Radiation Reaction fields for an accelerated dipole for scalar and electromagnetic radiation

The radiation reaction fields are calculated for an accelerated changing dipole in scalar and electromagnetic radiation fields. The acceleration reaction is shown to alter the damping of a time varying dipole in the EM case, but not the scalar case. In the EM case, the dipole radiation reactionfield can exert a force on an accelerated monopole charge associated with the accelerated dipole. The radiation reaction of an accelerated charge does not exert a torque on an accelerated magnetic dipole, but an accelerated dipole does exert a force on the charge. The technique used is that originally developed by Penrose for non-singular fields and extended by the author for an accelerated monopole charge. It is well known that an accelerated charge radiates and that the emitted field from the accelerated charge exerts a force ( the radiation reaction force) back on the charge itself. This radiation reaction force is usually derived either by an appeal to a balance of the energy and momentum emitted by the charge or by a detailed examination of the energymomentum tensor just near the charge. These techniques invariably have difficulties with the fact that the fields from a point charge diverge, and necessitate re-normalisation of various quantities (eg the mass) in order to extract reasonable results. However, it was discovered by Penrose and Unruh that the radiation reaction field for a charge could be extracted from the radiation field by means of an integral over the future null cone of the the particle. This integral, which in the absence of any sources, exactly gives the field strength at a point, also gives a finite result whan applied to the field emanating from a point charge, and that finite result is exactly the radiation reaction fields at the particle. In this paper I will show that this approach can be generalised to the case of an accelerating dipole and leads to finite radiation reaction fields at the location of the point dipole. These fields lead to the damping forces on that accelerating dipole. These results will ultimately be applied in another paper on the question of the equilibrium polarisation of an accelerating particle with spin, but seem to be of sufficient general interest that they are here separated out for detailed study. In this paper, I will derive the radiation reaction fields at the location of point source for a massless scalar field, and the reaction fields at the location of a point dipole source for the electromagnetic field, using the Penrose integral to do so. Thus I will begin by giving a very brief review of the Newmann-Penrose (NP) spinor formalism, and the natural null tetrad metric for an accelerated path in Minkowski spacetime. That accelerated path is assumed