Asymptotic Precision Corrections to Radiation Reaction

The radiative correction to the equation of motion for a moving charged particle is one of the oldest open problems in physics. The problem originates in the emission of radiation by an accelerated charge, which must result in a loss of energy and recoil of the charge, adding a correction to the well-known Lorentz force. When radiation reaction is neglected, it is well known that the dynamics of a charge in an ideal plane-wave field is periodic. Here we investigate the long-time dynamics of a charge in such a field and show that all current models of radiation reaction strictly forbid periodic dynamics. Consequently, we show that under the influence of the external field, the loss of energy to radiation reaction causes particles to accelerate toward an infinite kinetic energy. Such a phenomenon persists even in weak laser fields and puts forward the possibility of testing radiation reaction through long-duration weak-field precision measurements, rather than through strong-field experiments. We further provide numerical examples suggesting realistic conditions for such measurements through the asymptotic frequency shift and energy loss of a charge, which for example can be detected using electron energy spectrometers in ultrafast electron microscopes.