  The conditions for the existence of force-free non-relativistic
translationally invariant one-dimensional (1D) Vlasov-Maxwell (VM) equilibria
are investigated using general properties of the 1D VM equilibrium problem. As
has been shown before, the 1D VM equilibrium equations are equivalent to the
motion of a pseudo-particle in a conservative pseudo-potential, with the
pseudo-potential being proportional to one of the diagonal components of the
plasma pressure tensor. The basic equations are here derived in a different way
to previous work. Based on this theoretical framework, a necessary condition on
the pseudo-potential (plasma pressure) to allow for force-free 1D VM equilibria
is formulated. It is shown that linear force-free 1D VM solutions, which so far
are the only force-free 1D VM solutions known, correspond to the case where the
pseudo-potential is an attractive central potential. A general class of
distribution functions leading to central pseudo-potentials is discussed.

Plasma Physics