Magnetic Shock Research Articles

Magnetic flux shock waves and hydrodynamic dendritic instability in type-II superconducting film

In recent experiments, trapped magnetic flux is initially generated by abrupt laser heating of a strip of a type-II superconducting film subjected to a weak magnetic filed. We study herein the non-equilibrium penetration of a magnetic flux into the Meissner state area. A sharp shock wave (SW) front of the magnetic induction is formed due to the singularity of the resistivity at the transition from the mixed to the normal state. In vicinity of the front, superconductivity is suppressed by strong screening currents. The magnetic shock wave front and the temperature profile are moving with a constant velocity determined by the joule heat produced by the electric current in the normal domain at the flux front and the film thickness. It is shown that tangential instability is responsible for a crush of the straight front. For a sufficiently small heat diffusion constant, an ultra-fast dendrite-shaped magnetic flux structure is predicted, while for large thermal diffusion constant the shock wave front is found to be stable.

Magnetic flux shock wave and hydrodynamic dendritic instability in type-II superconducting film

Non-equilibrium flux penetration into the Meissner state in type-II superconducting film is studied. Effects of heat dissipation and transport on the motion and stability of the interface between the magnetic flux and flux-free domains are considered. It is shown that the magnetic induction and temperature, form shock wave with a narrow normal front moving with a constant velocity. It is shown that tangential instability is responsible for a crush of the shock wave front. For a sufficiently small heat diffusion constant, a ultrafast dendrite-shaped magnetic flux structure is predicted, while for large thermal diffusion the shock wave front is found to be stable. We conclude that the heat ballistic transport rather than magnetic non-locality in the film plays the essential role in the shock wave front properties. The dendritic velocity increases along with a reciprocal thickness of the film.

Protostar Formation in Magnetic Molecular Clouds beyond Ion Detachment. II. Typical Axisymmetric Solution

We follow the ambipolar-diffusion--driven formation and evolution of a fragment in a magnetically supported molecular cloud, until a hydrostatic protostellar core forms at its center. This problem was formulated in Paper I. We determine the density, velocity and magnetic field as functions of space and time, and the contribution of ambipolar diffusion and Ohmic dissipation to the resolution of the magnetic flux problem of star formation. The issue of whether the magnetic field ever decouples from the (neutral) matter is also addressed. We also find that the electrons do not decouple from the field lines before thermal ionization becomes important and recouples the magnetic field to the neutral matter. Ohmic dissipation becomes more effective than ambipolar diffusion as a flux reduction mechanism only at the highest densities (a few times 10^12 particles per cubic cm). In the high-density central parts of the core, the magnetic field acquires an almost spatially uniform structure, with a value that, at the end of the calculation (number density ~ 5 times 10^14 particles per cubic cm), is found to be in excellent agreement with meteoritic measurements of magnetic fields in the protosolar nebula. Outside the hydrostatic protostellar core, a concentration of magnetic flux (a "magnetic wall") forms, which gives rise to a magnetic shock. This magnetic shock is the precursor of the repeated shocks found by Tassis & Mouschovias (2005) which cause spasmodic accretion onto the hydrostatic core at later times.

Effects of overshoots on electron distributions upstream and downstream of quasi‐perpendicular collisionless shocks

We use test particle simulations to investigate the effect of overshoots on electron distributions upstream and downstream of quasi‐perpendicular collisionless shocks as functions of angle θbn between upstream magnetic field and shock normal. The main results are: (1) The development of overshoots leads to obvious loss cone structures in upstream electron distributions, increases the reflection of upstream electrons, and reduces the leakage of downstream electrons. An electron beam associated with the escape cutoff effect exists in upstream reduced electron distribution functions for large θbn shocks. (2) Overshoots significantly affect the downstream electron distribution, too, preventing the upstream and downstream electrons with high perpendicular speeds from crossing the shock and leading to a loss cone and beam features rather than arc features in downstream distributions. (3) The shock‐reflected electrons conserve their magnetic moments on average. Demagnetized electrons are mainly those transmitted, and most are overadiabatic electrons. The assumption of conservation of magnetic moment is an increasingly good approximation as θbn increases. (4) The major temporal changes in ramp overshoot structure expected from shock nonstationarity should lead to significant changes in electron distributions and associated waves upstream and downstream.

Protostar Formation in Magnetic Molecular Clouds beyond Ion Detachment. III. A Parameter Study

In two previous papers we formulated and solved, for a fiducial set of free parameters, the problem of the formation and evolution of a magnetically supercritical core inside a magnetically subcritical parent cloud. In this paper we present a parameter study to assess the sensitivity of the results (1) to the density at which the equation of state becomes adiabatic; (2) to the initial mass-to-flux ratio of the parent cloud; and (3) to ionization by radioactive decay of different nuclei (40K and 26Al) at high densities (number density > 10^12 particles per cubic cm). We find that (1) the results depend only slightly on the density at which the onset of adiabaticity occurs; (2) memory of the initial mass-to-flux ratio is completely lost at late times, which emphasizes the relevance of this work, idependently of the adopted theory of core formation; and (3) the precise source of radioactive ionization alters the degree of attachment of the electrons to the field lines (at high densities), and the relative importance of ambipolar diffusion and Ohmic dissipation in reducing the magnetic flux of the protostar. The value of the magnetic field at the end of the runs is insensitive to the values of the free parameters and in excellent agreement with meteoritic measurements of the protosolar nebula magnetic field. The magnetic flux problem of star formation is resolved for at least strongly magnetic newborn stars. A complete detachment of the magnetic field from the matter is unlikely. The formation of a "magnetic wall" (with an associated magnetic shock) is independent of the assumed equation of state, although the process is enhanced and accelerated by the formation of a central hydrostatic core.

Variations in the IMF vertical component in isolated solar wind streams

The regularities of the variations in the IMF Bz component have been studied based on the data on the solar wind streams and their solar sources. Isolated solar wind streams such as magnetic clouds and shock layers before them, undisturbed heliospheric current sheets (HCSs), leading edges and bodies of high-speed streams from coronal holes (HSSs from CHs) have been considered. It has been revealed that each type of isolated streams in the interplanetary medium has it own features in the variations in the value and direction of the Bz component related to the stream immanent properties and conditions of propagation in the interplanetary plasma. The appearance of the southward Bz component is obligatory for all these streams which are, therefore, geoeffective.

Cosmic ray anisotropies in the outer heliosphere

The observation of the directional distribution of energetic and cosmic ray particles has been done with the Voyager spacecraft over a long period. Since 2002, when the first flux enhancements of charged particles associated with the approach of Voyager 1 to the solar wind termination shock were observed, these anisotropy measurements have become of special interest. They play an important role to understand the magnetic field and shock structure and the basics of the modulation of cosmic ray and anomalous particles at and beyond the termination shock. They also serve as motivation to study the spatial behavior of galactic and anomalous cosmic ray anisotropies with numerical modulation models in order to illustrate how the radial anisotropy, at different energies, change from upstream to downstream of the termination shock. Observations made by Voyager 1 indicate that the termination shock is a complicated region than previously thought, hence the effects of the latitude dependence of the termination shock’s compression ratio and injection efficiency on the radial anisotropies of galactic and anomalous protons will be illustrated. We find that the magnitude and direction of the radial anisotropy strongly depends on the position in the heliosphere and the energy of particles. The effect of the TS on the radial anisotropy is to abruptly increase its value in the heliosheath especially in the A > 0 cycle for galactic protons and in both polarity cycles for anomalous protons. Furthermore, the global effect of the latitude dependence of the shock’s compression ratio is to increase the radial anisotropy for galactic protons throughout the heliosphere, while when combined with the latitude dependence of the injection efficiency this increase depends on modulation factors for anomalous protons and can even alter the direction of the radial anisotropy.

Electron‐Ion Coupling Upstream of Relativistic Collisionless Shocks

We argue and demonstrate by particle-in-cell simulations that the synchrotron maser instability could develop at the front of a relativistic, magnetized shock. The instability generates strong low-frequency electromagnetic waves propagating both upstream and downstream of the shock. Upstream of the shock, these waves make electrons lag behind ions so that a longitudinal electric field arises and the electrons are accelerated up to the ion kinetic energy. Then thermalization at the shock front results in a plasma with equal temperatures of electrons and ions. Downstream of the shock, the amplitude of the maser-generated wave may exceed the strength of the shock-compressed background magnetic field. In this case the shock-accelerated particles radiate via nonlinear Compton scattering rather than via a synchrotron mechanism. The spectrum of the radiation differs, in the low-frequency band, from that of the synchrotron radiation, providing possible observational tests of the model.

The Cosmic‐Ray Precursor of Relativistic Collisionless Shocks: A Missing Link in Gamma‐Ray Burst Afterglows

Collisionless shocks are commonly argued to be the sites of cosmic-ray (CR) acceleration. We study the influence of CRs on weakly magnetized relativistic collisionless shocks and apply our results to external shocks in gamma-ray burst (GRB) afterglows. The common view is that the transverse Weibel instability (TWI) generates a small-scale magnetic field that facilitates collisional coupling and thermalization in the shock transition. The TWI field is expected to decay rapidly, over a finite number of proton plasma skin depths from the transition. However, the synchrotron emission in GRB afterglows suggests that a strong and persistent magnetic field is present in the plasma that crosses the shock; the origin of this field is a key open question. Here we suggest that the common picture involving TWI demands revision. Namely, the CRs drive turbulence in the shock upstream on scales much larger than the skin depth. This turbulence generates a large-scale magnetic field that quenches TWI and produces a magnetized shock. The new field efficiently confines CRs and enhances the acceleration efficiency. The CRs modify the shocks in GRB afterglows at least while they remain relativistic. The origin of the magnetic field that gives rise to the synchrotron emission is plausibly in the CR-driven turbulence. We do not expect ultra-high-energy cosmic-ray production in external GRB shocks.

Giant Ringlike Radio Structures Around Galaxy Cluster Abell 3376

In the current paradigm of cold dark matter cosmology, large-scale structures are assembling through hierarchical clustering of matter. In this process, an important role is played by megaparsec (Mpc)-scale cosmic shock waves, arising in gravity-driven supersonic flows of intergalactic matter onto dark matter-dominated collapsing structures such as pancakes, filaments, and clusters of galaxies. Here, we report Very Large Array telescope observations of giant ( approximately 2 Mpc by 1.6 Mpc), ring-shaped nonthermal radio-emitting structures, found at the outskirts of the rich cluster of galaxies Abell 3376. These structures may trace the elusive shock waves of cosmological large-scale matter flows, which are energetic enough to power them. These radio sources may also be the acceleration sites where magnetic shocks are possibly boosting cosmic-ray particles with energies of up to 10(18) to 10(19) electron volts.

Heating and Nonthermal Particle Acceleration in Relativistic, Transverse Magnetosonic Shock Waves in Proton‐Electron‐Positron Plasmas

We report the results of 1D particle-in-cell simulations of ultrarelativistic shock waves in proton-electron-positron plasmas. We consider magnetized shock waves, in which the upstream medium carries a large scale magnetic field, directed transverse to the flow. Relativistic cyclotron instability of each species as the incoming particles encounter the increasing magnetic field within the shock front provides the basic plasma heating mechanism. The most significant new results come from simulations with mass ratio $m_p/m_\pm = 100$. We show that if the protons provide a sufficiently large fraction of the upstream flow energy density (including particle kinetic energy and Poynting flux), a substantial fraction of the shock heating goes into the formation of suprathermal power-law spectra of pairs. Cyclotron absorption by the pairs of the high harmonic ion cyclotron waves, emitted by the protons, provides the non-thermal acceleration mechanism. As the proton fraction increases, the non-thermal efficiency increases and the pairs' power-law spectra harden. We suggest that the varying power law spectra observed in synchrotron sources powered by magnetized winds and jets might reflect the correlation of the proton to pair content enforced by the underlying electrodynamics of these sources' outflows, and that the observed correlation between the X-ray spectra of rotation powered pulsars with the X-ray spectra of their nebulae might reflect the same correlation.

Formation of Spiral‐Arm Spurs and Bound Clouds in Vertically Stratified Galactic Gas Disks

(Abridged) We investigate the growth of spiral-arm substructure in vertically stratified, self-gravitating, galactic gas disks, using local numerical MHD simulations. Our new models extend our previous 2D studies (Kim & Ostriker 2002), which showed that a magnetized spiral shock in a thin disk can undergo magneto-Jeans instability (MJI), resulting in interarm spur structures and massive fragments. Similar spur features have recently been seen in high-resolution observations of several galaxies. Here, we consider two sets of numerical models: 2D models that use a thick-disk gravitational kernel, and 3D runs with explicit vertical stratification. When disks are sufficiently magnetized and self-gravitating, the result in both sorts of models is the growth of spiral-arm substructure similar to that in our previous razor-thin models. Reduced self-gravity in thick disks increases the spur spacing to ~10 times the Jeans length at the arm peak. Bound clouds that form from spur fragmentation have masses ~(1-3)x10^7 Msun each, a factor ~3-8 times larger than in razor-thin models with the same gas surface density and stellar spiral arm strength. We find that unmagnetized or weakly magnetized 2D models are unstable to the wiggle instability (WI) previously identified by Wada & Koda (2004), and proposed as a potential spur- and clump-forming mechanism. However,our fully 3D models do not show this effect. Non-steady motions and strong vertical shear prevent coherent vortical structures from forming, evidently suppressing the WI that appears in 2D (isothermal) runs. We also find no clear traces of Parker instability in the nonlinear spiral arm substructures that emerge (in self-gravitating models), although conceivably Parker modes may help seed the MJI at early stages since azimuthal wavelengths are similar.

Envelope expansion with core collapse - III. Similarity isothermal shocks in a magnetofluid

We explore magnetohydrodynamic (MHD) solutions for envelope expansions with core collapse (EECC) with isothermal MHD shocks in a quasi-spherical symmetry, and outline potential astrophysical applications of such magnetized shock flows. By including a random magnetic field in a gas medium, we further extend the recent isothermal shock results of Bian & Lou who have unified earlier similarity isothermal shock solutions of Tsai & Hsu, of Shu et al. and of Shen & Lou in a more general framework. MHD shock solutions are divided into three classes according to the downstream characteristics near the core. Class I solutions are those characterized by free-fall collapses towards the core downstream of an MHD shock, while Class II solutions are those characterized by Larson–Penston (LP) type near the core downstream of an MHD shock. Class III solutions are novel, sharing both features of Class I and II solutions with the presence of a sufficiently strong magnetic field as a prerequisite. Various MHD processes may occur within the regime of these isothermal MHD shock similarity solutions, such as submagnetosonic oscillations, free-fall core collapses, radial contractions and expansions. Both possibilities of perpendicular and oblique MHD shocks are analysed. Under the current approximation of MHD EECC (MEECC) solutions, only perpendicular shocks are systematically calculated. These similar MHD shocks propagate at either submagnetosonic or supermagnetosonic constant speeds. We can construct Class I, II and III MHD shocks matching with an isothermal magnetostatic outer envelope or an MHD breeze. We can also construct families of twin MHD shock solutions as well as an ‘isothermal MHD shock’ separating two magnetofluid regions of two different yet constant temperatures. The versatile behaviours of such MHD shock solutions may be utilized to model a wide range of astrophysical problems, including star formation in magnetized molecular clouds, ‘MHD champagne flows’ in H-ii regions around luminous massive OB stars, MHD link between the asymptotic giant branch (AGB) phase and the protoplanetary nebula (pPN) phase with a hot central magnetized white dwarf, relativistic MHD pulsar winds in supernova remnants (SNRs), radio afterglows of soft gamma-ray repeaters (SGRs) and so forth.

Divergence cleaning techniques in smoothed particle magnetohydrodynamics simulations

AbstractSmoothed Particle Magnetohydrodynamics (SPMHD) algorithms are tested with a Brio & Wu shocktube in order to find a suitable algorithm for treating magnetic shocks in clusters of galaxies. In particular the treatment of a nonvanishing divergence of B is discussed because of its appearance due to numerical errors. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On the Forming of Metallic Parts through Electromagnetic and Electrohydraulic Processing

Forming of metallic parts by the application of high intensity transitory magnetic pulses or shock waves is a challenge task from industrial perspectives as this offers extended scope of forming highly precise parts that result from material behavior at high deformation rates. Electromagnetic forming requires that the part must be intrinsically very conducting. The electrohydraulic forming is exempt from this material constraint as the deformation is generated by a shock wave in a fluid through electric discharge in between the electrodes. The application of a static pressure during forming is used to reduce the discharge energy for a given deformation. Work has been conducted to form different parts through these two techniques involving aluminum, copper and steels. The paper presents the technical obstacles still facing the electromagnetic techniques and gives examples of formed parts and joints in relation with microstructures.

Numerical 3+1 General Relativistic Magnetohydrodynamics: A Local Characteristic Approach

We present a general procedure to solve numerically the general relativistic magnetohydrodynamics (GRMHD) equations within the framework of the 3+1 formalism. The work reported here extends our previous investigation in general relativistic hydrodynamics (Banyuls et al. 1997) where magnetic fields were not considered. The GRMHD equations are written in conservative form to exploit their hyperbolic character in the solution procedure. All theoretical ingredients necessary to build up high-resolution shock-capturing schemes based on the solution of local Riemann problems (i.e. Godunov-type schemes) are described. In particular, we use a renormalized set of regular eigenvectors of the flux Jacobians of the relativistic magnetohydrodynamics equations. In addition, the paper describes a procedure based on the equivalence principle of general relativity that allows the use of Riemann solvers designed for special relativistic magnetohydrodynamics in GRMHD. Our formulation and numerical methodology are assessed by performing various test simulations recently considered by different authors. These include magnetized shock tubes, spherical accretion onto a Schwarzschild black hole, equatorial accretion onto a Kerr black hole, and magnetized thick accretion disks around a black hole prone to the magnetorotational instability.

The cluster relic source in A 521

We present high sensitivity radio observations of the merging cluster A 521, at a mean redshift z = 0.247. The observations were carried out with the GMRT at 610 MHz and cover a region of ∼1 square degree, with a sensitivity limit of 1 σ = 35 μJy b −1. The most relevant result of these observations is the presence of a radio relic at the cluster periphery, at the edge of a region where group infalling into the main cluster is taking place. Thanks to the wealth of information available in the literature in the optical and X-ray bands, a multi-band study of the relic and its surroundings was performed. Our analysis is suggestive of a connection between this source and the complex ongoing merger in the A 521 region. The relic might be “revived’ fossil radio plasma through adiabatic compression of the magnetic field or shock re-acceleration due to the merger events. We also briefly discussed the possibility that this source is the result of induced ram pressure stripping of radio lobes associated with the nearby cluster radio galaxy J0454–1016a. Allowing for the large uncertainties due to the small statistics, the number of radio emitting early-type galaxies found in A 521 is consistent with the expectations from the standard radio luminosity function for local ( z ⩽ 0.09) cluster ellipticals.

Magnetohydrodynamics in full general relativity: Formulation and tests

A new implementation for magnetohydrodynamics (MHD) simulations in full general relativity (involving dynamical spacetimes) is presented. In our implementation, Einstein's evolution equations are evolved by a Baumgarte-Shapiro-Shibata-Nakamura formalism, MHD equations by a high-resolution central scheme, and induction equation by a constraint transport method. We perform numerical simulations for standard test problems in relativistic MHD, including special relativistic magnetized shocks, general relativistic magnetized Bondi flow in stationary spacetime, and a long-term evolution for self-gravitating system composed of a neutron star and a magnetized disk in full general relativity. In the final test, we illustrate that our implementation can follow winding-up of the magnetic field lines of magnetized and differentially rotating accretion disks around a compact object until saturation, after which magnetically driven wind and angular momentum transport inside the disk turn on.

Dissipative Photosphere Models of Gamma‐Ray Bursts and X‐Ray Flashes

We consider dissipative effects occurring in the optically thick inner parts of the relativistic outflows producing gamma-ray bursts and X-ray flashes, emphasizing specially the Comptonization of the thermal radiation flux that is advected from the base of the outflow. Such dissipative effects --e.g. from magnetic reconnection, neutron decay or shocks -- would boost the energy density of the thermal radiation. The dissipation can lead to pair production, in which case the pairs create an effective photosphere further out than the usual baryonic one. In a slow dissipation scenario, pair creation can be suppressed, and the effects are most important when dissipation occurs below the baryonic photosphere. In both cases an increased photospheric luminosity is obtained. We suggest that the spectral peak in gamma ray bursts is essentially due to the Comptonized thermal component from the photosphere, where the comoving optical depth in the outflow falls to unity. Typical peak photon energies range between those of classical bursts and X-ray flashes. The relationship between the observed photon peak energy and the luminosity depends on the details of the dissipation, but under plausible assumptions can resemble the observed correlations.

Relativistic magnetohydrodynamics in dynamical spacetimes: Numerical methods and tests

Many problems at the forefront of theoretical astrophysics require the treatment of magnetized fluids in dynamical, strongly curved spacetimes. Such problems include the origin of gamma-ray bursts, magnetic braking of differential rotation in nascent neutron stars arising from stellar core collapse or binary neutron star merger, the formation of jets and magnetized disks around newborn black holes, etc. To model these phenomena, all of which involve both general relativity (GR) and magnetohydrodynamics (MHD), we have developed a GRMHD code capable of evolving MHD fluids in dynamical spacetimes. Our code solves the Einstein-Maxwell-MHD system of coupled equations in axisymmetry and in full $3+1$ dimensions. We evolve the metric by integrating the Baumgarte-Shapiro-Shibata-Nakamura equations, and use a conservative, shock-capturing scheme to evolve the MHD equations. Our code gives accurate results in standard MHD code-test problems, including magnetized shocks and magnetized Bondi flow. To test our code's ability to evolve the MHD equations in a dynamical spacetime, we study the perturbations of a homogeneous, magnetized fluid excited by a gravitational plane wave, and we find good agreement between the analytic and numerical solutions.