Magnetohydrodynamic Shock Research Articles

Entropy generation at multi-fluid magnetohydrodynamic shocks with emphasis to the solar wind termination shock

In a series of earlier papers, we developed expressions for ion and electron velocity distribution functions and their velocity moments at the passage over the solar wind termination shock. As we have shown there, with the introduction of appropriate particle invariants and the use of Liouville’s theorem one can get explicit solutions for the resulting total downstream pressure by adding up from partial pressure contributions of solar wind protons, solar wind electrons and pick-up protons. These expressions are the first step toward delivering the main contributions to the total plasma pressure in the downstream plasma flow and consistently determine the shock compression ratio. Here we start from these individual fluid pressures downstream of the shock and thereafter evaluate for the first time the shock-induced entropy production of the different fluids, when they are passing over the shock to the downstream side. As shown here, the resulting ion entropy production substantially deviates from earlier calculations using a pseudo-polytropic reaction of the ions to the shock compression, with polytropies selected to describe fluid-specific reactions at the shock passage similar to those seen by the Voyagers. From these latter models, ion entropy jumps are derived that depend on the pick-up ion abundance, while our calculations deliver an abundance-independent ion entropy production that only depends on the shock compression ratio and the tilt angle between the upstream magnetic field and the normal to the shock surface. We also show here that the thermodynamically permitted upper limit in the entropy production is only reached when strongly heated electrons are included in the entropy balance.

Impacts of pure shocks in the BHR71 bipolar outflow

During the formation of a star, material is ejected along powerful jets that impact the ambient material. This outflow regulates star formation by e.g. inducing turbulence and heating the surrounding gas. Understanding the associated shocks is therefore essential to the study of star formation. We present comparisons of shock models with CO, H2, and SiO observations in a 'pure' shock position in the BHR71 bipolar outflow. These comparisons provide an insight into the shock and pre-shock characteristics, and allow us to understand the energetic and chemical feedback of star formation on Galactic scales. New CO (Jup = 16, 11, 7, 6, 4, 3) observations from the shocked regions with the SOFIA and APEX telescopes are presented and combined with earlier H2 and SiO data (from the Spitzer and APEX telescopes). The integrated intensities are compared to a grid of models that were obtained from a magneto-hydrodynamical shock code which calculates the dynamical and chemical structure of these regions combined with a radiative transfer module based on the 'large velocity gradient' approximation. The CO emission leads us to update the conclusions of our previous shock analysis: pre-shock densities of 1e4 cm-3 and shock velocities around 20-25 km s-1 are still constrained, but older ages are inferred ( 4000 years). We evaluate the contribution of shocks to the excitation of CO around forming stars. The SiO observations are compatible with a scenario where less than 4% of the pre-shock SiO belongs to the grain mantles. We infer outflow parameters: a mass of 1.8x1e-2 Msun was measured in our beam, in which a momentum of 0.4 Msun km s-1 is dissipated, for an energy of 4.2x1e43erg. We analyse the energetics of the outflow species by species. Comparing our results with previous studies highlights their dependence on the method: H2 observations only are not sufficient to evaluate the mass of outflows.

Magnetohydrodynamic Cylindrical Shock in a Rotational Axisymmetric Non-Ideal Gas Under the Action of Monochromatic Radiation

A self-similar MHD cylindrical shock wave is investigated in a non-uniform rotating non-ideal gas under the action of monochro- matic radiation. The fluid velocities and the initial magnetic field of the ambient medium are assumed to be varying and obeying power laws. The gas is assumed to be non-ideal having infinite electrical conductivity and as the distance from the axis in- creases the angular velocity of the ambient medium decreases. Also, when the surrounding medium is of constant density then only similarity solutions exist. It is investigated that increase in the non-idealness of the gas, the adiabatic exponent of the gas and the strength of ambient magnetic field have decaying effect on the shock wave. Also, it is observed that an increase in the non-idealness of the gas and adiabatic exponent of the gas has same effect on the flow variables except the radial component of fluid velocity, the pressure and the magnetic field.

Effects of seed magnetic fields on magnetohydrodynamic implosion structure and dynamics

The effects of various seed magnetic fields on the dynamics of cylindrical and spherical implosions in ideal magnetohydrodynamics are investigated. Here, we present a fundamental investigation of this problem utilizing cylindrical and spherical Riemann problems under three seed field configurations to initialize the implosions. The resulting flows are simulated numerically, revealing rich flow structures, including multiple families of magnetohydrodynamic shocks and rarefactions that interact non-linearly. We fully characterize these flow structures, examine their axi- and spherisymmetry-breaking behaviour, and provide data on asymmetry evolution for different field strengths and driving pressures for each seed field configuration. We find that out of the configurations investigated, a seed field for which the implosion centre is a saddle point in at least one plane exhibits the least degree of asymmetry during implosion.

Solar Type II Radio Bursts Recorded by the Compound Astronomical Low-Frequency Low-Cost Instrument for Spectroscopy in Transportable Observatories in Brazil

It is well established that solar Type-II radio bursts are signatures of magnetohydrodynamical (MHD) shock waves propagating outward through the solar corona. Nevertheless, there are long-standing controversies about how these shocks are formed; solar flares and the coronal mass ejections (CMEs) are considered to be the most likely drivers. We present the results of the analysis of four solar Type-II bursts recorded between 20 January 2010 and 17 November 2011 by the Compound Astronomical Low-frequency Low-cost Instrument for Spectroscopy in Transportable Observatories (CALLISTO-BR) (in Brazil), which operates in the frequency range of 45 – 870 MHz. For all four solar Type-II radio bursts, which consisted of one event without band splitting and three split-band variants, the outcomes are consistent with those reported in the literature. All four Type-II radio bursts were accompanied by both solar flares and CMEs, which are associated with the impulsive phase of the flares and, very likely, with the acceleration phase of the CMEs.

A pressure-based high resolution numerical method for resistive MHD

In the paper we describe in detail a numerical method for the resistive magnetohydrodynamic (MHD) equations involving viscous flow and report the results of application to a number of typical MHD test cases. The method is of the finite volume type but mixes aspects of pressure-correction and density based solvers; the algorithm arrangement is patterned on the well-known PISO algorithm, which is a pressure method, while the flux computation makes use of the AUSM-MHD scheme, which originates from density based methods. Five groups of test cases are addressed to verify and validate the method. We start with two resistive MHD cases, namely the Shercliff and Hunt flow problems, which are intended to validate the method for low-speed resistive MHD flows. The remaining three test cases, namely the cloud-shock interaction, the MHD rotor and the MHD blast wave, are standard 2D ideal MHD problems that serve to validate the method under high-speed flow and complex interaction of MHD shocks. Finally, we demonstrate the method with a more complex application problem, and discuss results of simulation for a quasi–bi-dimensional self-field magnetoplasmadynamic (MPD) thruster, for which we study the effect of cathode length upon the electromagnetic nozzle performance.

Propagation of Magnetohydrodynamic Shock Waves

The propagation of magnetohydrodynamic shock waves in a self gravitating gas sphere has been studied. The shock is supposed to be generated as a result of sudden release of energy at the centre of symmetry. A similarity solution for the flow is developed. Numerical results for three different values of mach-number given by M/sup2/=200, 100 and 10 are obtained. The magnetic field affects the boundary conditions at the shock as well as the flow behind it. For a fixed increase M, the particle velocity, density and gas pressure decreases as the initial magnetic field increase. In the flow field behind the shock, there exists a transition region across which the effect of magnetic field is reversed.

A MAGNETOHYDRODYNAMIC MODEL OF THE M87 JET. II. SELF-CONSISTENT QUAD-SHOCK JET MODEL FOR OPTICAL RELATIVISTIC MOTIONS AND PARTICLE ACCELERATION

We describe a new paradigm for understanding both relativistic motions and particle acceleration in the M87 jet: a magnetically dominated relativistic flow that naturally produces four relativistic magnetohydrodynamic (MHD) shocks (forward/reverse fast and slow modes). We apply this model to a set of optical super- and subluminal motions discovered by Biretta and coworkers with the {\em Hubble Space Telescope} during 1994 -- 1998. The model concept consists of ejection of a {\em single} relativistic Poynting jet, which possesses a coherent helical (poloidal + toroidal) magnetic component, at the remarkably flaring point HST-1. We are able to reproduce quantitatively proper motions of components seen in the {\em optical} observations of HST-1 with the same model we used previously to describe similar features in radio VLBI observations in 2005 -- 2006. This indicates that the quad relativistic MHD shock model can be applied generally to recurring pairs of super/subluminal knots ejected from the upstream edge of the HST-1 complex as observed from radio to optical wavelengths, with forward/reverse fast-mode MHD shocks then responsible for observed moving features. Moreover, we identify such intrinsic properties as the shock compression ratio, degree of magnetization, and magnetic obliquity and show that they are suitable to mediate diffusive shock acceleration of relativistic particles via the first-order Fermi process. We suggest that relativistic MHD shocks in Poynting-flux dominated helical jets may play a role in explaining observed emission and proper motions in many AGNs.

On the structure of MHD shock waves in a viscous non-ideal gas

The structure of one-dimensional magnetohydrodynamics (MHD) shock waves is studied using the Navier–Stokes equations for the non-ideal gas phase. The exact solutions are obtained for the flow variables (i.e. particle velocity, temperature, pressure and change-in-entropy) within the shock transition region. The equation of state for a non-ideal gas is considered as given by Landau and Lifshitz. The effects of the non-idealness parameter and coefficient of viscosity of the gas are analysed on the flow variables assuming the magnetic field having only constant axial component. The findings confirm that the thickness of MHD shock front increases with decreasing values of the non-idealness parameter.

Oblique magnetohydrodynamic shocks: Space-like and time-like characteristics

Shock waves constitute discontinuities in matter which are relevant in the study of plasma behavior in astrophysical scenarios and in heavy-ion collision. They can produce conical emission in relativistic collisions and are also thought to be the mechanism behind the acceleration of energetic particles in active galactic nuclei and $\ensuremath{\gamma}$-ray bursts. The shocks are mostly hydrodynamic shocks. In a magnetic background they become magnetohydrodynamic (MHD) shocks. For that reason we study the space-like and time-like shock discontinuity in a magnetic plasma. The shocks induce a phase transition in the plasma, here assuming a transition from hadron to quarks. The MHD conservation conditions are derived across the shock. The conservation conditions are solved for downstream velocities and flow angles for given upstream variables. The shock conditions are solved at different baryon densities. For the space-like shocks the anisotropy in the downstream velocity arises due to the magnetic field. The downstream velocity vector always points downward with respect to the shock normal. With the increase in density the anisotropy is somewhat reduced. The magnetic field has effectively no impact on time-like shocks. The slight anisotropy in the downstream flow velocities is caused by the boosting that brings the quantities from the fluid frame to a normal incidence frame.

Time-dependent model of particle acceleration in the vicinity of approaching magnetohydrodynamic flows

Supernova explosions and powerful stellar winds with strong shocks can convert a sizeable part of the kinetic energy release into energetic particles. The starforming regions are argued as a favorable site of energetic particle acceleration and could be efficient sources of nonthermal emission. We present the analytic solution for the time-dependent diffusion-convection equation for the case of two approaching shocks. We also present here time-dependent model of particle acceleration in the vicinity of two closely approaching fast magnetohydrodynamic (MHD) shocks. Such MHD flows are expected to occur in rich young stellar cluster where a supernova is exploding in the vicinity of a strong stellar wind of a nearby massive star. We find that the spectrum of the high energy particles accelerated at the stage of two closely approaching shocks can be harder than that formed at a forward shock of an isolated supernova remnant. The presented method can be applied to model particle acceleration in a variety of systems with colliding MHD flows.

Mechanisms of field‐aligned current formation in magnetic reconnection

Satellite observations provide strong evidence for the generation of significant field‐aligned currents (FACs) during magnetic reconnection. Reconnection of antiparallel magnetic field does not generate FACs in magnetohydrodynamics (MHD) due to coplanarity in MHD shocks. However, a guide magnetic field and a sheared velocity component are almost always present at the magnetopause and their absence is a singular case. It is illustrated that the presence of these noncoplanar fields requires FACs. Contrary to intuition, such currents are generated more efficiently for a small guide field and are more likely to be a result of the redistribution of already present FACs for large guide fields. It is demonstrated that moderate values of shear flow can generate significant ionospheric FACs. Similar to shear flow, the presence of Hall physics leads to significant FACs and we examine the scaling of these current with the ion inertia length.

Impact of MHD shock physics on magnetosheath asymmetry and Kelvin‐Helmholtz instability

We have performed 13 three‐dimensional global magnetohydrodynamic (MHD) simulations of the magnetosheath plasma and magnetic field properties for Parker spiral (PS) and ortho‐Parker spiral interplanetary magnetic field (IMF) orientations corresponding to a wide range of solar wind plasma conditions. To study the growth of the Kelvin‐Helmholtz instability on the dawn and dusk flank magnetopause, we have performed 26 local two‐dimensional MHD simulations, with the initial conditions taken from global simulations on both sides of the velocity shear layer at the dawn‐dusk terminator. These simulations indicate that while the MHD physics of the fast shocks does not directly lead to strong asymmetry of the magnetosheath temperature for typical solar wind conditions, the magnetosheath on the quasi‐parallel shock side has a smaller tangential magnetic field along the magnetosheath flow which enables faster growth of the Kelvin‐Helmholtz instability (KHI). Because the IMF is statistically mostly in the PS orientation, the KHI formation may statistically favor the dawnside flank. For all the 26 simulations, the growth rates of the KHI correlated well with the ratio of the velocity shear and Alfvén speed along the wave vector, k. Dynamics of the KHI may subsequently lead to formation of kinetic Alfvén waves and reconnection in the Kelvin‐Helmholtz vortices which can lead to particle energization. This may partly help to explain the observed plasma sheet asymmetry of cold‐component ions, which are heated more on the dawnside plasma sheet.

MOLECULAR LINE EMISSION FROM MULTIFLUID SHOCK WAVES. I. NUMERICAL METHODS AND BENCHMARK TESTS

We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a neutral molecular fluid plus a fluid of ions and electrons. The scheme is based on operator splitting, wherein time integration of the governing equations is split into separate parts. In one part independent homogeneous Riemann problems for the two fluids are solved using Godunov's method. In the other equations containing the source terms for transfer of mass, momentum, and energy between the fluids are integrated using standard numerical techniques. We show that, for the frequent case where the thermal pressures of the ions and electrons are << magnetic pressure, the Riemann problems for the neutral and ion-electron fluids have a similar mathematical structure which facilitates numerical coding. Implementation of the scheme is discussed and several benchmark tests confirming its accuracy are presented, including (i) MHD wave packets ranging over orders of magnitude in length and time scales; (ii) early evolution of mulitfluid shocks caused by two colliding clouds; and (iii) a multifluid shock with mass transfer between the fluids by cosmic-ray ionization and ion-electron recombination, demonstrating the effect of ion mass loading on magnetic precursors of MHD shocks. An exact solution to a MHD Riemann problem forming the basis for an approximate numerical solver used in the homogeneous part of our scheme is presented, along with derivations of the analytic benchmark solutions and tests showing the convergence of the numerical algorithm.

Interaction of a biased cylinder with a flowing dusty plasma

AbstractExperimental observations of supersonically flowing dusty plasmas and their interaction with an electrically biased circular cylinder are presented. Two methods for producing flowing dusty plasmas are described. The dusty plasma is produced in a DC anode glow discharge plasma. In Configuration I, a secondary dust cloud, initially formed near a biased grid, flowed away from the grid at supersonic speeds when the grid voltage was suddenly changed. In Configuration II, a pencil-like dust beam was produced using a nozzle-like (converging-diverging) electrostatic potential structure. Using Configuration I, the streaming dust encountered a biased cylinder (wire) whose axis was oriented transverse to the dust flow. The flowing dust particles were repelled by the electrostatic field of the negatively charged cylinder, and a dust void was formed around the cylinder. A detached electrohydrodynamic bow shock, akin to the Earth's magnetohydrodynamic bow shock, was formed on the upstream side of the cylinder, while an extended teardrop-shaped wake region was formed on the downstream side. Video imaging of the dust stream allowed for observations of the structure and evolution of the bow shock. Configuration II was used to produce a narrow beam of dust particles and observe how the beam was deflected around the biased cylinder. Three multimedia files (movies) of the observed phenomena are provided in the online Supplementary material.

A pressure‐based method with AUSM‐type fluxes for MHD flows at arbitrary Mach numbers

SUMMARYIn this paper, we propose an extension of a PISO method, previously developed to solve the Euler equations, and which is here extended to the ideal magnetohydrodynamic (MHD) equations. By following a pressure‐based approach, we make use of the flexibility given by pressure equation for calculating flows at arbitrary Mach numbers. To handle MHD discontinuities, we have adapted the MHD‐Advection Upstream Splitting Method for our pressure‐based formulation. With the purpose of validation, four sets of test cases are presented and discussed. We start with the circularly polarized Alfvén waves that serves as a smooth flow validation. The second case is the 1‐D Riemann problem that is calculated using both 1‐D and 2‐D formulation of the MHD equations. The third and fourth problems are the Orszag–Tang vortex and the supersonic low‐ β cylinder allowing validation of the method in complex 2‐D MHD shock interaction. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Non-linear model of particle acceleration at colliding shock flows

Powerful stellar winds and supernova explosions with intense energy release in the form of strong shock waves can convert a sizeable part of the kinetic energy release into energetic particles. The starforming regions are argued as a favorable site of energetic particle acceleration and could be efficient sources of nonthermal emission. We present here a non-linear time-dependent model of particle acceleration in the vicinity of two closely approaching fast magnetohydrodynamic (MHD) shocks. Such MHD flows are expected to occur in rich young stellar cluster where a supernova is exploding in the vicinity of a strong stellar wind of a nearby massive star. We find that the spectrum of the high energy particles accelerated at the stage of two closely approaching shocks can be harder than that formed at a forward shock of an isolated supernova remnant. The presented method can be applied to model particle acceleration in a variety of systems with colliding MHD flows.

Magnetohydrodynamic Fast Shocks and Their Relation to Solar Energetic Particle Event Intensities

Gradual solar energetic particles (SEPs) are associated with interplanetary (IP) shock driven by coronal mass ejections. Testing theories/models that are built around shock acceleration mechanisms is difficult due to the complexity of SEP fluxes acquired by single-point measurements. To circumvent this, we correlate fast-forward shock Mach numbers derived from a 1.5D magnetohydrodynamics simulation with the intensity of solar energetic oxygen (O) and helium-4 (^4He) particles acquired by instruments aboard the ACE spacecraft during a series of coronal mass ejections in 2003 (October 28 - 31). A good correlation at the 5% significance level is found for O and ^4He with energy (E) > ~10 MeV n^(-1), with the peak correlation coefficient r = 0.82 for O (E = 63.8 - 89.8 MeV n^(-1)) and r = 0.77 for ^4He (E = 18.0 - 29.4 MeV n^(-1)), respectively, for hourly averaged data. This result not only bolsters the causal relationship between IP fast shocks and SEPs, but also suggests that the Mach number of IP shocks is one of the major controlling parameters for the intensity of SEPs measured in the near-Earth space.

Jump relations for magnetohydrodynamic shock waves in non-ideal gas flow

The generalized jump relations across the magnetohydrodynamic (MHD) shock front in non-ideal gas are derived considering the equation of state for non-ideal gas as given by Landau and Lifshitz. The jump relations for pressure, density, and particle velocity have been derived, respectively in terms of a compression ratio. Further, the simplified forms of the MHD shock jump relations have been obtained in terms of non-idealness parameter, simultaneously for the two cases viz., (i) when the shock is weak and, (ii) when it is strong. Finally, the cases of strong and weak shocks are explored under two distinct conditions viz., (i) when the applied magnetic field is strong and, (ii) when the field is weak. The aim of this paper is to contribute to the understanding of how shock waves behave in magnetized environment of non-ideal gases.

Probing magnetohydrodynamic shocks with high-JCO observations: W28F

Context. Observing supernova remnants (SNRs) and modelling the shocks they are associated with is the best way to quantify the energy SNRs re-distribute back into the Interstellar Medium (ISM). Aims. We present comparisons of shock models with CO observations in the F knot of the W28 supernova remnant. These comparisons constitute a valuable tool to constrain both the shock characteristics and pre-shock conditions. Methods. New CO observations from the shocked regions with the APEX and SOFIA telescopes are presented and combined. The integrated intensities are compared to the outputs of a grid of models, which were combined from an MHD shock code that calculates the dynamical and chemical structure of these regions, and a radiative transfer module based on the 'large velocity gradient' (LVG) approximation. Results. We base our modelling method on the higher J CO transitions, which unambiguously trace the passage of a shock wave. We provide fits for the blue- and red-lobe components of the observed shocks. We find that only stationary, C-type shock models can reproduce the observed levels of CO emission. Our best models are found for a pre-shock density of 104 cm-3, with the magnetic field strength varying between 45 and 100 {\mu}G, and a higher shock velocity for the so-called blue shock (\sim25 km s-1) than for the red one (\sim20 km s-1). Our models also satisfactorily account for the pure rotational H2 emission that is observed with Spitzer.