Rapoport-Zink spaces are moduli spaces of p-divisible groups (with extra structure). These are p-adic analogues of integral models of Shimura varieties. Their function field versions were introduced by Hartl-Viehmann. I want to explain a construction approximating Hartl-Viehmann spaces via Rapoport-Zink spaces using the philosophy of close p-adic fields. If time permits I want to sketch how one may use this construction to deduce the Arithmetic Fundamental Lemma in the function field case. This is joint work, partly in progress, with Andreas Mihatsch.