Particle accelerators play a fundamental role in many technological and scientific fields, both for fundamental research, as in the case of high-energy physics, and for interdisciplinary applications, such as in the case of synchrotron radiation sources or proton accelerators in medical field. Most accelerators have a critical frequency in the X-ray region: for example, in the case of the Φ-Factory DAΦNE at Frascati National Laboratories, λc falls into soft X-rays, for a wavelength of about 6

more »

... . This feature is important for diagnostic applications that generally employ frequencies in the visible region, where it is easier to design focusing optics. This work concerns the discovery of a time-domain "anomaly" in the Infra-Red synchrotron radiation emitted by electrons and positrons from both the DAΦNE Φ-Factory (Frascati National Laboratories, Italy) and HFL (Hefei Light Source at NSRL(National Synchrotron Radiation Laboratory, People's Republic of China). The study was conducted with an unconventional statistical category calculus system, developed and patented by the present author for the analysis of complex systems. The "anomaly" has been resolved in the IR synchrotron radiation emission profile of each single bunch of electrons and positrons, in two distinct waveforms, one of which is "delayed" by a few hundred of ps with respect to the other. A detailed and in-depth analysis excludes that the anomaly is the result of systematic errors The measured time differences between the two signals leads to an apparent discrepancy in the value of the speed of light in vacuum. A study of the anomaly with time series, based on considerations about the coherent emission of synchrotron radiation (CSR), allows us to exclude the validity of the "rigid bunch" model (J. Schwinger 1945) We therefore propose a model called "CFNM" (Coherent Fractal Nematic Mesophase), based on considerations of statistical mechanics of complex systems, exploiting the (strong) analogies with the nematic mesophase of liquid crystals. This model could have significant consequences in the study, modeling and measurement of the operating parameters of future machines and collectors of accelerators, in particular with regard to emission and brightness.