  Local shtukas are the function field analogs for $p$-divisible groups.
Similar to the $p$-adic theory, one defines Rapoport-Zink functors and
Rapoport-Zink spaces for these local shtukas. The associated Hodge-Pink
structures are described uniquely by a morphism, called the period morphism of
the moduli problem. We will prove the ind-representability of the Rapoport-Zink
functor in a particular case and compute the corresponding Rapoport-Zink space
as well as the corresponding period morphism. In this case, the period morphism
is given by the Carlitz logarithm.
