Abraham-Lorentz versus Landau-Lifshitz

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.