Towards Precision Measurements of Radiation Reaction in the Presence of Periodic Electromagnetic Fields

Finding the exact equation of motion for a moving charge in an electromagnetic field, including its reaction to the radiation it emits, is one of the oldest open problems in physics. Despite attempts by luminaries like Lorentz, Abraham, Dirac, Landau and Lifshitz, the correct description of the motion remained unknown. In recent months, frontier high intensity laser experiments have yielded the first insights into this old problem; currently, no theory fully explains the data, which illustrates the persistence of this century old paradox.
Discussions of radiation reaction typically distinguish “weak” radiation reaction, in which the radiative correction can be calculated perturbatively , from “strong” radiation reaction, as seen in interactions of electrons with very-high intensity lasers, in which the correct treatment is still unknown. Therefore, it is believed that high intensity lasers are necessary in order to probe the physics of radiation reaction.
Here we show that “strong” radiation reaction effects can also be observed in the presence of weak electromagnetic fields, by studying the long-time dynamics of a particle under a periodic field. We show that while the Lorentz force equations (i.e., no radiation reaction correction) of a moving charge in a plane wave have a periodic solution, the introduction of a radiation reaction term leads to surprising long-time behaviors. Such behaviors include the divergence of the particle energy, distinct from the already known runaway solutions, for some widely accepted equations of radiation reaction, and the convergence to a single periodic trajectory for others. We also present a universal approach for varying the trajectory’s parameters. Consequently, our findings show that radiation reaction can be tested through optical precision measurements (e.g., observing the frequency shift) rather than through strong field experiments.