Hall dynamics of the Kelvin-Helmholtz instability (original) (raw)
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Monthly Notices of the Royal Astronomical Society, 2011
The Kelvin-Helmholtz instability is well known to be capable of converting wellordered flows into more disordered, even turbulent, flows. As such it could represent a path by which the energy in, for example, bowshocks from stellar jets could be converted into turbulent energy thereby driving molecular cloud turbulence. We present the results of a suite of fully multifluid magnetohydrodynamic simulations of this instability using the HYDRA code. We investigate the behaviour of the instability in a Hall dominated and an ambipolar diffusion dominated plasma as might be expected in certain regions of accretion disks and molecular clouds respectively.
The Hall instability of unsteady inhomogeneous axially symmetric magnetized plasmas
Physics of Plasmas, 2004
The Hall instability in cylindrically symmetric resistive magnetized plasmas in vacuum is investigated. The unperturbed self-similar equilibrium solutions for imploding Z-pinches with time-dependent total current I t ϳ t S , S Ͼ 1 / 3, are subjected by short-wave sausage perturbations. The instability criterion is derived in slow-time, frozen-radius approximation. In cylindrically symmetric configurations the instability is driven by the magnetic field curvature. The near-axis and near-edge branches of the neutral curve in the plane of the inverse Hall parameter and phase velocity with the frozen radial coordinate as a parameter are separated by the critical point, where the modified gradient from the unperturbed number density changes sign. The critical radius may be treated as a new characteristic size of the Z-pinch that emerges due to the instability: the pinch is envisaged restructured by the short-scale high-frequency Hall instability, in which a central stable core is surrounded by an outer shell. Such a modified equilibrium may explain the observed enhanced stability against magnetohydrodynamic modes.
Shear-driven Instabilities in Hall-magnetohydrodynamic Plasmas
2011
The large-scale dynamics of plasmas is well described within the framework of magnetohydrodynamics (MHD). However, whenever the ion density of the plasma becomes sufficiently low, the Hall effect is likely to become important. The role of the Hall effect has been studied in several astrophysical plasma processes, such as magnetic reconnection, magnetic dynamo, MHD turbulence or MHD instabilities. In particular, the development of small-scale instabilities is essential to understand the transport properties in a number of astrophysical plasmas.
Nonlinear evolution of the magnetized Kelvin-Helmholtz instability: From fluid to kinetic modeling
Physics of Plasmas, 2013
The nonlinear evolution of collisionless plasmas is typically a multi-scale process, where the energy is injected at large, fluid scales and dissipated at small, kinetic scales. Accurately modelling the global evolution requires to take into account the main micro-scale physical processes of interest. This is why comparison of different plasma models is today an imperative task aiming at understanding cross-scale processes in plasmas. We report here the first comparative study of the evolution of a magnetized shear flow, through a variety of different plasma models by using magnetohydrodynamic (MHD), Hall-MHD, two-fluid, hybrid kinetic, and full kinetic codes. Kinetic relaxation effects are discussed to emphasize the need for kinetic equilibriums to study the dynamics of collisionless plasmas in non trivial configurations. Discrepancies between models are studied both in the linear and in the nonlinear regime of the magnetized Kelvin-Helmholtz instability, to highlight the effects o...
Hall MHD effects on the 2D Kelvin–Helmholtz/tearing instability
Physics Letters A, 2003
The Kelvin-Helmholtz (KHI)/tearing (TMI) instability is studied with a 2D incompressible Hall MHD model. In the equilibrium configuration of interest, the magnetic and ion velocity fields are parallel and identically sheared. While in resistive MHD simultaneous growth of a TMI and a KHI is precluded, Hall physics, by decoupling electrons and ions, destabilizes both modes, leading to a more complex interaction. Nonlinearly, saturation occurs with the formation of a magnetic island and an ion flow vortex in both sub-and super-Alfvénic regimes. For moderately large c/ω pi , the electron flow shows good alignment with the magnetic field, while demagnetized ions still show KH activity.
Kinetic plasma turbulence during the nonlinear stage of the Kelvin-Helmholtz instability
Using a full kinetic, implicit particle-in-cell code, iPiC3D, we studied the properties of plasma kinetic turbulence, such as would be found at the interface between the solar wind and the Earth magnetosphere at low latitude during northwards periods. In this case, in the presence of a magnetic field B oriented mostly perpendicular to the velocity shear, turbulence is fed by the disruption of a Kelvin-Helmholtz vortex chain via secondary instabilities, vortex pairing and non-linear interactions. We found that the magnetic energy spectral cascade between ion and electron inertial scales, d i and d e , is in agreement with satellite observations and other previous numerical simulations; however, in our case the spectrum ends with a peak beyond d e due to the occurrence of the lower hybrid drift instability. The electric energy spectrum is influenced by effects of secondary instabilities: anomalous resistivity, fed by the development of the lower hybrid drift instability, steepens the spectral decay and, depending on the alignment or anti-alignment of B and the shear vorticity, peaks due to ion-Bernstein waves may dominate the spectrum around d i. These waves are generated by counter-streaming flow structures, through flux freezing also responsible for reconnection of the in-plane component of the magnetic field, which then generates electron pressure anisotropy and flattening of the field-aligned component of the electron distribution function.
Shear-driven instabilities in Hall-MHD plasmas
2010
The large-scale dynamics of plasmas is well described within the framework of magnetohydrodynamics (MHD). However, whenever the ion density of the plasma becomes sufficiently low, the Hall effect is likely to become important. The role of the Hall effect has been studied in several astrophysical plasma processes, such as magnetic reconnection, magnetic dynamo, MHD turbulence or MHD instabilities. In particular, the development of small-scale instabilities is essential to understand the transport properties in a number of astrophysical plasmas. The magneto-rotational instability, which takes place in differentially rotating accretion disks embedded in relatively weak magnetic fields, is just one example. The influence of the large-scale velocity flows on small-scale instabilities is often approximated by a linear shear flow. In this paper we quantitatively study the role of the Hall effect on plasmas embedded in large-scale shear flows. More precisely, we show that an instability develops when the Hall effect is present,
Kelvin-Helmholtz versus Hall magnetoshear instability in astrophysical flows
Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
We study the stability of shear flows in a fully ionized plasma. Kelvin-Helmholtz is a well-known macroscopic and ideal shear-driven instability. In sufficiently low-density plasmas, also the microscopic Hall magnetoshear instability can take place. We performed three-dimensional simulations of the Hall-magnetohydrodynamic equations where these two instabilities are present, and carried out a comparative study. We find that when the shear flow is so intense that its vorticity surpasses the ion-cyclotron frequency of the plasma, the Hall magnetoshear instability is not only non-negligible, but it actually displays growth rates larger than those of the Kelvin-Helmholtz instability.
A review of magneto-vorticity induction in Hall-MHD plasmas
The ideal induction of vector fields in fluids and plasmas is presented as invariance under local convection, 'freezing' into flowlines and transfer of potential. Related consequences are discussed, namely the conservation of local flux and total helicity and the force-free relaxation state. In the framework of single-fluid Hall-MHD plasma flow model, the magnetic field and vorticity (which are formally analogous and generally anti-correlated, but each not ideally inducted, i.e. perfectly 'frozen-into' the flow) are shown to combine in a unified magneto-vorticity field, which is ideally inducted in perfectly-conducting, however even forced, non-isentropic and viscous plasmas. Relaxation plasma states of conserved or extreme helicity magneto-vorticity fields are derived and shown to be generalized force-free states, similar to those previously derived in the framework of Hall-MHD and the multi-component plasma model. The magneto-vorticity induction in visco-resistive plasmas is also discussed. Application of the magneto-vorticity field concept in the study of type I superconductors and the spontaneous generation of magnetic fields are reviewed. The Cowling 'anti-dynamo' theorem for axisymmetric flows is extended in Hall-MHD and for arbitrary flows and is shown that, in principle, the resistive (ohmic) dissipation of the magnetic field can be balanced by non-isentropic heating and/or helical forcing effects.