Tommaso Andreussi

Magnetic reconnection and Kelvin–Helmholtz instabilities at the Earth's magnetopause

Kelvin–Helmholtz instability (KHI), driven by the velocity inhomogeneity at Earths magnetopause, has been shown to play a major role in mixing the magnetospheric and the solar wind plasma during northward periods. In fact, when the magnetospheric and interplanetary magnetic fields are mostly perpendicular to the equatorial plane, KHI can develop at a low latitude without being significantly inhibited by the magnetic tension. In contrast, at a high latitude, the more complex magnetic configuration is believed to totally stabilize the instability. This intrinsic 3D dynamics is investigated in a simplified geometry showing that KHI is able to kink the magnetic field lines at a mid-latitude and to create current layers where magnetic reconnection spontaneously develops. It is shown that a mid-latitude reconnection is able to change the global topology of the magnetic field and to connect interplanetary field lines to the Earths cups, allowing the solar wind to directly enter the magnetosphere.

Hamiltonian magnetohydrodynamics: Helically symmetric formulation, Casimir invariants, and equilibrium variational principles

The noncanonical Hamiltonian formulation of magnetohydrodynamics (MHD) is used to construct variational principles for continuously symmetric equilibrium configurations of magnetized plasma, including flow. In particular, helical symmetry is considered, and results on axial and translational symmetries are retrieved as special cases of the helical configurations. The symmetry condition, which allows the description in terms of a magnetic flux function, is exploited to deduce a symmetric form of the noncanonical Poisson bracket of MHD. Casimir invariants are then obtained directly from the Poisson bracket. Equilibria are obtained from an energy-Casimir principle and reduced forms of this variational principle are obtained by the elimination of algebraic constraints.

MHD equilibrium variational principles with symmetry

ThechainruleforfunctionalsisusedtoreducethenoncanonicalPoissonbracket formagnetohydrodynamics(MHD)tooneforaxisymmetricandtranslationally symmetric MHD and hydrodynamics. The procedure for obtaining Casimir invariants from noncanonical Poisson brackets is reviewed and then used to obtain the Casimir invariants for the considered symmetrical theories. It is shown why extrema of the energy plus Casimir invariants correspond to equilibria, thereby giving an explanation for the ad hoc variational principles thathaveexistedinplasmaphysics. Variationalprinciplesforgeneralequilibria are obtained in this way.

Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory

Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable energy principle is described and sufficient stability conditions are presented. Next, plasma flows are described in terms of Eulerian variables and the noncanonical Hamiltonian formulation of MHD is exploited. For symmetric equilibria, the energy-Casimir principle is expanded to second order and sufficient conditions for stability to symmetric perturbation are obtained. Then, dynamically accessible variations, i.e., variations that explicitly preserve invariants of the system, are introduced and the respective energy principle is considered. General criteria for stability are obtained, along with comparisons between the three different approaches.

Double mid-latitude dynamical reconnection at the magnetopause: An efficient mechanism allowing solar wind to enter the Earth's magnetosphere

Three-dimensional simulations of the Kelvin-Helmholtz (KH) instability in a magnetic configuration reproducing typical conditions at the flank Earths magnetosphere during northward periods show the systems ability to generate favorable conditions for magnetic reconnection to occur at mid-latitude. Once these conditions are established, magnetic reconnection proceeds spontaneously in both hemispheres generating field lines that close on Earth but are connected to the solar wind at low latitude, allowing direct entrance of solar wind plasma into the magnetosphere. These results are consistent with recent observations of KH vortices showing the signature of reconnection events occurring well outside the equatorial plane (Bavassano M. B. et al., Ann. Geophys., 28 (2010) 893).

On the variational approach to axisymmetric magnetohydrodynamic equilibria

The variational formulation of the axisymmetric magnetohydrodynamic equilibrium equations with plasma flows is addressed and a more comprehensive method is presented that allows, in particular, for open boundary conditions and discontinuous (shock) solutions. A numerical procedure based on the variational formulation is described and a validation test for an open conical geometry, including also hydrodynamic shocks, is investigated.

Magnetized plasma flows and magnetoplasmadynamic thrusters

An axisymmetric magnetohydrodynamics (MHD) model of the acceleration channel of an applied-field magnetoplasmadynamic thruster is presented. A set of general relationships between the flow features and the thruster performance is obtained. The boundary conditions and the flow regime, which depends on the Alfven Mach number, are shown to provide the ideal limits of steady state thruster operation. In the present analysis, a Hamiltonian formulation of the MHD plasma flow model is adopted. This formulation makes it possible to cast the model equations in a variational form, which is then solved by using a finite element numerical algorithm.

Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability-Examples with translation symmetry

Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, Eulerian (energy-Casimir), or dynamical accessible frameworks. This is in particular the case when flows are present. These differences are explored explicitly by working out in detail two magnetohydrodynamic examples: convection against gravity in a stratified fluid and translationally invariant perturbations of a rotating magnetized plasma pinch. In this second example we show in explicit form how to perform the time-dependent relabeling introduced in Andreussi {\it et al.}\ [Phys.\ Plasmas {\bf20}, 092104 (2013)] that makes it possible to reformulate Eulerian equilibria with flows as Lagrangian equilibria in the relabeled variables. The procedures detailed in the present article provide a paradigm that can be applied to more general plasma configurations and in addition extended to more general plasma descriptions where dissipation is absent.

Erratum: “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory” [Phys. Plasmas 20, 092104 (2013)]

An algebraic mistake in the rendering of the Energy Casimir stability condition for a symmetric magnetohydrodynamics plasma configuration with flows made in the article Andreussi et al. “Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory,” Phys. Plasmas 20, 092104 (2013) is corrected.