On filter design and critical thickness of synchrotron x-ray filters

Abstract

A ‘‘critical thickness’’ for a synchrotron radiation x-ray filter exists. Because x-ray absorption in media is an exponential function of depth and because radiation and conduction both play a role in the cooling of the filter assembly, the heat transfer mechanism changes from radiation dominant to conduction dominant as the thickness increases. For a thin filter, radiative heat transfer is the main mechanism. The maximum temperature in the filter increases as the thickness increases due to the fact that the total heat load increases while the total area for radiative heat transfer remains the same. For a thick filter, conductive heat transfer is the main cooling mechanism. When the filter thickness increases, the heat absorption per unit thickness decreases and so does the maximum temperature. At a certain thickness, the temperature in the filter is the maximum. This is the critical thickness. For third-generation synchrotron radiation facilities, the maximum temperature and thermal stresses in a filter are the main factors considered in a filter assembly design. It is very important to avoid designing a filter inside the critical thickness range.