The dependence of the gravity effect in elliptic

8 Elliptic neutron guides are expected to be widely used for construction of long neutron 9 beamlines at the future European Spallation Source and other facilities due to their superiour 10 transmission properties compared to conventional straight guides. At the same time, neutrons 11 traveling long distances are subject to the action of gravity that can significantly modify their 12 flight paths. In this work, the influence of gravity on a neutron beam propagating through elliptic 13 guides is studied for the first time in a systematic way with Monte-Carlo simulations. It is shown 14 that gravity leads to significant distortions of the phase space during propagation through long 15 elliptic guides, but this effect can be recovered by a sufficiently large source size. The results 16 of this analysis should be taken into account during design of long neutron instruments at the 17 ESS and other facilities. 18