  In non-collisional magnetized astrophysical plasmas, vortices can form as it
is the case of the Venus plasma wake where Lundin et al. (2013) identified a
large vortex through the integration of data of many orbits from the Venus
Express (VEX) spacecraft. On the one hand, our purpose is to develop a
theoretical foundation in order to explain the occurrence and formation of
vortices in non-collisional astrophysical plasmas. On the other hand, to apply
the latter in order to study the vorticity in the wakes of Venus and Mars. We
introduce two theorems and two corollaries, which may be applicable to any
non-collisional plasma system, that relate the vorticity to electromagnetic
variables such as the magnetic field and the electric current density. We also
introduce a toy vortex model for the wakes of non-magnetized planetary bodies.
From the proposed theorems and model and using magnetic data of the VEX and the
Mars Global Surveyor (MGS) spacecraft, we identify vortices in the wakes of
Venus and Mars in single spacecraft wake crossings. We also identify a spatial
coincidence between current density and vorticity maxima confirming the
consistency of our theorems and model. We conclude that vortices in
non-collisional magnetized plasmas are always linked to electric currents and
that both vortices and currents always coexist. This suggests that the
mechanism that produces this type of vortices is the mutual interaction between
the electric current and the magnetic field, that to a first approximation is
explained considering that plasma currents due to a non-zero net charge density
induce magnetic fields that modify the existing field and also produce a
helical field configuration that drives charged particles along helical
trajectories.
