  A new constant of motion for helically symmetric equilibria in the vicinity
of the magnetic axis is obtained in the framework of Vlasov theory. In view of
this constant of motion the Vlasov theory is compared with drift kinetic and
gyrokinetic theories near axis. It turns out that as in the case of
axisymmetric equilibria [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas 18,
064507 (2011)] the Vlasov current density thereon can differ appreciably from
the drift kinetic and gyrokinetic current densities. This indicates some
limitation on the implications of reduced kinetic theories, in particular as
concerns the physics of energetic particles in the central region of
magnetically confined plasmas.
