Slow Shocks Research Articles

Obliquely propagating low frequency electromagnetic shock waves in two dimensional quantum magnetoplasmas

Linear and nonlinear propagation characteristics of low frequency magnetoacoustic waves in quantum magnetoplasmas are studied employing the quantum magnetohydrodynamic model. In this regard, a quantum Kadomtsev–Petviashvili–Burgers (KPB) equation is derived using the small amplitude expansion method. The dissipation is introduced by taking into account the kinematic viscosity among the plasma constituents. Furthermore, the solution of KPB equation is presented using the tangent hyperbolic (tanh) method. The variation in the fast and slow magnetoacoustic shock profiles with the quantum Bohm potential via increasing number density, obliqueness angle θ, magnetic field, and the resistivity are also investigated. It is observed that the aforementioned plasma parameters significantly modify the propagation characteristics of nonlinear magnetoacoustic shock waves in quantum magnetoplasmas. The relevance of the present investigation with regard to dense astrophysical environments is also pointed out.

Drift ion acoustic shock waves in an inhomogeneous two-dimensional quantum magnetoplasma

Linear and nonlinear propagation characteristics of drift ion acoustic waves are investigated in an inhomogeneous quantum plasma with neutrals in the background employing the quantum hydrodynamics (QHD) model. In this regard, a quantum Kadomtsev–Petviashvili–Burgers (KPB) equation is derived for the first time. It is shown that the ion acoustic wave couples with the drift wave if the parallel motion of ions is taken into account. Discrepancies in the earlier works on drift solitons and shocks in inhomogeneous plasmas are also pointed out and a correct theoretical framework is presented to study the one-dimensional as well as the two-dimensional propagation of shock waves in an inhomogeneous quantum plasma. Furthermore, the solution of KPB equation is presented using the tangent hyperbolic (tanh) method. The variation of the shock profile with the quantum Bohm potential, collision frequency, and ratio of drift to shock velocity in the comoving frame, v∗/u, are also investigated. It is found that increasing the number density and collision frequency enhances the strength of the shock. It is also shown that the fast drift shock (i.e., v∗/u>0) increases, whereas the slow drift shock (i.e., v∗/u<0) decreases the strength of the shock. The relevance of the present investigation with regard to dense astrophysical environments is also pointed out.

Two‐spacecraft observations of an interplanetary slow shock

Slow‐mode shocks in space have been identified via one spacecraft observation by many authors since 1970. However, Feng et al. suggested that the analysis using single‐spacecraft observation based only on the Rankine‐Hugoniot relations could misinterpret a tangential discontinuity as a slow shock. In this paper, we identify a slow‐mode shock using a model fitting based on both the Rankine‐Hugoniot relations and intraspacecraft timing. As a result, we found a slow‐shock solution that, including the local parameters and propagation time, agrees well with the observations. The slow shock may be associated with an asymmetric reconnection exhaust at a heliospheric current sheet.

Parametric interaction of coronal loops with p modes

Parametric interaction of coronal loops with p modes

GAS-DYNAMIC SHOCK HEATING OF POST-FLARE LOOPS DUE TO RETRACTION FOLLOWING LOCALIZED, IMPULSIVE RECONNECTION

We present a novel model in which shortening of a magnetic flux tube following localized, three-dimensional reconnection generates strong gas-dynamic shocks around its apex. The shortening releases magnetic energy by progressing away from the reconnection site at the Alfven speed. This launches inward flows along the field lines whose collision creates a pair of gas-dynamic shocks. The shocks raise both the mass density and temperature inside the newly shortened flux tube. Reconnecting field lines whose initial directions differ by more that 100 degrees can produce a concentrated knot of plasma hotter that 20 MK, consistent with observations. In spite of these high temperatures, the shocks convert less than 10% of the liberated magnetic energy into heat - the rest remains as kinetic energy of bulk motion. These gas-dynamic shocks arise only when the reconnection is impulsive and localized in all three dimensions; they are distinct from the slow magnetosonic shocks of the Petschek steady-state reconnection model.

Conditions for substorm onset by the fast reconnection mechanism

Abstract. The fast reconnection mechanism, involving slow shocks and Alfvénic fast plasma jets, is most responsible for the explosive conversion of magnetic energy associated with geomagnetic substorms and solar flares. In this paper, the spontaneous fast reconnection model is applied to well-known phenomena of substorms. When the east-west width of the tail current sheet becomes 3–4 times larger than its north-south thickness, the fast reconnection mechanism can fully be established, which may lead to substorm onset. The resulting Alfvénic jet can exactly explain, both qualitatively and quantitatively, the in-situ satellite observations of the traveling compression regions (TCRs) associated with large-scale plasmoids propagating down the tail. Also, the earthward fast reconnection jet causes drastic magnetic field dipolarization, so that the sheet current ahead of the magnetic loop of closed field lines suddenly turns its direction toward the loop footpoint and a large-scale current wedge is formed according to the growth of field-aligned currents. It is demonstrated that an MHD generator arises ahead of the magnetic loop and drives the current wedge to distinctly enhance the current density in a pair of thin layers of the loop footpoint, giving rise to drastic heating in the form of two ribbons.

DISSIPATIVE ENTROPY AND GLOBAL SMOOTH SOLUTIONS IN RADIATION HYDRODYNAMICS AND MAGNETOHYDRODYNAMICS

The equations of ideal radiation magnetohydrodynamics (RMHD) serve as a fundamental mathematical model in many astrophysical applications. It is well known that radiation can have a damping effect on solutions of associated initial-boundary-value problems. In other words, singular solutions like shocks can be prohibited. In this paper, we consider discrete-ordinate approximations of the RMHD-system for general equations of state. If the magnetic fields are absent (i.e. if we consider radiation hydrodynamics), we prove the existence of global-in-time classical solutions for the Cauchy problem in one space dimension under an appropriate smallness condition on the inital data. We also show that counterparts of the compressive shock waves for the full RHD case and counterparts of the slow and fast MHD shock waves for the full RMHD-system can have structures in the presence of radiation if the amplitude is sufficiently small. Moreover, a new entropy function for the RMHD-system is presented.

Nonlinear fast magnetoacoustic wave propagation in the neighbourhood of a 2D magnetic X-point: oscillatory reconnection

This paper extends the models of Craig & McClymont (1991) and McLaughlin & Hood (2004) to include finite $\beta$ and nonlinear effects. We investigate the nature of nonlinear fast magnetoacoustic waves about a 2D magnetic X-point. We solve the compressible and resistive MHD equations using a Lagrangian remap, shock capturing code (Arber et al. 2001) and consider an initial condition in $ {\bf{v}}\times{\bf{B}} \cdot {\hat{\bf{z}}}$ (a natural variable of the system). We observe the formation of both fast and slow oblique magnetic shocks. The nonlinear wave deforms the X-point into a 'cusp-like' point which in turn collapses to a current sheet. The system then evolves through a series of horizontal and vertical current sheets, with associated changes in connectivity, i.e. the system exhibits oscillatory reconnection. Our final state is non-potential (but in force balance) due to asymmetric heating from the shocks. Larger amplitudes in our initial condition correspond to larger values of the final current density left in the system. The inclusion of nonlinear terms introduces several new features to the system that were absent from the linear regime.

The disruption of the Magellanic Stream

AbstractWe present evidence that the accretion of warm gas onto the Galaxy today is at least as important as cold gas accretion. For more than a decade, the source of the bright Hα emission (up to 750 mR†) along the Magellanic Stream has remained a mystery. We present a hydrodynamical model that explains the known properties of the Hα emission and provides new insights on the lifetime of the Stream clouds. The upstream clouds are gradually disrupted due to their interaction with the hot halo gas. The clouds that follow plough into gas ablated from the upstream clouds, leading to shock ionisation at the leading edges of the downstream clouds. Since the following clouds also experience ablation, and weaker Hα (100–200 mR) is quite extensive, a disruptive cascade must be operating along much of the Stream. In order to light up much of the Stream as observed, it must have a small angle of attack (≈ 20°) to the halo, and this may already find support in new H i observations. Another prediction is that the Balmer ratio (Hα/Hβ) will be substantially enhanced due to the slow shock; this will soon be tested by upcoming WHAM observations in Chile. We find that the clouds are evolving on timescales of 100–200 Myr, such that the Stream must be replenished by the Magellanic Clouds at a fairly constant rate (≳ 0.1 M⊙ yr−1). The ablated material falls onto the Galaxy as a warm drizzle; diffuse ionized gas at 104 K is an important constituent of galactic accretion. The observed Hα emission provides a new constraint on the rate of disruption of the Stream and, consequently, the infall rate of metal-poor gas onto the Galaxy. When the ionized component of the infalling gas is accounted for, the rate of gas accretion is ≳ 0.4 M⊙ yr−1, roughly twice the rate deduced from H i observations alone.

Warm gas accretion onto the Galaxy

AbstractWe present evidence that the accretion of warm gas onto the Galaxy today is at least as important as cold gas accretion. For more than a decade, the source of the bright Hα emission (up to 750 mR†) along the Magellanic Stream has remained a mystery. We present a hydrodynamical model that explains the known properties of the Hα emission and provides new insights on the lifetime of the Stream clouds. The upstream clouds are gradually disrupted due to their interaction with the hot halo gas. The clouds that follow plough into gas ablated from the upstream clouds, leading to shock ionisation at the leading edges of the downstream clouds. Since the following clouds also experience ablation, and weaker Hα (100–200 mR) is quite extensive, a disruptive cascade must be operating along much of the Stream. In order to light up much of the Stream as observed, it must have a small angle of attack (≈ 20°) to the halo, and this may already find support in new Hi observations. Another prediction is that the Balmer ratio (Hα/Hβ) will be substantially enhanced due to the slow shock; this will soon be tested by upcoming WHAM observations in Chile. We find that the clouds are evolving on timescales of 100–200 Myr, such that the Stream must be replenished by the Magellanic Clouds at a fairly constant rate (≳ 0.1 M⊙ yr−1). The ablated material falls onto the Galaxy as a warm drizzle; diffuse ionized gas at 104 K is an important constituent of galactic accretion. The observed Hα emission provides a new constraint on the rate of disruption of the Stream and, consequently, the infall rate of metal-poor gas onto the Galaxy. We consider the stability of Hi clouds falling towards the Galactic disk and show that most of these must break down into smaller fragments that become partially ionized. The Galactic halo is expected to have huge numbers of smaller neutral and ionized fragments. When the ionized component of the infalling gas is accounted for, the rate of gas accretion is ~0.4 M⊙ yr−1, roughly twice the rate deduced from Hi observations alone.

Observations of a switch‐off shock in interplanetary space

An interplanetary slow shock event was observed by Voyager 1 on 1 November 1980. The structure is identified to be a switch‐off shock which is a special type of slow shocks by fitting the Rankine‐Hugoniot relations. The shock has the following properties: (1) Observed parameters meet the R‐H relations well. (2) Number density increases from the upstream region to the downstream region. On the contrary, total magnetic field strength decreases. (3) The slow‐mode Mach number is greater than unity in the preshock state and less than unity in the postshock state. (4) The normal Alfvén‐Mach number is almost equal to 1 in the preshock state; the tangential component of the downstream magnetic field is “turned off,” leaving only a minor quantity along the shock normal.

Analysis of the protective effect of shock-absorbing shoes for patients treated with hip and knee endoprostheses

Biomechanical loading of total knee and hip replacement is one of the essential factors which limit the longterm-function of the implant components. A simple and cheap safety provision to avoid mechanical overload seems to be wearing of shock-absorbing shoes. The performed study analyzes the effect of that type of shoe. For judgement the parameters: energy absorption while slow shock, damping while hard shock and safety against sliding were taken. The experiments showed the shock-absorbing shoe is an easy, inexpensive, but very efficient protection measure to improve the longterm-stability of endoprosthesis of the lower extremity.

Optimizing the fragmentation and clearance after shock wave lithotripsy

Shock wave lithotripsy is the treatment of choice for small renal and upper ureteric stones. This review examines the factors that improve fragmentation and clearance of stones, and recent advances in this area. Several randomized trials published recently have demonstrated the role of tamsulosin in helping the clearance of ureteric fragments after shock wave lithotripsy. The role of slow shock wave delivery rate has been well established. Percussion, diuresis and inversion have been used to improve results in lower calyceal stones. Few clinical studies have explored the role of position during treatment. The effects of progressive increase of lithotripter output have been demonstrated only in experimental studies. Tamsulosin can be used to increase clearance, and reduce episodes of ureteric colic and the need for analgesics after shock wave lithotripsy. Shock waves at slow rate improve both the safety and efficacy of shock wave lithotripsy. Percussion, diuresis and inversion augments clearance of lower calyceal fragments.

A Shock Fitting Procedure Based on Monte Carlo Calculations: Application to Slow Shocks

Recent derived procedure of fitting the Rankine‐Hugoniot shock jump relations for fast MHD shocks (Lin et al., 2006) is here applied to slow‐mode shocks. The present paper is a continuation of Lin et al. (2006). We modify the method to be applicable to slow shocks. We have tested the new method via a simulated slow shock. The result shows that the method can find a best fit solution that is close to the “true answer” as long as the systematic errors in the synthetic data are not too large. We also apply the method to one interplanetary slow shock and two slow shocks observed in the magnetotail. The results have been compared to the previous studies. The new method of shock fitting is demonstrated successfully for identifying slow shocks.

Energy balance in the course of relativistic magnetic reconnection

Magnetic reconnection plays an important role in space physics, for example, in Earth's magnetosphere, on the Sun, in the magnetospheres of magnetars, pulsars, black holes, etc. Reconnection starts with abrupt drop of plasma conductivity in a small part of a current sheet, so called, diffusion region. As a result electric field is generated and is transferred by relativistic MHD surface wave from the diffusion region to the current sheet which leads to decay of the disturbed part of the current sheet into a system of slow shocks. Plasma is highly accelerated and heated at the shock fronts forming outflow region with relativistic plasma jets and weak magnetic field (Semenov & Bernikov 1991). At some stage the reconnection process has to switch-off, then outflow regions must detach from the site where the electric field was initiated, and propagate along the current sheet as solitary waves (Tolstykh et al. 2005). The energy balance of relativistic reconnection is investigated in details. It is shown that magnetic and thermal energy from the inflow region is spent for acceleration and heating of the plasma in jets. It is interesting that the temperature of the plasma in the wake of the propagating outflow regions drops after each pulse of reconnection. This differ from usual explosion which heats the plasma behind the shock front (Tolstykh et al. 2007).

Structure of fast shocks in the presence of heat conduction

There are three types of magnetohydrodynamic (MHD) shocks: the fast shock, intermediate shock, and slow shock. The structure of slow shocks and intermediate shocks in the presence of heat conduction has been studied earlier [C. L. Tsai, R. H. Tsai, B. H. Wu, and L. C. Lee, Phys. Plasmas 9, 1185 (2002); C. L. Tsai, B. H. Wu, and L. C. Lee, Phys. Plasmas 12, 82501 (2005)]. Based on one-dimensional MHD numerical simulations with a heat conduction term, the evolution and structure of fast shocks are studied. The fast shock will form a foreshock in the presence of heat conduction. The foreshock is formed due to the heat flow from downstream to upstream and located in the immediate upstream of the main shock. In the steady state, the value of diffusion velocity Vd in the foreshock is found to nearly equal the upstream convection velocity in the fast shock frame. It is found that the density jump across the main shock in high Mach number case can be much larger than 4 in the early simulation time. However the density jump will gradually evolve to a value smaller than 4 at steady state. By using the modified Rankine-Hugoniot relations with heat flux, the density jump across the fast shock is examined for various upstream parameters. The results show that the calculated density jump with heat flux is very close to the simulation value and the density jump can far exceed the maximum value of 4 without heat conduction. The structure of foreshock and main shock is also studied under different plasma parameters, such as the heat conductivity K0, the ratio of upstream plasma pressure to magnetic pressure β1, Alfvén Mach number MA1, and the angle θ1 between shock normal and magnetic field. It is found that as the upstream shock parameters K0, β1, and MA1 increase or θ1 decreases, the width of foreshock Ld increases. The present results can be applied to fast shocks in the solar corona, solar wind, and magnetosphere, in which the heat conduction effects are important.

From Rankine‐Hugoniot relation fitting procedure: Tangential discontinuity or intermediate/slow shock?

To identify an observed intermediate/slow shock, it is important to fit the measured magnetic fields and plasma on both sides using Rankine‐Hugoniot (R‐H) relations. It is not reliable to determine an intermediate/slow shock only by the shock properties and fitting procedure based on one spacecraft observation, though previous reported intermediate/slow shocks are confirmed in such a way. We investigated two shock‐like discontinuities, which satisfy the R‐H relations well. One meets the criterions of slow shocks and was reported as a slow shock, and another has all the characters of intermediate shock based on one spacecraft observation. However, both discontinuities also meet the requirements of tangential discontinuities and were confirmed as tangential discontinuities on large‐scale perspective by using multi‐spacecraft observations. We suggest that intermediate/slow shocks should be identified as carefully as possible and had better be determined by multi‐spacecraft.

A Resistive MHD Simulation of the Shear Flow Effects on the Structure of Reconnection Layer

By using a one-dimensional resistive magnetohydrodynamic (MHD)model, the Riemann problem is solved numerically for the structureof the reconnection layer under a sheared flow along theanti-parallel magnetic field components. The simulation is carriedout for general cases with symmetric or asymmetric plasma densitiesand magnetic fields on the two sides of the initial current sheet,and cases with or without a guide magnetic field, as in variousspace and fusion plasmas. The generation of MHD discontinuities inthe reconnection layer is discussed, including time-dependentintermediate shocks, intermediate shocks, slow shocks, slowexpansion waves, and the contact discontinuity. It is shown that thestructure of the reconnection layer is significantly affected by thepresence of the shear flow. For an initial symmetric current sheet,the symmetry condition is altered due to the shear flow. For caseswith an asymmetric initial current sheet, as at the Earth'smagnetopause, the strengths of MHD discontinuities changesignificantly with the shear flow speed. Moreover, the generalresults for the reconnection layers in the outflow regions on eitherside of the X line are discussed systematically for the first time.

V arc interplanetary coronal mass ejections observed with the Solar Mass Ejection Imager

Since February 2003, the Solar Mass Ejection Imager (SMEI) has been observing interplanetary coronal mass ejections (ICMEs) at solar elongation angles ε > 20°. The ICMEs generally appear as loops or arcs in the sky, but five show distinct outward concave shapes that we call V arcs. We expect to observe some V arcs, formed by trailing edges of ICME flux ropes or by leading ICME edges sheared by solar wind (SW) speed gradients at the heliospheric current sheet. We characterize the properties of these V arcs and compare them with average properties of all SMEI ICMEs. The typical V arc speeds argue against a slow MHD shock interpretation for their structures. We estimate the V arc solar source locations and their opening angle dynamics as tests for SW shearing. The first test contradicts but the second supports the SW shearing explanation. The implications of the small number of V arcs observed with SMEI is considered. The point P approximation used to determine the V arc locations and inferred solar source regions is critically examined in Appendix A.

Kinetic Alfvén waves and electron physics. II. Oblique slow shocks

One-dimensional (1D) particle-in-cell (PIC; kinetic ions and electrons) and hybrid (kinetic ions; adiabatic and massless fluid electrons) simulations of highly oblique slow shocks (θBn=84° and β=0.1) [Yin et al., J. Geophys. Res., 110, A09217 (2005)] have shown that the dissipation from the ions is too weak to form a shock and that kinetic electron physics is required. The PIC simulations also showed that the downstream electron temperature becomes anisotropic (Te‖>Te⊥), as observed in slow shocks in space. The electron anisotropy results, in part, from the electron acceleration/heating by parallel electric fields of obliquely propagating kinetic Alfvén waves (KAWs) excited by ion-ion streaming, which cannot be modeled accurately in hybrid simulations. In the shock ramp, spiky structures occur in density and electron parallel temperature, where the ion parallel temperature decreases due to the reduction of the ion backstreaming speed. In this paper, KAW and electron physics in oblique slow shocks are further examined under lower electron beta conditions. It is found that as the electron beta is reduced, the resonant interaction between electrons and the wave parallel electric fields shifts to the tail of the electron velocity distribution, providing more efficient parallel heating. As a consequence, for βe=0.02, the electron physics is shown to influence the formation of a θBn=75° shock. Electron effects are further enhanced at a more oblique shock angle (θBn=84°) when both the growth rate and the range of unstable modes on the KAW branch increase. Small-scale electron and ion phase-space vortices in the shock ramp formed by electron-KAW interactions and the reduction of the ion backstreaming speed, respectively, are observed in the simulations and confirmed in homogeneous geometries in one and two spatial dimensions in the accompanying paper [Yin et al., Phys. Plasmas 14, 062104 (2007)]. Results from this study conclude that the inability of the hybrid method to model the Landau resonance of KAW with electrons and the resulting time-evolving electron parallel heating lead to differences between the PIC and hybrid simulations.