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.

Reduced-order Abraham-Lorentz-Dirac equation and the consistency of classical electromagnetism

“…First, one replaces the ALD equation by a better approximation to the exact equation of motion of a charged spherical shell (equation (3.7) of [4], called the 'Caldirola equation'; see also [3,7,8]), and then one insists that an entity of given charge and observed mass cannot have a radius below a certain minimum. This both ensures the absence of pathological behavior [4,[8][9][10][11], and is physically to be expected because it is the condition that the observed mass must exceed the electromagnetic contribution (as we will expound further in the following). However there is continuing argument about what is the right way to in- * Electronic address: a.steane@physics.ox.ac.uk terpret this situation [4,7,[11][12][13], and there is resurgent interest in this whole area because modern laser technology makes it possible to experimentally investigate radiation reaction phenomena [14].…”

Guiding-centre transformation of the radiation–reaction force in a non-uniform magnetic field

“…These issues have generated discussion regarding what expression to use for the RR-force (see, e.g., the excellent text in Ref. [14]). Landau and Lifshitz [5], for example, suggest a perturbative approach where the velocity derivatives in Eq.…”

Electromagnetic Self-Force Mechanisms and Origin of <i>R</i><sup>-1</sup> Term

“…Many attempts have been made to clarify and solve these problems. For example, these problems will disappear if we replace this equation with an approximate or alternative one (see [12] for argument on which one is better) known as Landau-Lifshitz equation which basically expresses the acceleration perturbatively in terms of external force [3] and also another way to get rid of these problems is to throw away point particle model and put a lower bound on its radius. For example, if electron's radius is bigger than electron classical radius ( ) class R R > [4], these problems will disap-pear, but the electron radius is known to be smaller than this [15].…”

“…Here we just report the results for a particle modeled as spherical shell of radius R . For the nonrelativistic case ( ) v c  , this force can be written in a neat form as follows [12]:…”