Radiation reaction of a classical quasirigid extended particle
Abstract
The problem of the selfinteraction of a quasirigid classical particle with an arbitrary spherically symmetric charge distribution is completely solved up to the first order in the acceleration. No ad hoc assumptions are made. The relativistic equations of conservation of energy and momentum in a continuous medium are used. The electromagnetic fields are calculated in the reference frame of instantaneous rest using the Coulomb gauge; in this way the troublesome power expansion is avoided. Most of the puzzles that this problem has aroused are due to the inertia of the negative pressure that equilibrates the electrostatic repulsion inside the particle. The effective mass of this pressure is U_{e}/(3c^{2}), where U_{e} is the electrostatic energy. When the pressure mass is taken into account the dressed mass m turns out to be the bare mass plus the electrostatic mass m = m_{0} + U_{e}/c^{2}. It is shown that a proper mechanical behaviour requires that m_{0} > U_{e}/3c^{2}. This condition poses a lower bound on the radius that a particle of a given bare mass and charge may have. The violation of this condition is the reason why the LorentzAbrahamDirac formula for the radiation reaction of a point charge predicts unphysical motions that run away or violate causality. Provided the mass condition is met the solutions of the exact equation of motion never run away and conform to causality and conservation of energy and momentum. When the radius is much smaller than the wavelength of the radiated fields, but the mass condition is still met, the exact expression reduces to the formula that Rohrlich (2002 Phys. Lett. A 303 307) has advocated for the radiation reaction of a quasipoint charge.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 April 2006
 DOI:
 10.1088/03054470/39/14/021
 arXiv:
 arXiv:physics/0508031
 Bibcode:
 2006JPhA...39.3801M
 Keywords:

 Physics  Classical Physics;
 High Energy Physics  Theory
 EPrint:
 18 pages, IoP LaTeX, submitted to Journal of Physics A