  Magnetic flux rope, formed by the helical magnetic field lines, can sometimes
remain its shape while carrying significant plasma flow that is aligned with
the local magnetic field. We report the existence of such structures and static
flux ropes by applying the Grad-Shafranov-based algorithm to the Parker Solar
Probe (PSP) in-situ measurements in the first five encounters. These structures
are detected at heliocentric distances, ranging from 0.13 to 0.66 au, in a
total of 4-month time period. We find that flux ropes with field-aligned flows,
although occur more frequently, have certain properties similar to those of
static flux ropes, such as the decaying relations of the magnetic fields within
structures with respect to heliocentric distances. Moreover, these events are
more likely with magnetic pressure dominating over the thermal pressure. About
one-third of events are detected in the relatively fast-speed solar wind.
Taking into account the high Alfvenicity, we also compare with switchback
spikes identified during three encounters and interpret their inter-relations.
We find that some switchbacks can be detected when the spacecraft traverses
flux rope-like structures. The cross-section maps for selected events are
presented via the new Grad-Shafranov type reconstruction. Finally, the possible
evolution of the magnetic flux rope structures in the inner heliosphere is
discussed.
