Linear stability analysis of relativistic magnetized jets

In the present paper, we examine the convergence behavior and inter-code reliability of astrophysical jet simulations in axial symmetry. We consider both pure hydrodynamic jets and jets with a dynamically significant magnetic field. The setups were chosen to match the setups of two other publications, and recomputed with the MHD code NIRVANA. We show that NIRVANA and the two other codes give comparable, but not identical results. We explain the differences by the different application of artificial viscosity in the three codes and numerical details, which can be summarized in a resolution effect, in the case without magnetic field: NIRVANA turns out to be a fair code of medium efficiency. It needs approximately twice the resolution as the code by Lind (Lind et al. 1989) and half the resolution as the code by Kössl (Kössl & Müller 1988). We find that some global properties of a hydrodynamical jet simulation, like e.g. the bow shock velocity, converge at 100 points per beam radius (ppb) with NIRVANA. The situation is quite different after switching on the toroidal magnetic field: in this case, global properties converge even at 10 ppb. In both cases, details of the inner jet structure and especially the terminal shock region are still insufficiently resolved, even at our highest resolution of 70 ppb in the magnetized case and 400 ppb for the pure hydrodynamic jet. The magnetized jet even suffers from a fatal retreat of the Mach disk towards the inflow boundary, which indicates that this simulation does not converge, in the end. This is also in definite disagreement with earlier simulations, and challenges further studies of the problem with other codes. In the case of our highest resolution simulation, we can report two new features: first, small scale Kelvin-Helmholtz instabilities are excited at the contact discontinuity next to the jet head. This slows down the development of the long wavelength Kelvin-Helmholtz instability and its turbulent cascade to smaller wavelengths. Second, the jet head develops Rayleigh-Taylor instabilities which manage to entrain an increasing amount of mass from the ambient medium with resolution. This region extends in our highest resolution simulation over 2 jet radii in the axial direction.

We extend investigations of mass entrainment by jets, which previously have focused on cylindrical supermagnetosonic jets and expanding trans-Alfvenic jets, to a set of expanding supermagnetosonic jets. We precess these jets at the origin to excite the helical mode of the Kelvin-Helmholtz (KH) instability, in order to compare the results with predictions from linear stability analysis. We analyze this simulation set for the spatial development of magnetized mass, which we interpret as jet plus entrained, initially unmagnetized external mass. As with the previous simulation sets, we find that the growth of magnetized mass is associated with the growth of the KH instability through linear, nonlinear, and saturated stages and with the expansion of magnetized material in simulated observations of the jet. From comparison of measured wavelengths and wave speeds with the predictions from linear stability analysis, we see evidence that the KH instability is the primary cause for mass entrainment in these simulations and that the expansion reduces the rate of mass entrainment. This reduced rate can be observed as a somewhat greater distance between the two transition points separating the three stages of expansion.

During periods of southward IMF magnetic reconnection appears to be the dominant process for the transport of magnetic flux and magnetosheath plasma into the magnetosphere. However, for northward IMF the transport of mass into the magnetosphere is not well understood. In particular for strongly parallel magnetic fields on the two sides of the magnetopause, magnetic reconnection does not operate or is inefficient for the mass transport. For largely parallel fields the Kelvin-Helmholtz (KH) mode is unstable for k vectors largely perpendicular to the magnetic field. Although the KH mode is an ideal instability, the deformation of the boundary magnetic field through the KH can generate strong current layers and force magnetic reconnection within the KH vortex motion. We will discuss this process, onset conditions, and implications for the structure of the Low Latitude Boundary Layer (LLBL). The transport of mass appears consistent with the diffusion required at the LLBL and with the typical correlation time for the magnetospheric plasma density in response to changes in the solar wind.

We have studied three-dimensional hydrodynamic interactions of relativistic extragalactic jets with two-phase ambient media. These jets propagate through a denser homogeneous gas and then impact clouds with densities 100 to 1000 times higher than the initial beam density. The deflection angle of the jet is influenced more by the density contrast of the cloud than by the beam Mach number of the jet. A relativistic jet with low relativistic beam Mach number can eventually be slightly bent after it crosses the dense cloud; however, we have not seen permanently bent structures in the interaction of a high relativistic beam Mach number jet with a cloud. The relativistic jet impacts on dense clouds do not necessarily destroy the clouds completely, and much of the cloud body can survive as a coherent blob. This enhancement of cloud durability is partly due to the geometric influence of the off-axis collisions we consider and also arises from the lower rate of cloud fragmentation through the Kelvin-Helmholtz instability for relativistic jets. To compare our simulations with observed extragalactic radio jets, we have computed the approximate surface distributions of synchrotron emission at different viewing angles. These surface intensity maps show that relativistic jets interacting with clouds can produce synchrotron emission knots similar to structures observed in many VLBI-scale radio sources. We find that the synchrotron emission increases steeply at the moment of impact and the emission peaks right before the jet passes through the cloud

Introduction: Kelvin-Helmholtz (KH) and tearing mode (TM) instabilities are one of the most important mechanisms of solar wind energy, momentum and plasma transport within the magnetosphere.Methods: To investigate the conditions under which KHTM instabilities occur in the Earth environment it is fundamental to combine simultaneous multipoint in situ measurements and MHD simulations. We analyzed data from the THEMIS and Cluster spacecraft considering two Space Weather (SWE) events starting with an M2.0 flare event (hereafter Case-1) that occurred on 21 June 2015 and the most-intensive flare (X9.3) of solar cycle 24 that occurred on 6 September 2017 (hereafter Case-2).Results: Our analysis utilized a 2D MHD model for incompressible and viscous flow. The results from Case-1 indicate the presence of KH and TM instabilities, suggesting existence of observed low-amplitude oscillations at the nose of the magnetopause. However, the MHD simulations for Case-2 did not show any evidence of KH vortices, but did reveal the presence of “magnetic island” structures during a low-shear condition. The reconnection rate derived from the observations is compared with the computed one in the presence of developed instabilities inside the Earth’s magnetopause.

The relativistic dispersion relation describing the growth and propagation of the harmonic components of a perturbation to the surface of a cylindrical relativistic jet are analyzed numerically for relativistic flows. The results are used to extend previous expressions for resonant frequencies, wavelengths, and the maximum growth rate at resonance valid for nonrelativistic flows to relativistic flows. The results are used to develop a model for the helical twisting of a light relativistic jet expanding in response to an external pressure gradient. The model equations are applied to observed motions of the components in the jet in 3C 345 to show how a light, helically twisted jet produced by the Kelvin-Helmholtz instability can explain the apparent motions and accelerations of components along the jet in 3C 345.

Context. The internal structure and stability of relativistic jets from active galactic nuclei (AGNs) still presents open questions relevant to high-energy astrophysics, with recollimation shocks often invoked to explain the jet morphology, particle acceleration, and variability. Yet, the role of instabilities triggered downstream of these shocks is not fully understood, particularly in magnetized jets. Aims. We aim to investigate how jet magnetization and other physical parameters influence the development of instabilities beyond the first recollimation shock. In particular, we focus on identifying the conditions under which the centrifugal instability (CFI) is effective, and how it affects the jet propagation and internal dynamics. Methods. We performed high-resolution 2D and 3D simulations using the relativistic magnetohydrodynamics (RMHD) code PLUTO . The jets are initialized with a conical geometry and propagate into an ambient medium, and we followed by axisymmetric simulations how they evolve toward a steady-state. In 2D we explored a range of magnetizations (from 0 to 1), pressure contrasts, and inertia ratios to characterize the formation and evolution of recollimation shocks. The results are further evaluated using linear stability analysis to assess the growth and suppression of CFI. Finally, we performed 3D simulations of unstable and stable jets. Results. We discuss how the different parameters of the axisymmetric steady solutions influence the location and strength of recollimation. We found that, even in moderately magnetized jets, σ = 0.1, the CFI can still develop under suitable local conditions and disrupt the jet structure. This instability is governed by the jet radius, curvature, Lorentz factor, and magnetization, and is not always predictable from injection conditions. While magnetization can delay or locally suppress instability growth, it does not guarantee long-term jet stability. Our 3D results highlight the limitations of 2D models in capturing non-axisymmetric and nonlinear effects, and underline the complex interplay between magnetic confinement and destabilizing mechanisms. These findings have implications for interpreting variability, knot formation, and polarization structure in AGNs jets.

In this work, we numerically study linear stability of multiple steady-state solutions to a type of steric Poisson-Nernst-Planck equations with Dirichlet boundary conditions, which are applicable to ion channels. With numerically found multiple steady-state solutions, we obtain S-shaped current-voltage and current-concentration curves, showing hysteretic response of ion conductance to voltages and boundary concentrations with memory effects. Boundary value problems are proposed to locate bifurcation points and predict the local bifurcation diagram near bifurcation points on the S-shaped curves. Numerical approaches for linear stability analysis are developed to understand the stability of the steady-state solutions that are only numerically available. Finite difference schemes are proposed to solve a derived eigenvalue problem involving differential operators. The linear stability analysis reveals that the S-shaped curves have two linearly stable branches of different conductance levels and one linearly unstable intermediate branch, exhibiting classical bistable hysteresis. As predicted in the linear stability analysis transition dynamics, from a steady-state solution on the unstable branch to one on the stable branches, are led by perturbations associated to the mode of the dominant eigenvalue. Further numerical tests demonstrate that the finite difference schemes proposed in the linear stability analysis are second-order accurate. Numerical approaches developed in this work can be applied to study linear stability of a class of time-dependent problems around their steady-state solutions that are computed numerically.

Combustion-Transition Interaction in a Jet Flame

The effects of different initial perturbations on the evolution of stratified shear flows that are subject to Kelvin-Helmholtz instability and vortex pairing have been investigated through Direct Numerical Simulation (DNS). The effects of purely random perturbations of the background flow are sensitive to the phase of the subharmonic component of the perturbation that has a wavelength double that of the Kelvin-Helmholtz instability. If the phase relationship between the Kelvin-Helmholtz mode and its subharmonic mode is optimal, or close to it, vortex pairing occurs. Vortex paring is delayed when there is a phase difference, and this delay increases with increasing phase difference. In three dimensional simulations vortex pairing is suppressed if the phase difference is sufficiently large, reducing the amount of mixing and mixing efficiency. For a given phase difference close enough to the optimal phase, the response of the flow to eigenvalues perturbations is very similar to the response to random perturbations. In addition to traditional diagnostics, we show quantitatively that a non-modal Fourier component in a random perturbation quickly evolves to be modal and describe the process of vortex pairing using Lagrangian trajectories.

A typical property of magnetopause reconnection is a significant perpendicular shear flow due to the fast streaming magnetosheath plasma. Therefore, the magnetopause represents a large magnetic and flow shear boundary during periods of southward interplanetary magnetic field, which can be unstable to Kelvin‐Helmholtz (KH) modes and to magnetic reconnection. A series of local three‐dimensional MHD and Hall MHD simulations is carried out to investigate the interaction of reconnection and nonlinear KH waves considering magnetic reconnection as the primary process. It is demonstrated that the onset reconnection causes a thinning of the shear flow layer, thereby generating small wavelength KH modes. In turn, the growing KH modes modify the current layer width, which modulate the diffusion regions, increase the local reconnection rates, and generate field‐aligned currents. The simulation results imply a limitation of total amount of open flux likely caused by nonlinear saturation of KH growth and the associated diffusion. It is also demonstrated that the reconnection rate maximizes for conditions that allow a strong nonlinear evolution of KH waves, i.e., fast shear flow and limited guide magnetic field. The presence of Hall physics increases the reconnection rate in the early stage; however, the maximum reconnection rate and the total amount of open flux at saturation are the same as in the MHD case.

We have investigated particle acceleration and shock structure associated with an unmagnetized relativistic jet propagating into an unmagnetized plasma. Strong magnetic fields generated in the trailing jet shock lead to transverse deflection and acceleration of the electrons. We have self-consistently calculated the radiation from the electrons accelerated in the turbulent magnetic fields. We find that the synthetic spectra depend on the bulk Lorentz factor of the jet, the jet temperature, and the strength of the magnetic fields generated in the shock. We have also begun study of electron acceleration in the strong magnetic fields generated by kinetic shear (Kelvin-Helmholtz) instabilities. Our calculated spectra should lead to a better understanding of the complex time evolution and/or spectral structure from gamma-ray bursts, relativistic jets, and supernova remnants.

Linear and non-linear properties of slab drift waves in the negative sheared slab configuration modelling of the qmin surface region in negative shear tokamaks are studied, where qmin is the minimum value of the safety factor q. Linear calculations show that both the slab ion temperature gradient (ITG) driven mode and the slab electron temperature gradient (ETG) driven mode become strongly unstable around the qmin surface. Non-linear simulations are performed for ETG turbulence, which evolves on a much faster timescale than ITG turbulence. It is found that quasi-steady Er × B zonal flows are generated by an inverse wave energy cascade process. Linear stability analyses of the electrostatic Kelvin-Helmholtz (KH) mode show that the quasi-steady Er × B zonal flow profile is closely related to the q profile or to the magnetic shear, which has a stabilizing effect on the KH mode. It is shown that the microscopic quasi-steady Er × B zonal flows arising from ETG turbulence have a strong stabilizing effect on the slab ITG mode.

Bridging simulations of kink instability in relativistic magnetized jets with radio emission and polarisation

We study the properties of the chromohydrodynamical instabilities induced by a relativistic jet that crosses the quark-gluon plasma. Assuming that the jet of particles and the plasma can be described using a hydrodynamical approach, we derive and discuss the dispersion laws for the unstable collective modes. In our analysis, the chromohydrodynamical equations for the collective modes are tackled in the linear response approximation. Such an approximation, valid for short time scales, allows one to study in a straightforward way the dependence of the dispersion laws of the collective modes on the velocity of the jet, on the magnitude of the momentum of the collective mode and on the angle between these two quantities. In the conformal limit, we find that unstable modes arise for velocity of the jet larger than the speed of the sound of the plasma and only modes with momenta smaller than a certain value are unstable. Moreover, for ultrarelativistic velocities of the jet, the longitudinal mode becomes stable and the most unstable modes correspond to relative angles between the velocity of the jet and momentum of the collective mode larger than {approx}{pi}/8. Our results suggest an alternative mechanism for the description of the jet quenching phenomenon,more » where the jet crossing the plasma loses energy exciting colored unstable modes.« less