Total power radiated by an accelerated charge

We have recently presented a new approach to the It follows that the solution of our equation of moproblem of radiation reaction in non-relativistic tion (1) is electrodynamics and obtained an equation of mov(t)_=x(t) tion which does not exhibit the problems associated with the well-knownAbraham—Lorentz equation [1]. 1 r But since the latter result can be derived using only =v(—oo)+ ~ J dt’f(t’ )+ ~f(t), (3) energy conservation and the Larmorformula (forthe total power radiated by a non-relativistic electron) and, in particular, one might suspect that the latter needs modification. This suspicion is borne out, as we shall now v(~)=v(—~)+ _!~~ J dt’f(t’). (4) demonstrate. M —~ Our starting-point (ref. [1], eq. (8)) is the classical equation of motion for an electron of mass Al Hence, the final velocity is exactly what it would and charge e, moving in one dimension, in an exbe without radiation. This is not as surprising as it ternal c-number force f( t): might seem at first glance, since, in the dipole approximation, the radiation is symmetrical about the