Dynamics of ultrarelativistic charged particles with strong radiation reaction

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 regim.