  Previous studies from the astrophysics and laser physics communities have
identified an interesting phenomenon wherein ultrarelativistic charged
particles experiencing strong radiation reaction tend to move along special
directions fixed by the local electromagnetic field. In the relativity
literature these are known as the "principal null directions" (PNDs) of the
Maxwell field. A particle in this regime has "Aristotelian" dynamics in the
sense that its velocity (rather than acceleration) is determined by the local
field. We study this Aristotelian equilibrium in detail, starting from the
Landau-Lifshitz equation describing charged particle motion including radiation
reaction. Using a Frenet-Serret frame adapted to the PNDs, we derive the
Lorentz factor describing motion along the local PND, together with drift
velocities reflecting slower passage from one PND to another. We derive
conditions on the field configuration that are necessary for such an
equilibrium to occur. We demonstrate agreement of our analytic formulas with
full numerical solutions of the Landau-Lifshitz equation in the appropriate
regime.
