  A previous proof of non existence of tokamak equilibria with purely poloidal
flow within macroscopic theory [Throumoulopoulos, Weitzner, Tasso, Physics of
Plasmas Vol. 13, 122501 (2006)] motivated this microscopic analysis near
magnetic axis for toroidal and "straight" tokamak plasmas. Despite the new
exact solutions of Vlasov's equation found here, the structure of macroscopic
flows remains elusive.
