Abraham–Lorentz versus Landau–Lifshitz

Abstract

The classical Abraham–Lorentz formula for the radiation reaction on a point charge suffers from two notorious defects: runaways and preacceleration. Recently, several authors have advocated as an alternative the Landau–Lifshitz formula, which has neither fault. The latter formula is often presented as an approximation to Abraham–Lorentz, raising the delicate question of how an approximation can be considered more accurate than the original. For a spherical shell of finite size, the equation for the radiation reaction is noncontroversial. We begin there, obtain the Abraham–Lorentz and Landau–Lifshitz expressions as limiting cases, and undertake some numerical studies to determine which is superior.