  We derive axisymmetric equilibrium equations in the context of the hybrid
Vlasov model with kinetic ions and massless fluid electrons, assuming
isothermal electrons and deformed Maxwellian distribution functions for the
kinetic ions. The equilibrium system comprises a Grad-Shafranov partial
differential equation and an integral equation. These equations can be utilized
to calculate the equilibrium magnetic field and ion distribution function,
respectively, for given particle density or given ion and electron toroidal
current density profiles. The resulting solutions describe states characterized
by toroidal plasma rotation and toroidal electric current density.
Additionally, due to the presence of fluid electrons, these equilibria also
exhibit a poloidal current density component. This is in contrast to the fully
kinetic Vlasov model, where axisymmetric Jeans equilibria can only accommodate
toroidal currents and flows, given the absence of a third integral of the
microscopic motion.
