Frozen-in Magnetic Field Research Articles

Invariant finite-difference schemes for cylindrical one-dimensional MHD flows with conservation laws preservation

On the basis of the recent group classification of the one-dimensional magnetohydrodynamics (MHD) equations in cylindrical geometry, the construction of symmetry-preserving finite-difference schemes with conservation laws is carried out. New schemes are constructed starting from the classical completely conservative Samarsky–Popov schemes. In the case of finite conductivity, schemes are derived that admit all the symmetries and possess all the conservation laws of the original differential model, including previously unknown conservation laws. In the case of a frozen-in magnetic field (when the conductivity is infinite), various schemes are constructed that possess conservation laws, including those preserving entropy along trajectories of motion. The peculiarities of constructing schemes with an extended set of conservation laws for specific forms of entropy and magnetic fluxes are discussed.

Surface brightness discontinuities in radio halos

Context. Dynamical motions in the intra-cluster medium (ICM) can imprint distinctive features on X-ray images that map the thermal bremsstrahlung emission from galaxy clusters, such as sharp surface brightness discontinuities due to shocks and cold fronts. The gas dynamics during cluster mergers may also drive large-scale turbulence in the ICM, which in turn generates extended (megaparsec-scale) synchrontron sources known as radio halos. Aims. Surface brightness edges have been found numerous times in the thermal gas of clusters based on X-ray observations. In contrast, edges in radio halos have only been observed in a handful of cases. Our goal is to search for new radio surface brightness discontinuities in the ICM. Methods. We inspected the images of the Bullet Cluster and the other 25 radio halos reported in the MeerKAT Galaxy Cluster Legacy Survey. To aid the identification of surface brightness discontinuities, we applied a gradient-filtering edge-detection method to the radio images. Results. We find that the adopted filtering technique is helpful in identifying surface brightness edges in radio images, allowing us to identify at least one gradient in half of the radio halos studied. For the Bullet Cluster, we find excellent agreement between the locations of the four radio discontinuities detected and the X-ray edges. This similarity informs us that there is substantial interplay between thermal and nonthermal components in galaxy clusters. This interplay is likely due to the frozen-in ICM magnetic field, which mediates the advection of cosmic rays while being dragged by thermal gas flows. Conclusions. We conclude that radio halos are shaped by dynamical motions in the ICM and that they often display surface brightness discontinuities, which appear to be co-located with edges in the thermal gas emission. Our results demonstrate that new and future generations of radio telescopes will provide an approach to efficiently detecting shocks and cold fronts in the ICM that is complementary to X-rays.

A model of EUV emission from clusters of galaxies

ABSTRACT With tantalizing evidence of the recent e-Rosita mission, re-discovering very soft X-rays and Extreme-Ultraviolet (EUV) radiation from a cluster of galaxies or its environment, the question of the origin of cluster EUV excess is revisited in this work. It will be shown that the gas temperature, density, and frozen-in magnetic field of the intracluster medium, collectively support the emission and propagation of coherent C̆erenkov radiation, which is low frequency and large amplitude radiation capable of accelerating charged particles to relativistic speeds. Owing to the spectrum of C̆erenkov radiation, most of the incipient relativistic electrons undergo inverse-Compton scattering with the cosmic microwave background. It turns out the scattered radiation has observable ramifications only in the EUV band, of photon energy 70–100 eV, having a luminosity ≈1044 ergs s−1. This luminosity is on par with the EUV excess level detected from Abell 1795 and the Coma cluster. It should be stressed, as caveat emptor, that although the main subject is the putative large amplitude coherent C̆erenkov modes which are highly non-linear, the results presented were derived using a quasi-linear approach to highlight the observable features of the phenomenon, namely, the EUV emission.

Two negative experimental results and analysis of Alfvén's theorem.

Alfvén's theorem concerning "frozen-in magnetic field" states that the magnetic field lines, passing through an ideal conductive fluid, are frozen with the fluid, and the fluid can move along the magnetic field lines but cannot cross them. Here, we present two negative experimental results and an analysis of the theorem. The experimental results prove that Alfvén's theorem cannot correctly explain the evolution of the magnetic field and magnetic resistance; therefore, it is incorrect. Mathematical analysis explains why this theorem is incorrect.

Damping of long wavelength gravitational waves by the intergalactic medium

The problem of radiation by the charged particles of the intergalactic medium (IGM) when a passing gravitational wave (GW) accelerates them is investigated. The largest acceleration (taking a charge from rest to a maximum speed which remains non-relativistic in the rest frame of the unperturbed spacetime) is found to be limited by the curvature of a propagating spherical gravitational wavefront. Interesting physics arises from the ensuing emission of radiation into the warm hot IGM, which to lowest order is a fully ionized hydrogen plasma with a frozen-in magnetic field B. It is found that for a vast majority of propagation directions, the radiation can penetrate the plasma at frequencies below the plasma frequency ω p, provided ω < ω b, where ω b = eB/m e satisfies ω b < ω p for typical IGM conditions. Moreover, the refractive index under such a scenario is n ≫ 1, resulting in an enhanced radiative dissipation of GW energy (relative to the vacuum scenario), which is more severe for electrons if both charge species are in thermal equilibrium and accelerated in the same way. The emission by the electrons then prevails, and is further amplified by coherent addition of amplitudes within the size one wavelength. The conversion of GWs of λ≳ 5 × 1013 cm to electromagnetic waves means such GWs can only propagate a distance ≲1 Gpc before being significantly damped by an IGM B field of ∼10−8 G. The low-frequency GWs targeted by pulsar-timing-arrays will not survive unless the IGM magnetic field is much lower than expected. The mHz frequency GW inspirals targeted by future space based detectors such as the Laser Interferometer Space Antenna remain intact and can be detected.

Stream-aligned Magnetohydrodynamics for Solar Wind Simulations

Abstract We present a reduced magnetohydrodynamic (MHD) mathematical model describing the dynamical behavior of highly conducting plasmas with frozen-in magnetic fields, constrained by the assumption that there exists a frame of reference, where the magnetic field vector, B , is aligned with the plasma velocity vector, u , at each point. We call this solution “stream-aligned MHD” (SA-MHD). Within the framework of this model, the electric field, E = − u × B ≡ 0, in the induction equation vanishes identically and so does the electromagnetic energy flux (Poynting flux), E × B ≡ 0, in the energy equation. At the same time, the force effect from the magnetic field on the plasma motion (the Ampère force) is fully taken into account in the momentum equation. Any steady-state solution of the proposed model is a legitimate solution of the full MHD system of equations. However, the converse statement is not true: in an arbitrary steady-state magnetic field, the electric field does not have to vanish identically (its curl has to, though). Specifically, realistic three-dimensional solutions for the steady-state (“ambient”) solar atmosphere in the form of so-called Parker spirals can be efficiently generated within the stream-aligned MHD (SA-MHD) with no loss in generality.

The Relationship of Magnetic Twist and Plasma Motion in a Magnetic Cloud

Abstract Our recent investigations indicate that interplanetary magnetic clouds (MCs) have a high-twist core and a weak-twist outer shell. Utilizing the velocity-modified uniform-twist force-free flux rope model, we further investigate the relationship between the twist profile of magnetic field lines and the distribution of the plasma poloidal angular velocity inside an MC. The poloidal velocity in the MC is 11 km s−1. There are evidently positive correlations between the absolute value of the twist and the plasma poloidal angular velocity in peeled flux ropes or flux rope layers, although the correlation coefficients in flux rope layers are less than those in peeled flux ropes. This finding suggests that plasma flows are frozen-in magnetic field lines as we expected for interplanetary medium, of which the magnetic Reynolds number is large. Furthermore, based on this picture, we infer the axial velocity in the MC frame, which is less than 10 km s−1 and almost uniform in the cross section of the MC. Besides, it is inferred that the plasma flows velocity in the MC is much less than the local Alfvén speed.

Rigidly connected magnetic lines: twisting and winding of magnetic lines

The dynamical process of magnetic flux variation in a fluid’s stream tube is described by constructing $$1+1+ (2)$$ decomposition of the gradient of fluid’s 4-velocity. The necessary and sufficient conditions are obtained for a spacelike congruence to be a congruence of rigidly connected spacelike curves. The evolution of magnetic flux in a magnetic tube is explored under the assumptions that magnetic lines are rigidly connected and the chemical potential of the fluid is constant along a magnetic tube. The interplay between magnetic and stream tubes is demonstrated. It is shown that the growth of magnetic energy in a magnetic tube cannot exceed to that of a stream tube. It is found that the proper time variation of twist of magnetic lines is caused by gravitation inside a neutron star if magnetic lines are rigidly connected and charge neutrality condition holds. Helmholtz-like magnetic vorticity flux conservation in a magnetic tube constituted by rigidly connected geodetic magnetic lines is derived under the assumption that the charge neutrality condition holds. It is shown that the winding of frozen-in poloidal magnetic field due to differential rotation requires meridional circulation in an axisymmetric stationary hydromagnetic configuration.

A small-scale dynamo in feedback-dominated galaxies – III. Cosmological simulations

Magnetic fields are widely observed in the Universe in virtually all astrophysical objects, from individual stars to entire galaxies, even in the intergalactic medium, but their specific generation has long been debated. Due to the development of more realistic models of galaxy formation, viable scenarios are emerging to explain cosmic magnetism, thanks to both deeper observations and more efficient and accurate computer simulations. We present here a new cosmological high-resolution zoom-in magnetohydrodynamic (MHD) simulation, using the adaptive mesh refinement (AMR) technique, of a dwarf galaxy with an initially weak and uniform magnetic seed field that is amplified by a small-scale dynamo driven by supernova-induced turbulence. As first structures form from the gravitational collapse of small density fluctuations, the frozen-in magnetic field separates from the cosmic expansion and grows through compression. In a second step, star formation sets in and establishes a strong galactic fountain, self-regulated by supernova explosions. Inside the galaxy, the interstellar medium becomes highly turbulent, dominated by strong supersonic shocks, as demonstrated by the spectral analysis of the gas kinetic energy. In this turbulent environment, the magnetic field is quickly amplified via a small-scale dynamo process and is finally carried out into the circumgalactic medium by a galactic wind. This realistic cosmological simulation explains how initially weak magnetic seed fields can be amplified quickly in early, feedback-dominated galaxies, and predicts, as a consequence of the small scale dynamo process, that high-redshift magnetic fields are likely to be dominated by their small scale components.

The structure of bow shocks formed by the interaction of pulsed-power driven magnetised plasma flows with conducting obstacles

We present an experimental study of the development and structure of bow shocks produced by the interaction of a magnetised, collisional, super-Alfvénic plasma flow with conducting cylindrical obstacles. The plasma flow with an embedded, frozen-in magnetic field (ReM ∼ 20) is produced by the current-driven ablation of fine aluminium wires in an inverse, exploding wire array z-pinch. We show that the orientation of the embedded field with respect to the obstacles has a dramatic effect on the bow shock structure. When the field is aligned with the obstacle, a sharp bow shock is formed with a global structure that is determined simply by the fast magneto-sonic Mach number. When the field is orthogonal to the obstacle, magnetic draping occurs. This leads to the growth of a magnetic precursor and the subsequent development of a magnetised bow shock that is mediated by two-fluid effects, with an opening angle and a stand-off distance, that are both many times larger than in the parallel geometry. By changing the field orientation, we change the fluid regime and physical mechanisms that are responsible for the development of the bow shocks. MHD simulations show good agreement with the structure of well-developed bow shocks. However, collisionless, two-fluid effects will need to be included within models to accurately reproduce the development of the shock with an orthogonal B-field.

Properties of the distribution of azimuthal magnetic field in a plasma flow during laboratory simulations of astrophysical jets in a plasma-focus installation

The results of laboratory simulations of astrophysical jets are presented. Plasma flows generated in the PF-3 plasma-focus installation of the NRC “Kurchatov Institute” and propagating to distances substantially exceeding their transverse dimensions are studied. It is shown usingmagnetic probes that the plasma flow propagates with a frozen-in magnetic field. The resulting radial distribution of the azimuthal magnetic field corresponds well to the distribution created by a longitudinal current of ~10 kA flowing in a region with a radius of 1–2 cm near the axis. Structures associated with return currents are observed at the periphery of the flow. The magnetic field decays rapidly as the flow propagates along the axis. Nevertheless, the leading lobe of the plasma flow is preserved to substantial distances in a neon discharge, possibly due to radiative cooling of the plasma.

Compression dynamics of quasi-spherical wire arrays with different linear mass profiles

Results of experimental studies of the implosion of quasi-spherical wire (or metalized fiber) arrays are presented. The goal of the experiments was to achieve synchronous three-dimensional compression of the plasma produced in different regions of a quasi-spherical array into its geometrical center. To search for optimal synchronization conditions, quasi-spherical arrays with different initial profiles of the linear mass were used. The following dependences of the linear mass on the poloidal angle were used: ml(θ) ∝ sin–1θ and ml(θ) ∝ sin–2θ. The compression dynamics of such arrays was compared with that of quasi-spherical arrays without linear mass profiling, ml(θ) = const. To verify the experimental data, the spatiotemporal dynamics of plasma compression in quasi-spherical arrays was studied using various diagnostics. The experiments on three-dimensional implosion of quasi-spherical arrays made it possible to study how the frozen-in magnetic field of the discharge current penetrates into the array. By measuring the magnetic field in the plasma of a quasi-spherical array, information is obtained on the processes of plasma production and formation of plasma flows from the wire/fiber regions with and without an additionally deposited mass. It is found that penetration of the magnetic flux depends on the initial linear mass profile ml(θ) of the quasi-spherical array. From space-resolved spectral measurements and frame imaging of plasma X-ray emission, information is obtained on the dimensions and shape of the X-ray source formed during the implosion of a quasi-spherical array. The intensity of this source is estimated and compared with that of the Z-pinch formed during the implosion of a cylindrical array.

CHARGED DUST GRAIN DYNAMICS SUBJECT TO SOLAR WIND, POYNTING–ROBERTSON DRAG, AND THE INTERPLANETARY MAGNETIC FIELD

ABSTRACT We investigate the combined effect of solar wind, Poynting–Robertson drag, and the frozen-in interplanetary magnetic field on the motion of charged dust grains in our solar system. For this reason, we derive a secular theory of motion by the means of an averaging method and validate it with numerical simulations of the unaveraged equations of motions. The theory predicts that the secular motion of charged particles is mainly affected by the z-component of the solar magnetic axis, or the normal component of the interplanetary magnetic field. The normal component of the interplanetary magnetic field leads to an increase or decrease of semimajor axis depending on its functional form and sign of charge of the dust grain. It is generally accepted that the combined effects of solar wind and photon absorption and re-emmision (Poynting–Robertson drag) lead to a decrease in semimajor axis on secular timescales. On the contrary, we demonstrate that the interplanetary magnetic field may counteract these drag forces under certain circumstances. We derive a simple relation between the parameters of the magnetic field, the physical properties of the dust grain, as well as the shape and orientation of the orbital ellipse of the particle, which is a necessary conditions for the stabilization in semimajor axis.

Neutrino magnetohydrodynamics

A new neutrino magnetohydrodynamics (NMHD) model is formulated, where the effects of the charged weak current on the electron-ion magnetohydrodynamic fluid are taken into account. The model incorporates in a systematic way the role of the Fermi neutrino weak force in magnetized plasmas. A fast neutrino-driven short wavelengths instability associated with the magnetosonic wave is derived. Such an instability should play a central role in strongly magnetized plasma as occurs in supernovae, where dense neutrino beams also exist. In addition, in the case of nonlinear or high frequency waves, the neutrino coupling is shown to be responsible for breaking the frozen-in magnetic field lines condition even in infinite conductivity plasmas. Simplified and ideal NMHD assumptions were adopted and analyzed in detail.

Frozen-In Magnetic Field Lines and Alfvén Wave Generation in Weakly Ionized Plasma

On the basis of the three-fluid approximation, we consider the generation of linear Alfven waves with periods \({\gtrsim}\,10^{-3}~\mbox{s}\) in the collisional partially ionized plasma of the solar photosphere. The results obtained in previous work (Tsap, Stepanov, and Kopylova in Solar Phys. 270, 205, 2011) are generalized for the case of the arbitrary ratio between the initial velocities of ions and neutral atoms. We find that the ponderomotive force plays an important role during Alfven wave excitation and propagation. Furthermore, the energy flux of Alfven waves does not depend on the degree of the plasma ionization if the magnetic field lines are frozen into the charged particles. These modes can be effectively generated in the weakly ionized plasma of the solar photosphere.

Lessons on collisionless reconnection from quantum fluids

Magnetic reconnection in space plasmas remains a challenge in physics in that the phenomenon is associated with the breakdown of frozen-in magnetic field in a collisionless medium. Such a topology change can also be found in superfluidity, known as the quantum vortex reconnection. We give a plasma physicists' view of superfluidity to obtain insights on essential processes in collisionless reconnection, including discussion of the kinetic and fluid pictures, wave dynamics, and time reversal asymmetry. The most important lesson from the quantum fluid is the scenario that reconnection is controlled by the physics of topological defects on the microscopic scale, and by the physics of turbulence on the macroscopic scale. Quantum vortex reconnection is accompanied by wave emission in the form of Kelvin waves and sound waves, which imprints the time reversal asymmetry.

Field topologies in ideal and near-ideal magnetohydrodynamics and vortex dynamics

Magnetic field topology frozen in ideal magnetohydrodynamics (MHD) and its breakage in near-ideal MHD are reviewed in two parts, clarifying and expanding basic concepts. The first part gives a physically complete description of the frozen field topology derived from magnetic flux conservation as the fundamental property, treating four conceptually related topics: Eulerian and Lagrangian descriptions of three dimensional (3D) MHD, Chandrasekhar-Kendall and Euler-potential field representations, magnetic helicity, and inviscid vortex dynamics as a fluid system in physical contrast to ideal MHD. A corollary of these developments clarifies the challenge of achieving a high degree of the frozen-in condition in numerical MHD. The second part treats field-topology breakage centered around the Parker Magnetostatic Theorem on a general incompatibility of a continuous magnetic field with the dual demand of force-free equilibrium and an arbitrarily prescribed, 3D field topology. Preserving field topology as a global constraint readily results in formation of tangential magnetic discontinuities, or, equivalently, electric current-sheets of zero thickness. A similar incompatibility is present in the steady force-thermal balance of a heated radiating fluid subject to an anisotropic thermal flux conducted strictly along its frozen-in magnetic field in the low-β limit. In a weakly resistive fluid the thinning of current sheets by these general incompatibilities inevitably results in sheet dissipation, resistive heating and topological changes in the field notwithstanding the small resistivity. Strong Faraday induction drives but also macroscopically limits this mode of energy dissipation, trapping or storing free energy in self-organized ideal-MHD structures. This property of MHD turbulence captured by the Taylor hypothesis is reviewed in relation to the Sun’s corona, calling for a basic quantitative description of the breakdown of flux conservation in the low-resistivity limit. A cylindrical initial-boundary value problem provides specificity in the general MHD ideas presented.

Laboratory model of magnetosphere created by strong plasma perturbation with frozen-in magnetic field

Transient interactions of a magnetic dipole with plasma flow carrying a southward magnetic field has been studied in laboratory experiments. Flow with a transverse frozen-in field was generated by means of laser-produced plasma cross-field expansion into background plasma, which filled a vacuum chamber, along with the external application of a magnetic field prior to interaction. Probe measurements showed that at the plasma parameters realized, effective collisionless Larmor coupling takes place resulting in the formation of strong compressive perturbations, which propagate in the background with super-Alfvenic velocity and generate a frame-transverse electric field comparable in value to the expected induction one in the laboratory. Compression pulses with a southward field interact with a dipole and create a well-defined magnetosphere after a short propagation. Comparison of the magnetospheres created by laser-produced plasma expanding in a vacuum field and in a magnetized background revealed fundamental differences in the structure and behaviour of the electric potential in plasma. In the presence of a frozen-in southward field direct «sub-solar» penetration of outside electric potential deep inside of the magnetosphere was observed to take place, with a velocity close to the upstream Alfven speed.

The thickness of a weakly magnetized accretion flow inside the last stable orbit of a Kerr black hole

If accretion disc contains weak frozen-in entangled magnetic fields, their dynamical effect may be important inside the last stable orbit because of the decompression near the sonic point. Here, I consider the radial and vertical structure of a nearly free-falling flow inside the last stable orbit of a thin disc around a Kerr black hole. The thickness of such a flow is determined primarily by the vertical stress created by radial and azimuthal magnetic fields. The thickness is predicted to oscillate vertically around its equilibrium value determined by the magnetic field balance with gravity. For thin discs, this thickness is much larger than that of the accretion disc itself. Numerical simulations with HARM2d show the vertical structure is more complicated. In particular, magnetically supported disc seems to be unstable to segregation of matter into thinner streams with the vertical scale determined by thermal pressure or other processes.

STEADY-STATE MAGNETOHYDRODYNAMIC FLOW AROUND AN UNMAGNETIZED CONDUCTING SPHERE

The non-collisional interaction between conducting obstacles and magnetized plasma winds can be found in different scenarios, from the interaction occurring between regions inside galaxy clusters to the interaction between the solar wind and Mars, Venus, active comets or even the interaction between Titan and the Saturnian's magnetospheric flow. These objects generate, through several current systems, perturbations in the streaming magnetic field leading to its draping around the obstacle's effective conducting surface. Recent observational results suggest that several properties associated with the magnetic field draping, such as the location of the polarity reversal layer of the induced magnetotail, are affected by variations in the conditions of the streaming magnetic field. To improve our understanding of these phenomena, we perform a characterization of several magnetic field draping signatures by analytically solving an ideal problem in which a perfectly conducting magnetized plasma (with frozen-in magnetic field conditions) flows around a spherical body for various orientations of the streaming magnetic field. In particular, we compute the shift of the inverse polarity reversal layer as the orientation of the background magnetic field is changed.