  A detailed discussion is presented of the Vlasov-Maxwell equilibrium for the
force-free Harris sheet recently found by Harrison and Neukirch (Phys. Rev.
Lett. 102, 135003, 2009). The derivation of the distribution function and a
discussion of its general properties and their dependence on the distribution
function parameters will be given. In particular, the distribution function can
be single-peaked or multi-peaked in two of the velocity components, with
possible implications for stability. The dependence of the shape of the
distribution function on the values of its parameters will be investigated and
the relation to macroscopic quantities such as the current sheet thickness will
be discussed.
