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In this paper, we develop a one-dimensional (1-D), quasineutral, hybridVlasov-Maxwell equilibrium model with kinetic ions and massless fluid electronsand derive associated solutions. The model allows for an electrostaticpotential that is expressed in terms of the vector potential components throughthe quasineutrality condition. The equilibrium states are calculated uponsolving an inhomogeneous Beltrami equation that determines the magnetic field,where the inhomogeneous term is the current density of the kinetic ions and thehomogeneous term represents the electron current density. We show that thecorresponding 1-D system is Hamiltonian, with position playing the role oftime, and its trajectories have a regular, periodic behavior for iondistribution functions that are symmetric in the two conserved particlecanonical momenta. For asymmetric distribution functions, the system isnonintegrable, resulting in irregular and chaotic behavior of the fields. Theelectron current density can modify the magnetic field phase space structure,inducing orbit trapping and the organization of orbits into large islands ofstability. Thus the electron contribution can be responsible for the emergenceof localized electric field structures that induce ion trapping. We alsoprovide a paradigm for the analytical construction of hybrid equilibria using arotating two-dimensional harmonic oscillator Hamiltonian, enabling thecalculation of analytic magnetic fields and the construction of thecorresponding distribution functions in terms of Hermite polynomials.

Chaotic and integrable magnetic fields in one-dimensional hybrid Vlasov-Maxwell equilibria