  Self-consistent chaotic transport is studied in a Hamiltonian mean-field
model. The model provides a simplified description of transport in marginally
stable systems including vorticity mixing in strong shear flows and electron
dynamics in plasmas. Self-consistency is incorporated through a mean-field that
couples all the degrees-of-freedom. The model is formulated as a large set of
$N$ coupled standard-like area-preserving twist maps in which the amplitude and
phase of the perturbation, rather than being constant like in the standard map,
are dynamical variables. Of particular interest is the study of the impact of
periodic orbits on the chaotic transport and coherent structures. Numerical
simulations show that self-consistency leads to the formation of a coherent
macro-particle trapped around the elliptic fixed point of the system that
appears together with an asymptotic periodic behavior of the mean field. To
model this asymptotic state, we introduced a non-autonomous map that allows a
detailed study of the onset of global transport. A turnstile-type transport
mechanism that allows transport across instantaneous KAM invariant circles in
non-autonomous systems is discussed. As a first step to understand transport,
we study a special type of orbits referred to as sequential periodic orbits.
Using symmetry properties we show that, through replication, high-dimensional
sequential periodic orbits can be generated starting from low-dimensional
periodic orbits. We show that sequential periodic orbits in the self-consistent
map can be continued from trivial (uncoupled) periodic orbits of standard-like
maps using numerical and asymptotic methods. Normal forms are used to describe
these orbits and to find the values of the map parameters that guarantee their
existence. Numerical simulations are used to verify the prediction from the
asymptotic methods.
