  In this paper, we develop a one-dimensional (1-D), quasineutral, hybrid
Vlasov-Maxwell equilibrium model with kinetic ions and massless fluid electrons
and derive associated solutions. The model allows for an electrostatic
potential that is expressed in terms of the vector potential components through
the quasineutrality condition. The equilibrium states are calculated upon
solving an inhomogeneous Beltrami equation that determines the magnetic field,
where the inhomogeneous term is the current density of the kinetic ions and the
homogeneous term represents the electron current density. We show that the
corresponding 1-D system is Hamiltonian, with position playing the role of
time, and its trajectories have a regular, periodic behavior for ion
distribution functions that are symmetric in the two conserved particle
canonical momenta. For asymmetric distribution functions, the system is
nonintegrable, resulting in irregular and chaotic behavior of the fields. The
electron current density can modify the magnetic field phase space structure,
inducing orbit trapping and the organization of orbits into large islands of
stability. Thus the electron contribution can be responsible for the emergence
of localized electric field structures that induce ion trapping. We also
provide a paradigm for the analytical construction of hybrid equilibria using a
rotating two-dimensional harmonic oscillator Hamiltonian, enabling the
calculation of analytic magnetic fields and the construction of the
corresponding distribution functions in terms of Hermite polynomials.
