Radiation reaction: A case study

We are interested in the motion of a classical charge coupled to the Maxwell self-field and subject to a uniform external magnetic field, B ₀. This is a physically relevant, but difficult, dynamical problem, to which contributions range over more than 100 years. Specifically, we will study the SommerfeldPage approximation, which assumes an extended charge distribution at small velocities. The memory equation is then linear and many details become available. We discuss how the effective friction equation arises in the limit of small B₀ and contrast this result with the standard Taylor expansion resulting in a second-order equation for the velocity of the charge.