Howe, Ian Martin2015-10-022015-10-022014-12http://hdl.handle.net/10125/101087Ph.D. University of Hawaii at Manoa 2014.Includes bibliographical references.The unbounded radiated fields of point charges interfere constructively or destructively such that the total power radiated depends on the collective effects. By using the far field approximation for the radiated fields there is a unique assignment of partial power for each individual point charge in the collection. The unique assignment of partial power is a new development in classical electromagnetism, with potential applications beyond the Kimel-Elias approach to radiation reaction. The Kimel-Elias approach uses the partial power to find the radiation reaction for each point charge including the collective effects. This dissertation derives the uniqueness condition for the assignment of partial power and finds that the Kimel-Elias approach is only valid for highly relativistic point charges with nearly completely overlapping radiation fields. Examples of the Kimel-Elias approach are evaluated for two point charges in the cases of longitudinal and transverse acceleration, as well as for an undulator. The Kimel-Elias approach has never been implemented before and could potentially be used to explore the current problems simulations have with Free-Electron Laser (FEL) startup. In addition, a non-relativistic example is done with the partial power assignment using the Poynting vector and retarded time integrals, the results are nearly the same as those obtained numerically via the Feynman Wheeler absorber theory [1]. By using the partial power assignment the power radiated by individual particles in a non-relativistic system were found, the author is unaware of any other such development, the radiated power is always for the entire system.engAll UHM dissertations and theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner.Kimel-Elias approachThesis