The European Spallation Source (ESS) is intended to become the most powerful spallation neutron source in the world and the flagship of neutron science in the upcoming decades. The exceptionally high neutron flux will provide unique opportunities for scientific experiments, but also set high requirements for the detectors. One of the most challenging aspects is the rate capability and in particular the peak instantaneous rate capability, i.e. the number of neutrons hitting the detector per channel or cm$^2$ at the peak of the neutron pulse. The primary purpose of this paper is to estimate the incident rates that are anticipated for the BIFROST instrument planned for ESS, and also to demonstrate the use of powerful simulation tools for the correct interpretation of neutron transport in crystalline materials. A full simulation model of the instrument from source to detector position, implemented with the use of multiple simulation software packages is presented. For a single detector tube instantaneous incident rates with a maximum of 1.7 GHz for a Bragg peak from a single crystal, and 0.3 MHz for a vanadium sample are found. This paper also includes the first application of a new pyrolytic graphite model, and a comparison of different simulation tools to highlight their strengths and weaknesses.
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