Slow Shocks Research Articles

A new look at driven magnetic reconnection at the terrestrial subsolar magnetopause

The physics of steady driven magnetic reconnection at Earth's subsolar magnetopause is addressed. Three‐dimensional, global magnetohydrodynamics (MHD) simulations of the magnetopause are compared with analytical solutions of the resistive MHD equations [Sonnerup and Priest, 1975] corresponding to magnetic field annihilation driven by an incompressible stagnation point flow. The simulations demonstrate that under steady southward interplanetary magnetic field conditions and when the plasma resistivity is spatially uniform, subsolar magnetopause reconnection occurs in long, thin Sweet‐Parker current sheets via a flux pileup mechanism [Sonnerup and Priest, 1975; Priest and Forbes, 1986] (rather than in Petschek slow shock configurations). Magnetic energy piles up upstream of the magnetopause current sheet to accommodate the sub‐Alfvénic solar wind inflow. The scaling of the pileup with Lundquist number, S, is consistent (approximately ∝ S1/4) with that predicted by the analytical, incompressible stagnation point flow solutions (though there are small corrections due to plasma compressibility in the simulations). Since there is a finite energy in the magnetosheath available to drive the magnetic pileup (and associated rapid magnetic reconnection), we expect the pileup to saturate and the reconnection rate to drop as the upstream plasma pressure drops to accommodate the pileup. Thus we expect the reconnection to stall, the rate vanishing in the limit S → ∞. We discuss the role of Hall electric fields in allowing the magnetic pileup to saturate before the reconnection begins to stall, permitting Alfvénic reconnection to occur in thin current sheets in the limit S → ∞.

Can ion-neutral damping help to form spicules?

The possible mechanism of generation of spicules by Alfvenic disturbances is studied in dissipative MHD where dissipation is mainly caused by ion-neutral collision damping, as suggested by Haerendel (1992). Ion-neutral damping becomes non-negligible in the upper chromosphere at high cyclic frequencies of typically greater than 0.1 Hz, and the potential role played by this effect in both forming and supporting solar spicules is investigated. The propagation of randomly generated Alfvenic disturbances on vertically open solar magnetic flux tubes is considered. The flux tubes are taken to be axisymmetric and initially untwisted with the field strength declining from 1600 G in the photo- sphere to 20 G in the corona. Their propagation is investigated by numerically solving a set of fully nonlinear, dissipative 1.5D MHD equations with waves being generated by a continuous random driver introduced into the equation of angular mo- mentum in the low atmosphere of the Sun. This work is a continuation of James et al. (2003) which studied the results for a continuous, monochromatic sinusoidal driver. As with the previous study, spicule-like structures were formed. The formation was again found to be primarily caused by the impact of a series of slow shocks generated by the continuous interaction between the upward propagating driven disturbance and the downward propagating disturbances reflected by the transition region. The formation was aided by the increased ther- mal pressure gradient caused by Joule heating due to ion-neutral collisions. There is some indication that an analogue of the momentum transfer effect suggested by Haerendel (1992) for simple sinusoidal waves is at work, but this effect on it's own is at best only of a similar order as the reduction in height caused by including damping in the first place. However, the effect is highly sensitive to the level of ionisation and therefore to the energy balance. Including the effects of thermal conduction and radiation may well lead to different results and thus it would be premature to dismiss the mechanism completely at this point. Significant damping and heating was again observed, strengthening the previously made suggestions that ion-neutral damping may play a more important role in the dynamics of the upper chromosphere than normally assumed in numerical simulations (where it is often neglected completely), although a treatment of radiative losses must be included before this can be confirmed. The heating provided by ion-neutral damping may be an appropriate counter to the low temperatures suffered by other mechanisms better able to reproduce spicule dynamics.

Shock-like free-surface perturbations in low-surface-tension, viscous, thin-film flow exterior to a rotating cylinder

Continuing from the work of Hinch & Kelmanson (2003 Proc. R. Soc. Lond. A459, 1193–1213), the lubrication approximation is used to investigate the drift and decay of free–surface perturbations in the viscous flow exterior to a circular cylinder rotating about its horizontal axis in a vertical gravitational field. Non–dimensional parameters corresponding to gravity, γ = ρg bar{ h } 2 /3 ωμa , and surface tension, α = γ h 3 /3 ωμa 4 , are used to characterize the flow, where ω and a are respectively the angular velocity and radius of the cylinder, μ , ρ , σ and h are respectively the kinematic viscosity, density, surface tension and mean film thickness of the fluid, and g is the acceleration due to gravity. Within the parameter hierarchy γ 2 << α γ α = o ( γ 2 ), the low–harmonic asymptotics of Hinch & Kelmanson (2003) cannot represent the shock–like solutions manifest in numerical simulations. Accordingly, the case of vanishingly small surface tension is investigated herein, and the resulting shock–like solutions are analysed. When the surface tension is identically zero, the resulting Hamiltonian problem may be solved explicitly via the method of characteristics, action–angle variables and strained–coordinate asymptotic expansions, which reveal a shock–formation time–scale of ω 2 μ 3 a 3 / 3 g 3 h 6 . The strained (fast) time–scale which can be deduced a priori via action–angle variables, is consistent with that obtained via the independent asymptotic approach of Hinch & Kelmanson (2003), and the (slow) shock time–scale T = 30 γ 3 t is derived and confirmed via spectral numerical integrations of the full lubrication approximation with vanishingly small, non–zero surface tension. With β = α /30 γ 3 O ( β 1/3 ) is discovered, and the leading–order transient in the surface elevation is found to satisfy a Kuramoto–Sivashinsky evolution equation, which is solved via multiple scales for the extreme cases β β >> 1, and numerically otherwise. A universal scaling of the transient results is discovered which gives good agreement with the quasi–steady shock solution, even when the transient shock thickens in response to its decreasing amplitude. Depending upon critical values of α / γ 2 , β and γ , the transient solution is discovered to decay in one of only four possible sequences comprising one or more of T −1 , T −½ and exp(−81 αγ 2 t ). Physical data indicate that all four decay sequences are observable in practice.

Walén and slow‐mode shock analyses in the near‐Earth magnetotail in connection with a substorm onset on 27 August 2001

We have examined Cluster spacecraft 1 (C1) magnetic field and particle observations from 27 August 2001 when the Cluster spacecraft separation was less than 0.27 RE and the spacecraft were located near the equatorial plane of the postmidnight magnetotail at xGSM ∼ −19 RE and yGSM ∼ −2.1 RE. A detailed examination of observations recorded between 0350 UT and 0435 UT is performed with special emphasis on the plasma flow reversal from strong tailward flows to earthward flows in the approximate time interval 0400 UT to 0410 UT. Evidence for the expansion phase onset of an isolated substorm between ∼0406 UT and ∼0408 UT was reported by Baker et al. [2002]. During the 0400–0410 UT interval, C1 was located in the plasma sheet where the observed plasma density N ∼ 0.3 cm−3 and the plasma ion β ∼ 1.5. The Walén analysis applied to the tailward flow interval from 0400:36 UT to 0403:14 UT is consistent with the ions being accelerated to ∼73% of the Alfvén speed across a slow‐mode shock connected to a near‐Earth neutral line located on the earthward side of the spacecraft. The occurrence of a small plasmoid‐type magnetic flux rope during the leading edge of the tailward flows provides further support in favor of an active region of magnetic reconnection earthward of Cluster. The more field‐aligned earthward flows between 0406 UT and 0408 UT, however, failed to satisfy the Walén test. Rankine‐Hugoniot analyses of upstream and downstream plasma and magnetic field parameters confirm the presence of a slow‐mode shock in connection with the passage of the tailward flow region but not with the 0406 UT to 0408 UT earthward flow interval. The confirmed shock satisfies the critical slow‐mode requirements: MI* ≤ 1.0 and MSM* &gt; 1.0 on the upstream side and MSM* &lt; 1.0 on the downstream side. Here, MI* and MSM* are the intermediate Alfvén speed and slow‐mode phase speed Mach numbers in the frame of the shock. The failure of both the Walén test and the Rankine‐Hugoniot analysis on the earthward flow portion of the plasma reversal event may be associated with the strong earthward ∇B of the inner magnetosphere. The successful joint Walén and slow shock analyses on the tailward flows within the plasma sheet present further evidence in favor of Petschek‐type reconnection at distances xGSM &gt; −19 RE of the near‐Earth magnetotail.

Evolution of fast and slow shock interactions in the inner heliosphere

We use a one-dimensional, time-dependent adaptive grid MHD code to study the interaction between fast and slow shocks in the solar wind. Our results show that: (1) a forward slow shock (FSS) can be destroyed by a forward fast shock (FFS) that overtakes it from behind; (2) two propagating FSSs can merge into a stronger FSS; (3) a strong FSS can survive by following a strong forward fast shock; and (4) the strength of a FSS is decreased by following an FFS. These simulation results reproduce an important feature of the Helios observations (Richter, 1987) where transient fast shocks were more frequently followed within a few hours by slow shock ype discontinuities rather than by fast reverse shocks.

Outflow Structure and Reconnection Rate of the Self‐similar Evolution Model of Fast Magnetic Reconnection

In order to understand the nature of magnetic reconnection in space, which is free from any influence of external circumstances, I have studied the structure of spontaneous reconnection outflow using a shock tube approximation. The reconnection system of this case continues to expand self-similarly. This work aims to (1) solve the structure of reconnection outflow and (2) clarify the determination mechanism of the reconnection rate of the self-similar evolution of fast reconnection. Many cases of reconnection in astrophysical phenomena are characterized by the huge dynamic range of expansion of the size (~107 for typical solar flares). Although such reconnection is intrinsically time dependent, the specialized model underlying the situation has not been established yet. The theoretical contribution of this paper is in obtaining a solution for outflow structure that is absent in our previous papers proposing the above new model. The outflow has a shock tube-like structure, i.e., forward slow shock, reverse fast shock, and contact discontinuity between them. By solving the structure in a sufficiently wide range of plasma-β, 0.001 ≤ β ≤ 100, we obtain an almost constant reconnection rate (~0.05: this value is the maximum for spontaneous reconnection and is consistent with previous models) and boundary value along the edge of the outflow (good agreement with our simulation result), which is important to solve the inflow region. Note that everything, including the reconnection rate, is spontaneously determined by the reconnection system itself in our model.

AChandraView of the Morphological and Spectral Evolution of Supernova Remnant 1987A

We present an update on the results of our monitoring observations of the X-ray remnant of supernova (SN) 1987A with the {\it Chandra X-Ray Observatory}. As of 2002 December, we have performed a total of seven observations of SN 1987A. The high angular resolution images from the latest data reveal developments of new X-ray bright spots in the northwestern and the southwestern portions of the remnant as well as changes on the eastern side. The latest 0.5-2 keV band flux ($f_X$ $\sim$ 6 $\times$ 10$^{-13}$ ergs cm$^{-2}$ s$^{-1}$) is four times brighter than three years earlier. The overall X-ray emission is primarily from the blast wave shock with $kT$ $\sim$ 2.4 keV. As the blast wave approaches the dense circumstellar material, the contribution from the decelerated slow shock ($kT$ $\sim$ 0.22 keV) to the observed X-ray emission is becoming significant. The increase of this slow shock contribution over the last two years is particularly noticeable in the western half of the remnant. These results indicate that the shock front is now reaching the main body of the inner circumstellar ring. Based on the best-fit two-shock spectral model, we derive approximate densities of the X-ray-emitting regions ($n_e$ $\sim$ 235 cm$^{-3}$ for the fast shock and $n_e$ $\sim$ 7500 cm$^{-3}$ for the slow shock). We obtain an upper limit on the observed X-ray luminosity of any embedded point source ($L_X$ $\le$ 1.5 $\times$ 10$^{34}$ ergs s$^{-1}$) in the 2$-$10 keV band. The X-ray remnant continues to expand linearly at a rate of 4167 km s$^{-1}$.

Wind observations of asymmetric magnetic reconnection in the distant magnetotail

On February 23, 2001, during southward and strongly dawnward IMF, Wind traversed the distant magnetotail near XGSM = −90 RE. Wind encountered the mantle in the southern hemisphere and a nearly empty lobe in the northern hemisphere. In the current layer (plasma sheet), high‐speed tailward plasma jets with plasma density intermediate between the mantle and the lobe were detected. The speed of these flows were 96–99% of the Alfvén speed measured in the deHoffmann‐Teller frame. We interpret these observations as evidence for asymmetric reconnection involving a rotational discontinuity in the distant tail when the density in the two inflow regions are vastly different. This is in contrast to typical symmetric magnetotail reconnection involving two lobes of equal density where the flow acceleration across the slow shock is usually sub‐Alfvénic and the outflow density is enhanced relative to the inflow density. Hall effects are also observed in this event.

Electron quasi-viscous effects in collisionless slow-mode shocks

[1] The dynamics of collisionless slow-mode shocks are examined using one-dimensional full particle (kinetic ions and electrons) and hybrid (kinetic ions, massless fluid electrons) simulations. Full particle simulations indicate that the downstream electron temperature becomes anisotropic (T e > T e ⊥) at very oblique angles. The anisotropy results from both the large mirror effects and the electron heating due to the parallel electric field of very obliquely propagating kinetic Alfven waves; it gives rise to finite off-diagonal electron pressure tensor terms in the simulation frame. Inclusion of these electron quasi-viscous effects in hybrid simulations allows slow shocks to be set up at very oblique angles, as observed in the distant tail, where dissipation from ion-ion streaming becomes much weaker.

Theory and observation of double discontinuities

Abstract. Recent research using high-resolution magnetic field data to examine the interior structures of MHD shocks in interplanetary space and in the magnetotail led to a surprising discovery that a slow-mode shock is often followed by an adjoining rotational discontinuity layer on the postshock side. The thickness of each layer is of the order of a few ion inertial lengths. Such a compound structure is known as a double discontinuity. When the magnetic field rotates by several degrees per ion inertial length inside a thin layer, the Hall current term becomes important in the generalized Ohm's law. Steady state solutions based on the Hall-MHD theory have been obtained to show the merging of a rotational layer and a slow shock layer to form a compound structure like the observed double discontinuities.

Computer studies on the three-dimensional spontaneous fast reconnection model as a nonlinear instability

The present paper studies the basic physics of the spontaneous fast reconnection model in a three-dimensional (3D) situation for different resistivity parameter values, where the threshold for occurrence of current-driven anomalous resistivity is allowed to increase with the thermal velocity (T), and the initial plasma density notably changes in space with the plasma pressure in the current sheet system. For any case, once the anomalous resistivity is ignited, the 3D fast reconnection mechanism explosively evolves as a nonlinear instability by the positive feedback between the anomalous resistivity and the reconnection flow, even if the threshold significantly increases with the thermal velocity; for the larger threshold values, the fast reconnection evolution becomes more drastic and the reconnection rate, finally attained on the nonlinear saturation phase, becomes larger. In the resulting 3D fast reconnection configuration, slow shocks stand and extend outwards in the finite extent; also, ahead of the fast reconnection jet, a large-scale 3D plasmoid swells and propagates in the central current sheet, and a vortex flow is formed near the plasmoid side boundary. In the wide range of parameter values, the basic physics of the 3D spontaneous fast reconnection evolution in the finite extent is found to be, qualitatively, consistent with the well-known two-dimensional one.

Steady state slow shock inside the Earth's magnetosheath: To be or not to be? 2. Numerical three‐dimensional MHD modeling

Large‐scale structures in the dayside terrestrial magnetosheath are studied in this paper. The question about existence of the steady state slow MHD shock in the inner magnetosheath is one of the principal theoretical and experimental problems which has not been solved yet. In part 1, the original observations have been revisited. In this part, the numerical results of the three‐dimensional MHD model are presented and discussed. It is shown that for the given observations the density enhancement identified previously as a slow mode transition region is explained by temporal variations of the magnetic field and density observed in the supersonic solar wind. There are three factors resulting in the density increase in the slow mode transition region: A density increase in the upstreamflow, a decrease of the IMF modulus, and a new IMF orientation which forms a quasi‐parallel bow shock in the subsolar region. We show that numerical solutions obtained by non‐stationary and stationary MHD models are significantly different for the same solar wind conditions. We discuss how the magnetopause motion may enlarge the observed variations of the magnetosheath density. Also we answer the question why the existed numerical MHD models do not predict the slow shock in the steady state solution and show how the magnetosheath flow may be organized without such shock.

Comparison of supersonic and subsonic expansion accelerations associated with fast magnetic reconnection

Supersonic and subsonic expansion acceleration mechanisms associated with spontaneous fast magnetic reconnection process are compared by two-dimensional magnetohydrodynamic (MHD) simulations and test fluid (non-charged) particle simulations. When the Petschek reconnection process is steadily established, the reconnection jet generated by a pair of slow shocks becomes either supersonic (Case 1) or subsonic (Case 2), depending on the upstream plasma condition. For Case 1, the jet generated by the slow shocks can be further accelerated by the adiabatic supersonic expansion process. Finally, the jet encounters a fast shock in front of the plasmoid. For Case 2, the jet generated by slow shocks can be further accelerated by the adiabatic subsonic expansion process. The acceleration of Case 1 is stronger than that of Case 2. In Case 2, a fast shock is not formed. In both cases, it is important that the propagation of the plasmoid is driven by slow shocks formed around the plasmoid itself, rather than the reconnection jet.

Analysis of a pressure disturbance in a homogeneous magnetic field

It is well known that in contrast to the Alfvén wave, which is propagating strictly along the direction of the magnetic field, a slow mode wave shows a deviation from the ambient magnetic field. This deviation is determined by the dispersion equation for the slow mode wave. With the help of this dispersion equation we present a theoretical study of the spatial and temporal evolution of an initial pressure disturbance in a homogeneous and constant background magnetic field. The main factor determining the amount of the deviation is the so-called plasma beta, i.e., the ratio of magnetic to thermal energy, which is investigated quantitatively. We obtain that for a low beta plasma, the disturbance propagates more or less strictly along the magnetic field. However, for increasing beta the disturbances across the magnetic field gets stronger. These results can be applied to magnetospheric phenomena, where slow shocks may play a role as a kind of energy carrier as in the case of the Io–Jupiter interaction or magnetic field line reconnection.

Study of three-dimensional plasmoid dynamics by the spontaneous fast reconnection model: effects of dawn–dusk magnetic field

The dawn–dusk magnetic field component ( B z ) in the plasmoid resulting of magnetic reconnections have been observed GEOTAIL satellite. We have studied the effects by B z component in the reconnection in geomagnetotail. This paper present the results of computer simulation about them. Our recent simulation apply the spontaneous fast reconnection model to the three-dimensional (3-D) plasmoid dynamics. Previous our original 3-D computational region (the first quadrant) is extended to the second quadrant and axis symmetry boundary conditions are used. Then, various initial values of dawn–dusk magnetic field component B z can be possibly assumed. As a result in all our simulation cases: (1) a large-scale plasmoid evolves, and (2) it propagates down to the geomagnetic tail, (3) slow shocks and finite amplitude intermediate waves simultaneously stand along the resulting plasmoid boundary layer. We also found that in the plasmoid where north–south magnetic field component ( B y ) changes its sign, B z also has a considerably big value, Which is consistent with the satellite observation result. We propose that the spontaneous fast reconnection mechanism could be most applicable to substorms.

Three separate ion populations observed simultaneously in the plasma sheet boundary layer in the distant geomagnetic tail

[1] The detailed structure of ion velocity space distributions in the plasma sheet boundary layer (PSBL) in the distant geomagnetic tail has been investigated. Three separate, tailward-streaming ion populations have been observed simultaneously in PSBL crossings in which the inner edge of the PSBL was identified as a slow mode shock: cold, low-energy, ions presumably of ionospheric origin that fill much of the tail lobes, and two more energetic populations. The more energetic of these latter populations, which was concentrated in the outer (lobe) layers of the PSBL, had a “kidney bean” shape. The less energetic population had a well-defined low-energy cutoff that decreased with increasing penetration into the PSBL from the lobe. The sources of these two populations may be cold lobe ions accelerated in the current sheet near the distant neutral line and plasma sheet ions that leak across the shock, respectively.

The dynamics of plasmoid in asymmetric spontaneous fast reconnection

The spontaneous fast reconnection evolution is studied in asymmetric magnetic field configuration. In particular, it is investigated how shear flow influences in magnetosheath region to the propagation of plasmoid results from magnetic reconnection using two-dimensional magnetohydrodynamic simulations. According to the fast reconnection development, the resulting large-scale plasmoids swell and propagate. Once the plasmoid fully develops, the propagation speed becomes almost constant in both the symmetric and asymmetric magnetic field configuration. An asymmetric plasmoid swells predominantly in the region of a weaker magnetic field and propagates along the field lines. The associated shock structure standing at the plasma boundary is the ordinary slow shock irrespective of the intensity of shear flow. However, velocity of plasmoid is proportional to shear flow velocity.

Magnetohydrodynamic Shock Heating of the Solar Corona

Coronal MHD waves excited by perturbations of magnetic field lines propagate upward, carrying with them the energy from the excitation. Under favorable conditions shocks form, and part of the wave energy is converted to plasma heating and motion. We use numerical simulations to accurately follow the shock formation and subsequent energy release. The model includes an adiabatic energy equation for the explicit evaluation of temperature increases and energy fluxes contributed by the shocks. Transverse, plane-polarized excitations are considered; they can be periodic, as in Alfven wave trains, or pulsed, as might result from nanoflares. The model is tested with a set of validation runs that produce good agreement with theoretical predictions. Our results show that nonlinear waves moving along large magnetic fields with low plasma β, with field amplitudes comparable to the background field, develop shocks that form important amounts of plasma heating and that mass outflow may occur. Fast and slow magnetoacoustic shocks are generated, each one making its own contribution. Most of the heating takes place in the low corona, but long-range distributed heating still occurs up to heights of several solar radii. The energy fluxes for the stronger cases are sufficient to compensate for thermal and convective losses, consistent with observations. We conclude that large-amplitude MHD shocks in low-β regions could be a viable mechanism for coronal heating and wind acceleration in regions of open magnetic field lines.

Can ion-neutral damping help to form spicules?

The possible mechanism of generation of spicules by Alfvénic waves is studied in dissipative MHD where dissipation is mainly caused by ion-neutral collision damping, as suggested by Haerendel ([CITE]). Ion-neutral damping becomes non-negligible at the high cyclic frequencies involved, typically greater than , and the potential role played by this effect in both forming and supporting solar spicules is investigated. The propagation of high frequency Alfvén waves on vertically open solar magnetic flux tubes is considered. The flux tubes are taken to be axisymmetric and initially untwisted with the field strength declining from in the photosphere to in the corona. Their propagation is investigated by numerically solving a set of fully nonlinear, dissipative 1.5D MHD equations with the waves being generated by a continuous sinusoidal driver introduced into the equation of angular momentum in the low atmosphere of the Sun. Spicule-like structures with heights of up to were formed. The formation was found to be caused by the impact of a series of slow shocks generated by the continuous interaction between the upward propagating driven wave train and the downward propagating train of waves created by reflection off the transition region and aided by the increased thermal pressure gradient caused by Joule heating due to ion-neutral collisions. The adiabatic results suggest that ion-neutral damping may not support spicules as described by Haerendel ([CITE]). However, the effect is highly sensitive to the level of ionisation and therefore to the energy balance. Including the effects of thermal conduction and radiation may well lead to different results and thus it would be premature to dismiss the mechanism completely at this point. In addition, the relatively high chromospheric temperatures obtained, even at frequencies for which ion-neutral damping and heating might be expected to be unimportant, suggest intriguing possibilities for combining the mechanism with others that are better able to recreate spicule dynamics but suffer from unrealistically low temperatures.

Suppression of the Richtmyer–Meshkov instability in the presence of a magnetic field

We present numerical evidence from two dimensional simulations that the growth of the Richtmyer–Meshkov instability is suppressed in the presence of a magnetic field. A bifurcation occurs during the refraction of the incident shock on the density interface which transports baroclinically generated vorticity away from the interface to a pair of slow or intermediate magnetosonic shocks. Consequently, the density interface is devoid of vorticity and its growth and associated mixing is completely suppressed.