The noncanonical Hamiltonian formulation of magnetohydrodynamics (MHD) is used to construct variational principles for 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. * Electronic address: t.andreussi@alta-space.com †
The different flow regimes occurring in T-mixers are investigated by means of direct numerical simulations. Three different values of the aspect ratio of the inlet channels, ki, that is their width to height ratio, are considered, namely ki= 0.75, 1 and 2. For the configurations with ki= 0.75 and 1, the same behavior as previously described in the literature, is found. In particular, as the Reynolds number is increased, the flow evolves from vortical to engulfment steady regimes, then to unsteady asymmetric and symmetric periodic regimes, until, finally, it becomes chaotic. All the critical values of the Reynolds number, at which the transitions between the different regimes occur, are found to be very similar for ki= 0.75 and 1, while some differences are highlighted in the vorticity dynamics and characteristic frequencies of the unsteady regimes. The observed scenario is completely different for ki= 2. Indeed, in this case, the flow evolves directly from the vortical regime to an unsteady symmetric behavior, with a vorticity dynamics that is significantly different from those observed for the other aspect ratios
The chain rule for functionals is used to reduce the noncanonical Poisson bracket for magnetohydrodynamics (MHD) to one for axisymmetric and translationally 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 that have existed in plasma physics. Variational principles for general equilibria are obtained in this way.
Three-dimensional simulations of the Kelvin-Helmholtz (KH) instability in a magnetic configuration reproducing typical conditions at the flank Earth's magnetosphere during northward periods show the system's 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 et al., 2010 Ann. Geophys. 28, 893 (2010)).
Kelvin-Helmholtz instability (KHI), driven by the velocity inhomogeneity at Earth's 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 Earth's cups, allowing the solar wind to directly enter the magnetosphere.
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.
One of the main oscillatory modes found ubiquitously in Hall thrusters is the so-called breathing mode. This is recognized as a relatively low-frequency (10–30 kHz), longitudinal oscillation of the discharge current and plasma parameters. In this paper, we present a synergic experimental and numerical investigation of the breathing mode in a 5 kW-class Hall thruster. To this aim, we propose the use of an informed 1D fully-fluid model to provide augmented data with respect to available experimental measurements. The experimental data consists of two datasets, i.e., the discharge current signal and the local near-plume plasma properties measured at high-frequency with a fast-diving triple Langmuir probe. The model is calibrated on the discharge current signal and its accuracy is assessed by comparing predictions against the available measurements of the near-plume plasma properties. It is shown that the model can be calibrated using the discharge current signal, which is easy to measure, and that, once calibrated, it can predict with reasonable accuracy the spatio-temporal distributions of the plasma properties, which would be difficult to measure or estimate otherwise. Finally, we describe how the augmented data obtained through the combination of experiments and calibrated model can provide insight into the breathing mode oscillations and the evolution of plasma properties.
We developed a novel measurement apparatus and data processing technique that allow for the quantitative reconstruction of the effects of breathing mode oscillations on the main properties of the plasma in Hall thrusters. The approach is based on the use of a triple Langmuir probe mounted on a rapidly moving arm to scan the channel centerline and was validated in an experimental campaign on a 5 kW-class Hall thruster. The probe data were sampled at high frequency during its motion, and a Bayesian methodology was used to reliably infer the plasma properties from the instantaneous voltage and current measurements. In order to model the interaction of the electrodes with the plasma, a parameterization of the Laframboise sheath solution was used. Data were collected continuously during the probe motion from the plume up to the near-anode region of the thruster, allowing for the reconstruction of the salient features of the plasma oscillations as a function of axial location. A time–frequency analysis of the measured plasma properties based on wavelets was then performed to gain insight into the evolution and phase shift of the oscillations over the investigated plasma domain. The developed diagnostic method can provide quantitative information on the instantaneous value of plasma density, electron temperature, and plasma potential along the thruster centerline with good spatial resolution and has proved to be a valid approach to investigate breathing mode oscillations in Hall thruster plasmas.
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