radiation reaction
If an accelerating charge carries energy away as radiation, that energy has to come from somewhere — so the charge must feel a recoil, a drag from its own emitted field. Radiation reaction (or radiation damping) is that self-force, the back-reaction of a charge's radiation on its own motion.
For a nonrelativistic charge the leading self-force is the Abraham-Lorentz formula F_rad = (mu_0 q^2 / 6 pi c) da/dt = q^2 / (6 pi epsilon_0 c^3) times the jerk (the time derivative of acceleration). Notice it depends on da/dt, not on a itself — a force built from the THIRD derivative of position, which is already a warning sign. Averaged over a cycle it does exactly the bookkeeping demanded by Larmor's formula, draining precisely the energy that is radiated, with a characteristic timescale tau = q^2/(6 pi epsilon_0 m c^3), about 6 x 10^-24 s for an electron.
The Abraham-Lorentz equation is notoriously pathological. Because the force involves da/dt, it admits runaway solutions where the acceleration grows exponentially with no applied force, and — if you cure those — pre-acceleration, where the charge starts moving before the force is applied, violating causality. These are signals that classical point-charge electrodynamics is being pushed past its domain; the honest statement is that radiation reaction is a reliable small correction only when the radiated energy over the timescale tau is tiny compared to the particle's energy, and a full resolution needs quantum electrodynamics.
For an electron the radiation-reaction timescale is tau ~ 6 x 10^-24 s — the time light takes to cross about a classical electron radius. Radiation reaction only bites when the motion changes appreciably on this absurdly short timescale, which is why it is negligible for almost all ordinary accelerations.
The self-force ~ jerk (da/dt); it matters only over the electron's ~10^-23 s timescale.
The Abraham-Lorentz force has runaway and pre-acceleration solutions — it is an approximation, not a fundamental exact law, and signals the breakdown of the classical point charge. It is a third-order (jerk-dependent) equation, unlike ordinary Newtonian dynamics.