Publisher’s Note: Radiated power and radiation reaction forces of coherently oscillating charged particles in classical electrodynamics [Phys. Rev. D91, 096006 (2015)]

Imperfect Energy Conservation of the Free-Electron Laser over the Timestep of Simulations

“…Therefore, for the radiation of a periodically oscillating electron or two periodically oscillating electrons, CED and CWFT dictate the same time integration of electrons' power over a period and do the same for the radiated energy flux, while net energy conservation over a period is preserved in CWFT [10]. Hence, CED and CWFT infer the same net energy conservation over a period, which corrects an analysis contradicting this [1] and demonstrates another similarity between CED and CWFT. This further demonstrates that CWFT is not offensive to CED and thus shows another suitability of the use of CWFT as a reliable alternative theory of CED in the analysis of this paper.…”

“…Therefore, it is well worth considering computing the electrons' power using CWFT to investigate the validity of net energy conservation over the timestep. Some aspects of CWFT remain controversial and it is conceptually challenging, but it is not aggressive to CED [1]; at large distance from the electrons radiating into free-space, the radiated energy flux in CED and CWFT become the same [7]. Furthermore, the CWFT's time integration of electrons' power over a period is shown to match the time integration of CED's radiated energy flux at large distance from the electrons, for the case of a periodically oscillating electron [7], and the case of two synchronously periodically oscillating non-relativistic electrons spaced by distances of the order of a wavelength [1].…”

“…Along the development of free-electron laser (FEL) operating at the wavelength of X-ray, the importance of FEL has increased. The X-ray radiation generated by available FELs is intense but only partially coherent [1]. Therefore, much work is being done to improve coherence [2].…”