The role of the Larmor radiation formula in the classical theory of electromagnetic radiation

This paper starts with a historical review of the development of the classical theory of electromagnetic radiation. Antenna theory is a special case of the Larmor (1897) radiation formula. Although this formula seems to suggest that neutral ensembles of charges should not produce electromagnetic radiation, this paper suggests that they, in the form of multipoles, can radiate, because of differences in the retardation of the fields of individual particles, if the accelerations change in time. This paper shows that the power radiated by a one-dimensional multipole, of order 2ⁿ, is P_n=2[M _n(dⁿv/dtⁿ)]²/[(4n² -1)c²ⁿ⁺¹] (cgs units). M_n is a scalar multipole moment. The other symbols have their usual meanings. The derivation assumes that a 2ⁿ pole consists of two opposing equal one-dimensional n-1 poles, separated by the distance z_n. The Larmor radiation formula is the n=1 case, with M₁=e. Corresponding to each radiation formula is one for the radiation reaction force, F_n=P_n/v, neglecting the interaction with the self-field. This formula for radiation reaction is more general than that given by previous authors, whose calculations have concerned only short pulses