7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Construction of chaotic and integrable equilibria
for a hybrid Vlasov-Maxwell system

D. A. Kaltsas1,2, P. J. Morrison3 and G. N. Throumoulopoulos1
1
Department of Physics, University of Ioannina, Greece2
Department of Physics, International Hellenic University, Greece
3
Department of Physics and Institute for Fusion Studies, University of Texas at Austin, USAe-mail (speaker): d.kaltsas@uoi.gr
The construction of self-consistent kinetic equilibriumstates is important for studying stability and wavepropagation in collisionless plasmas (e.g. [1]).
Consequently, many studies over the past decades havebeen focused on calculating Vlasov-Maxwell equilibria
using analytical and numerical methods. However, theproblem of kinetic equilibrium of hybrid models hasreceived less attention, and self-consistent treatments
often adopt restrictive assumptions ruling out cases withirregular and chaotic behavior, although such behavior isobserved in spacecraft observations of space plasmas(e.g. [2]).
In this contribution, we develop a one-dimensional,
quasineutral, hybrid Vlasov-Maxwell equilibrium modelwith kinetic ions and massless fluid electrons and derive
associated solutions. The model allows for anelectrostatic potential that is expressed in terms of thevector potential components through the quasineutrality
condition [3]. 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 the corresponding one-dimensionalsystem is Hamiltonian, with position playing the role oftime, and its trajectories have a regular, periodic
behavior for ion distribution functions that are symmetricin the two conserved particle canonical momenta.

For asymmetric distribution functions, the system isnonintegrable, resulting in irregular and chaotic behaviorof the fields. The electron current density can modify themagnetic field phase space structure, inducing orbit
trapping and the organization of orbits into large islandsof stability (cf. Fig. 1). Thus the electron contribution canbe responsible for the emergence of localized electricfield structures that induce ion trapping.
We also provide a paradigm for the analyticalconstruction of hybrid equilibria using a rotating twodimensional harmonic oscillator Hamiltonian, enabling
the calculation of analytic magnetic fields and theconstruction of the corresponding distribution functionsin terms of Hermite polynomials [4,5].
Acknowledgments
This work has received funding from the National Fusion
Programme of the Hellenic Republic - General
Secretariat for Research and Innovation. P.J.M. wassupported by the U.S. Department of Energy Contract
No. DE-FG05-80ET-53088
References[1] F. Malara et al, Phys. Rev. E 97, 053212 (2018).
[2] R. Wang et al, ApJ 889, L9 (2020).
[3] H. E. Mynick et al, Phys. Fluids 22, 1478 (1979).
[4] O. Allanson et al, J. Plasma Phys. 82, 905820306(2016).
[5] P. J. Channell, Phys. Fluids 19, 1541 (1976).

Figure 1. Poincaré surfaces of section of the nonintegrable equilibrium system resulting from non-symmetricion distribution functions, for different values of the parameter λ. The Coriolis parameter λ, linked to theelectron current density, induces orbit trapping and organization of the phase-space trajectories in large
islands of stability.