete photon emissions and recoil, and quantum corrections modify the classical result in sufficiently strong fields. Quantum radiation reaction is studied with stochastic approaches and is relevant for ultrahigh-intensity laser experiments and certain astrophysical environments.