Fast MHD Shock Research Articles

The influence of the Hall term on the development of magnetized laser-produced plasma jets

We present 2D axisymmetric simulation results describing the influence of the Hall term on laser-produced plasma jets and their interaction with an applied magnetic field parallel to the laser axis. Bending of the poloidal B-field lines produces an MHD shock structure surrounding a conical cavity, and a jet is produced from the convergence of the shock envelope. Both the jet and the conical cavity underneath it are bound by fast MHD shocks. We compare the MHD results generated using the extended-MHD code Physics as an Extended-MHD Relaxation System with an Efficient Upwind Scheme (PERSEUS) with MHD results generated using GORGON and find reasonable agreement. We then present extended-MHD results generated using PERSEUS, which show that the Hall term has several effects on the plasma jet evolution. A hot low-density current-carrying layer of plasma develops just outside the plume, which results in a helical rather than a purely poloidal B-field, and reduces magnetic stresses, resulting in delayed flow convergence and jet formation. The flow is partially frozen into the helical field, resulting in azimuthal rotation of the jet. The Hall term also produces field-aligned current in strongly magnetized regions. In particular, we find the influence of Hall physics on this problem to be scale-dependent. This points to the importance of mitigating the Hall effect in a laboratory setup, by increasing the jet density and system dimensions, in order to avoid inaccurate extrapolation to astrophysical scales.

Emergence of unstable modes for classical shock waves in isothermal ideal MHD

This note studies classical magnetohydrodynamic shock waves in an inviscid fluidic plasma that is assumed to be a perfect conductor of heat as well as of electricity. For this mathematically prototypical material, it identifies, mainly numerically, two critical manifolds in parameter space, across which slow resp. fast MHD shock waves undergo emergence of a complex conjugate pair of unstable transverse modes. For slow shocks, this emergence occurs in a particularly interesting way already in the parallel case, in which it happens at the spectral value λˆ≡λ∕|ω|=0 and the critical manifold possesses a simple explicit algebraic representation. Results of refined numerical treatment show that within the set of non-parallel slow shocks the unstable mode pair emerges from two generically different spectral values λˆ=±iγ. For fast shocks, the critical manifold does not intersect the parallel regime and the emergence within the set of non-parallel fast shocks again starts from two generically different spectral values.

SHOCKFIND - an algorithm to identify magnetohydrodynamic shock waves in turbulent clouds

The formation of stars occurs in the dense molecular cloud phase of the interstellar medium. Observations and numerical simulations of molecular clouds have shown that supersonic magnetised turbulence plays a key role for the formation of stars. Simulations have also shown that a large fraction of the turbulent energy dissipates in shock waves. The three families of MHD shocks --- fast, intermediate and slow --- distinctly compress and heat up the molecular gas, and so provide an important probe of the physical conditions within a turbulent cloud. Here we introduce the publicly available algorithm, SHOCKFIND, to extract and characterise the mixture of shock families in MHD turbulence. The algorithm is applied to a 3-dimensional simulation of a magnetised turbulent molecular cloud, and we find that both fast and slow MHD shocks are present in the simulation. We give the first prediction of the mixture of turbulence-driven MHD shock families in this molecular cloud, and present their distinct distributions of sonic and Alfvenic Mach numbers. Using subgrid one-dimensional models of MHD shocks we estimate that ~0.03 % of the volume of a typical molecular cloud in the Milky Way will be shock heated above 50 K, at any time during the lifetime of the cloud. We discuss the impact of this shock heating on the dynamical evolution of molecular clouds.

Magnetorotational Explosions of Core-Collapse Supernovae

Core-collapse supernovae are accompanied by formation of neutron stars. The gravitation energy is transformed into the energy of the explosion, observed as SN II, SN Ib,c type supernovae. We present results of 2-D MHD simulations, where the source of energy is rotation, and magnetic eld serves as a "transition belt" for the transformation of the rotation energy into the energy of the explosion. The toroidal part of the magnetic energy initially grows linearly with time due to dierential rotation. When the twisted toroidal component strongly exceeds the poloidal eld, magneto-rotational instability develops, leading to a drastic acceleration in the growth of magnetic energy. Finally, a fast MHD shock is formed, producing a supernova explosion. Mildly collimated jet is produced for dipole-like type of the initial field. At very high initial magnetic field no MRI development was found.

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.

Core-collapse supernovae: Magnetorotational explosions and jet formation

Core-collapse supernovae are accompanied by formation of neutron stars. The gravitational energy is transformed into the energy of the explosion, observed as SN II, SN Ib,c type supernovae. We present results of 2D MHD simulations, where the source of energy is rotation and the magnetic field serves as a “transition belt” for the transformation of the rotation energy into the energy of the explosion. The toroidal part of the magnetic energy initially grows linearly with time due to differential rotation. When the twisted toroidal component strongly exceeds the poloidal field, magneto-rotational instability develops, leading to a drastic acceleration in the growth of magnetic energy. Finally, a fast MHD shock is formed, producing a supernova explosion. A mildly collimated jet is produced for the dipolelike type of the initial field.

OUTFLOWS FROM MAGNETOROTATIONAL SUPERNOVAE

We discuss results of 2D simulations of magnetorotational (MR) mechanism of core collapse supernova explosions. Due to the nonuniform collapse, the collapsed core rotates differentially. In the presence of an initial poloidal magnetic field its toroidal component appears and grows with time. Increased magnetic pressure leads to the formation of a compression wave which moves outwards. It transforms into the fast MHD shock wave (supernova shock wave). The shape of the MR supernova explosion qualitatively depends on the configuration of the initial magnetic field. For a dipole-like initial magnetic field, the supernova explosion develops mainly along the rotational axis, forming a mildly collimated jet. A quadrupole-like initial magnetic field leads to the explosion developing mainly along the equatorial plane. The magnetorotational instability was found in our simulations. The supernova explosion energy grows with an increase of the initial core mass and rotational energy of the core, and corresponds to the observational data.

Core-Collapse Supernovae: Magnetorotational Explosions and Jet Formation

Core-collapse supernovae are accompanied by formation of neutron stars. The gravitational energy is transformed into the energy of the explosion, observed as SN II, SN Ib,c type supernovae. We present results of 2D MHD simulations, where the source of energy is rotation and the magnetic field serves as a “transition belt” for the transformation of the rotation energy into the energy of the explosion. The toroidal part of the magnetic energy initially grows linearly with time due to differential rotation. When the twisted toroidal component strongly exceeds the poloidal field, magneto-rotational instability develops, leading to a drastic acceleration in the growth of magnetic energy. Finally, a fast MHD shock is formed, producing a supernova explosion. A mildly collimated jet is produced for the dipolelike type of the initial field.

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.

Magnetorotational supernovae. Magnetorotational instability. Jet formation

2D numerical simulations of magnetorotational (MR) supernova mechanism are described. It is shown that magnetic field is amplified due to the differential rotation after core collapse. When magnetic pressure reaches some level, a compression wave starts to move outwards. Moving along steeply decreasing density profile the compression wave transforms quickly into fast MHD shock. The magnetorotational instability (MRI) was found in our simulations. MRI leads to the exponential growth of the components of the magnetic field. The MRI significantly reduces MR supernova explosion time. Configuration of the initial magnetic field qualitatively defines the shape of MR supernova explosion. For the quadrupole-like initial poloidal field the MR supernova explosion develops mainly along equatorial plane, the dipole-like initial field results in MR supernova developing as mildly collimated jet along axis of rotation. The explosion energy of MR supernova found in our simulations is ∼0.5–0.6×1051 erg.

Interaction of interplanetary shocks with the bow shock

Fast forward interplanetary (IP) shocks have been identified as a source of large geomagnetic disturbances. However, the shocks can evolve in the solar wind, they are modified by interaction with the bow shock and during their propagation through the magnetosheath. A few previous papers refer the inclination and deceleration of the IP shock front in this region. Our contribution continues this effort and presents the study of an IP shock interaction with the bow shock. Since the bow shock is a reversed fast shock, the interaction of the IP shock and bow shock is a problem of interaction of two fast MHD shocks. We compare profiles of magnetic field and plasma parameters observed by several spacecraft in the solar wind and magnetosheath with the profiles of the same parameters resulting from the MHD numerical model. The MHD model suggests that the interaction of an IP shock with the bow shock results in an inward bow shock displacement that is followed by its outward motion. Such motion will result in an indentation propagating along the bow shock surface. This scenario is confirmed by multipoint observations. Moreover, the model confirms also previous suggestions on the IP shock deceleration in the magnetosheath.

Solar wind–magnetosphere coupling efficiency for solar wind pressure impulses

[1] We investigate the solar wind–magnetosphere coupling efficiency in response to solar wind dynamic pressure impulses. We carry out a superposed epoch analysis of 236 pressure impulses from the years 1998–2002 detected by the ACE/SWEPAM instrument. For the coupling efficiency, we use four definitions based on: the polar cap potential from SuperDARN radars, the northern polar cap index (PCN), the available magnetospheric potential, and the interplanetary electric field (IEF). All definitions show consistent results: the coupling efficiency depends on the internal structure of the impulse. The coupling efficiency increases (decreases) for events mimicking slow (fast) MHD shocks. The coupling energy estimated from the IMAGE magnetometer chain is larger for the “fast-type” events and stronger drivers. Hence, our results indicate that the magnetosphere uses the energy from the weaker driver more geoeffectively, while the energy associated with stronger drivers is partly transmitted through the system.

Magnetorotational supernovae

We present the results of 2D simulations of the magnetorotational model of a supernova explosion. After the core collapse the core consists of rapidly a rotating proto-neutron star and a differentially rotating envelope. The toroidal part of the magnetic energy generated by the differential rotation grows linearly with time at the initial stage of the evolution of the magnetic field. The linear growth of the toroidal magnetic field is terminated by the development of magnetohydrodynamic instability, leading to drastic acceleration in the growth of magnetic energy. At the moment when the magnetic pressure becomes comparable with the gas pressure at the periphery of the proto-neutron star $\sim 10-15$km from the star centre the MHD compression wave appears and goes through the envelope of the collapsed iron core. It transforms soon to the fast MHD shock and produces a supernova explosion. Our simulations give the energy of the explosion $0.6\cdot 10^{51}$ ergs. The amount of the mass ejected by the explosion is $\sim 0.14M_\odot$. The implicit numerical method, based on the Lagrangian triangular grid of variable structure, was used for the simulations.

A Complete 2D Stability Analysis of Fast MHD Shocks in an Ideal Gas

An algorithm of numerical testing of the uniform Lopatinski condition for linearized stability problems for 1-shocks is suggested. The algorithm is used for finding the domains of uniform stability, neutral stability, and instability of planar fast MHD shocks. A complete stability analysis of fast MHD shock waves is first carried out in two space dimensions for the case of an ideal gas. Main results are given for the adiabatic constant γ=5/3 (mono-atomic gas), that is most natural for the MHD model. The cases γ=7/5 (two-atomic gas) and γ>5/3 are briefly discussed. Not only the domains of instability and linear (in the usual sense) stability, but also the domains of uniform stability, for which a corresponding linearized stability problem satisfies the uniform Lopatinski condition, are numerically found for different given angles of inclination of the magnetic field behind the shock to the planar shock front. As is known, uniform linearized stability implies the nonlinear stability, that is local existence of discontinuous shock front solutions of a quasilinear system of hyperbolic conservation laws.

Stability of fast parallel MHD shock waves in polytropic gas

The stability of plane shock waves in Magnetohydrodynamics for an ideal medium is studied. Stability results are obtained for the special case of fast parallel shock waves in a polytropic gas. Linear stability is proved for a polytropic gas with arbitrary γ. The domain of structural (nonlinear) stability, where the uniform Lopatinsky condition is fulfilled for the stability problem, is found.

Stability of fast parallel and transversal MHD shock waves in plasma with pressure anisotropy

The stability of plane magnetohydrodynamic shock waves in a collisionless strongly magnetised plasma (described by Chew, Goldberger and Low equations) is studied. Stability results are obtained for the special cases of parallel and transversal fast shock waves by the test of fulfilment of the uniform Lopatinsky condition for corresponding linear stability problems. It is shown that fast parallel shock waves are always stable. The stability domain for fast transversal shock waves is found.

A 2.5‐dimensional MHD parametric study of interplanetary shock interactions with the heliospheric current sheet/heliospheric plasma sheet

A study of the interaction of interplanetary shock waves with the heliospheric current sheet/heliospheric plasma sheet (HCS/HPS) and the disturbed flow behind them is made with a 2.5 dimensional MHD code that uses improved computational techniques. The aim is to determine if such interactions for typical shocks can produce sufficiently large changes in the interplanetary plasma and field to be geoeffective. The mutual interaction of the shock waves with the HCS/HPS is examined for several angles between the shock normal and the HCS/HPS. We separate the effects of the HCS from those due to angular distance of observer from the initial shock center. The shocks are initiated at 0.1 AU by a finite‐duration increase in initial radial velocity. We examine the transit times of the resultant shocks to 1‐AU and their strengths along their peripheries. We also examine the 1‐AU signatures of the polar component of the magnetic field, Bθ, in the interplanetary disturbance at and following the leading fast mode MHD shock. Note that Bθ = −Bz. We show the differences that result from the presence of the HCS, both qualitatively and quantitatively. The largest effects occur in Bθ, which reaches its largest excursions within 10° of the edge of the HPS. For the moderate shocks simulated in this study, deflections of the field lines produce values of Bθ between 4 and 5 nT in the presence of a HCS. These values are at the lower end of the range considered necessary for interplanetary events to initiate moderate geomagnetic storms. Further study is required to investigate the nature of input pulses and HCS that would give larger Bθ variations.

Evolution of Eruptive Flares. I. Plasmoid Dynamics in Eruptive Flares

We investigate the resistive processes of plasmoid dynamics in eruptive flares by performing 2.5-dimensional resistive MHD numerical simulations. We start with a linear force-free field arcade and impose the localized resistive perturbation on the symmetry axis of the arcade. Then the magnetic fields begin to dissipate, producing inflows toward this region. These inflows make the magnetic fields convex to the symmetry axis and hence a neutral point is formed on this axis, leading to a formation of a magnetic island around the symmetry axis. At the first stage, the magnetic island slowly rises by the upflow produced by the initial resistive perturbation. Then, once the anomalous resistivity sets in, the magnetic island begins to be accelerated. This acceleration stops after the fast MHD shock is formed at the bottom of the magnetic island, which implies that the upflow around the central part of the magnetic island is no longer strong. These three stages in the evolution of the plasmoid are confirmed to exist in the observational results. Moreover, a time lag between the start time when the magnetic island begins to be accelerated and the peak time of the neutral-point electric field can be explained by the inhibition of magnetic reconnection by the perpendicular magnetic field. We also study the difference of the initial rise motion of the plasmoid between the simulation results and the observational ones, and we conclude that, in actual situations, the initial resistive perturbation proceeds very weakly and at many positions inside the arcade.

Interaction of shocks with a current sheet and reconnection in the solar corona

Interaction of shocks with a current sheet is investigated within a 2D MHD model based on an improved FCT numerical scheme. Basic parameters of the problem are chosen to correspond to situations in the solar corona with low plasma β and moderate shock strength. Slow and fast MHD shocks are introduced with shock normal parallel to magnetic field lines. The interaction with the current sheet causes distortion of the shock front and this distorts the magnetic field lines and generates electric current. Large current densities are generated especially when the fast MHD shock becomes the intermediate MHD shock at the current sheet. Then peak values of the current density are about 3–4 times larger than the initial undisturbed values in the current sheet.

Neutron and electromagnetic emissions during the 1990 May 24 solar flare

In this paper, we are primarily concerened with the solar neutron emission during the 1990 May 24 flare, utilizing the counting rate of the Climax neutron monitor and the time profiles of hard X-rays and gamma-rays obtained with the GRANAT satellite (Pelaez et al., 1992; Talon et al., 1993; Terekhov et al., 1993). We compare the derived neutron injection function with macroscopic parameters of the flare region as obtained from the H-alpha and microwave observations made at the Big Bear Solar Observatory (BBSO) and the Owens Valley Radio Observatory (OVRO) respectively. Our results are summarized as folows: (1) to explain the neutron monitor counting rate and 57.5-110 MeV and 2.2 MeV gamma-ray time profiles, we consider a two-component neutron injection function, Q(E, t). (2) From the H-alpha observations, we find a relatively small loop of length approximattely equal to 2 x 10(exp 4) km, which may be regarded as the source for the fast-decaying component of gamma-rays (57.5-110 MeV) and for the first component of neutron emission. From microwave visibility and the microwave total power spectrum we postulate the presence of a rather big loop (approximately equal to 2 x 10(exp 5) km), which we regard as being responsible for the slow-decaying component of the high-energy emission. We show how the neutron and gamma-ray emission data can be explained in terms of the macroscopic parameters derived from the H-alpha and microwave observations. (3) The H-alpha observations also reveal the presence of a fast mode MHD shock (the Moreton wave) which precedes the microwave peak by 20-30 s and the peak of gamma-ray intensity by 40-50 s. From this relative timing and the single-pulsed time profiles of both radiations, we can attribute the whole event as due to a prompt acceleration of both electrons and protons by the shock and subsequent deceleration of the trapped particles while they propagate inside the magnetic loops.