The aim of this short note is to present an option for a source of ultracold neutrons (UCNs), which could profit from the pulse time-structure of the future ESS spallation neutron source in Lund, and thus which could produce a very high UCN density and a rather high UCN flux simultaneously. In order to realize this idea one has to install a relatively thin solid-deuterium UCN source in a close vicinity to the spallation target and to couple it with an extraction UCN guide with an entrance membrane window, which is moving periodically and synchronously with the operation cycle of the spallation source, as explained in the text below. This proposal profits from the fact that all characteristic parameters of the problem, such as the pulse duration of the ESS spallation source, the typical thickness of solid deuterium source that could be easily realized, the typical time of generation of UCNs in solid deuterium, the length and diameter of the extraction neutron guide and the time diagram of the membrane motion that is still realistic, they all fit nicely to optimum desired parameters. The UCN density produced in such a way could approach 10^6 UCN/cm3.
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