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

Journal Article · Thu Jul 06 00:00:00 EDT 2023 · Journal of Plasma Physics

DOI:https://doi.org/10.1017/S0022377823000557· OSTI ID:1988328

Kaltsas, Dimitrios A. ; Morrison, Philip J. ; Throumoulopoulos, George N.

The construction of kinetic equilibrium states is important for studying stability and wave propagation in collisionless plasmas. Thus, many studies over the past decades have been focused on calculating Vlasov–Maxwell equilibria using analytical and numerical methods. However, the problem of kinetic equilibrium of hybrid models is less studied, and self-consistent treatments often adopt restrictive assumptions ruling out cases with irregular and chaotic behaviour, although such behaviour is observed in spacecraft observations of space plasmas. 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 behaviour 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 behaviour 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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: FG05-80ET-53088
• OSTI ID: 1988328
• Journal Information: Journal of Plasma Physics, Journal Name: Journal of Plasma Physics Vol. 89 Journal Issue: 4; ISSN 0022-3778
• Publisher: Cambridge University Press (CUP)
• Country of Publication: United Kingdom
• Language: English