  The particle transport of impurities in magnetically confined plasmas under
some conditions does not find, neither quantitatively nor qualitatively, a
satisfactory theory-based explanation. This compromise the successful
realization of thermo-nuclear fusion for energy production since its
accumulation is known to be one of the causes that leads to the plasma
breakdown. In standard reactor-relevant conditions this accumulation is in most
stellarators intrinsic to the lack of toroidal symmetry, that leads to the
neoclassical electric field to point radially inwards. This statement, that the
standard theory allows to formulate, has been contradicted by some experiments
that showed weaker or no accumulation under such conditions
\cite{Ida_pop_16_056111_2009, Yoshinuma_nf_49_062002_2009}. The charge state of
the impurities makes its transport more sensitive to the electric fields. Thus,
the short length scale turbulent electrostatic potential or its long
wave-length variation on the flux surface $\Phi_{1}$ -- that the standard
neoclassical approach usually neglects -- might possibly shed some light on the
experimental findings. In the present work the focus is put on the second of
the two, and investigate its influence of the radial transport of C$^{6+}$. We
show that in LHD it is strongly modified by $\Phi_{1}$, both resulting in
mitigated/enhanced accumulation at internal/external radial positions; for
Wendelstein 7-X, on the contrary, $\Phi_{1}$ is expected to be considerably
smaller and the transport of C$^{6+}$ not affected up to an appreciable extent;
and in TJ-II the potential shows a moderate impact despite of the large
amplitude of $\Phi_1$ for the parameters considered.
