Three-dimensional MHD Simulations Research Articles

Three-dimensional MHD Simulations of the Magnetic Pileup at Mars

In this study, we introduced a quantitative parameter, the magnetic field strength difference, to denote the intensity of the magnetic pileup effect at Mars. Using a three-dimensional multispecies MHD model, the effects of the interplanetary magnetic field (IMF) and the solar wind dynamic pressure (P d ) constituted with different densities and velocities on the magnetic pileup were examined. Our results show that: (1) the magnetic pileup at Mars mainly occurs at the dayside region and its magnitude is generally decreasing with increasing solar zenith angle. The magnetic pileup is generally weak in the intense crustal field region, while it is strong in the weak crustal field region. (2) The perpendicular IMF components, B Y and B Z , dominate the magnetic pileup, while the radial IMF component, B X , has little effect. In the intense crustal field region, when the IMF and crustal field are primarily in the same direction, the magnetic field is piled up and the pileup magnitude is generally strong. While the directions of the crustal field and IMF are opposite, the occurrence of magnetic reconnection can weaken the local magnetic pileup. (3) Under the same P d , a higher solar wind velocity results in a higher intensity and a larger region of the magnetic pileup. When P d increases, the magnitude of the magnetic pileup is enhanced, but the pileup region shrinks. In addition, for an increasing P d , at the center of the induced magnetotail, the asymmetric current sheet can lead to similar asymmetries of the pileup.

Particle Acceleration by Magnetic Reconnection in Relativistic Jets: The Transition from Small to Large Scales

Several MHD works, and, in particular, the recent one by Medina-Torrejón et al. based on three-dimensional MHD simulations of relativistic jets, have evidenced that particle acceleration by magnetic reconnection driven by the turbulence in the flow occurs from the resistive up to the large injection scale of the turbulence. Particles experience Fermi-type acceleration up to ultrahigh energies, predominantly of the parallel velocity component to the local magnetic field, in the reconnection layers in all scales due to the ideal electric fields of the background fluctuations (V × B, where V and B are the velocity and magnetic field of the fluctuations, respectively). In this work, we show MHD-particle-in-cell (MHD-PIC) simulations following the early stages of the particle acceleration in the relativistic jet, which confirm these previous results, demonstrating the strong potential of magnetic reconnection driven by turbulence to accelerate relativistic particles to extreme energies in magnetically dominated flows. Our results also show that the dynamical time variations of the background magnetic fields do not influence the acceleration of the particles in this process.

Turbulent Magnetic Field Amplification by the Interaction of a Shock Wave and Inhomogeneous Medium

Magnetic fields of the order of 100 μG observed in young supernova remnants cannot be amplified by shock compression alone. To investigate the amplification caused by a turbulent dynamo, we perform three-dimensional MHD simulations of the interaction between a shock wave and an inhomogeneous density distribution with a shallow spectrum in the preshock medium. The postshock turbulence is mainly driven by the strongest preshock density contrast and follows the Kolmogorov scaling. The resulting turbulence amplifies the postshock magnetic field. The time evolution of the magnetic fields agrees with the prediction of the nonlinear turbulent dynamo theory of Xu & Lazarian. When the initially weak magnetic field is perpendicular to the shock normal, the maximum amplification of the field’s strength reaches a factor of ≈200, which is twice as large as that for a parallel shock. We find that the perpendicular shock exhibits a smaller turbulent Alfvén Mach number in the vicinity of the shock front than the parallel shock. However, the strongest magnetic field has a low volume filling factor and is limited by the turbulent energy due to the reconnection diffusion taking place in a turbulent and magnetized fluid. The magnetic field strength averaged along the z-axis is reduced by a factor ≳10. We decompose the turbulent velocity and magnetic field into solenoidal and compressive modes. The solenoidal mode is dominant and evolves to follow the Kolmogorov scaling, even though the preshock density distribution has a shallow spectrum. When the preshock density distribution has a Kolmogorov spectrum, the turbulent velocity’s compressive component increases.

Global MHD Simulation of the Weak Southward IMF Condition for Different Time Resolutions

We performed high-resolution three-dimensional global MHD simulations to determine the impact of weak southward interplanetary magnetic field (IMF) (Bz = −2 nT) and slow solar wind to the Earth’s magnetosphere and ionosphere. We considered two cases of differing, uniform time resolution with the same grid spacing simulation to find any possible differences in the simulation results. The simulation results show that dayside magnetic reconnection and tail reconnection continuously occur even during the weak and steady southward IMF conditions. A plasmoid is generated on closed plasma sheet field lines. Vortices are formed in the inner side of the magnetopause due to the viscous-like interaction, which is strengthened by dayside magnetic reconnection. We estimated the dayside magnetic reconnection which occurred in relation to the electric field at the magnetopause and confirmed that the enhanced electric field is caused by the reconnection and the twisted structure of the electric field is due to the vortex. The simulation results of the magnetic field and the plasma properties show quasi-periodic variations with a period of 9–11 min between the appearances of vortices. Also the peak values of the cross-polar cap potential are both approximately 50 kV, the occurrence time of dayside reconnections are the same, and the polar cap potential patterns are the same in both cases. Thus, there are no significant differences in outcome between the two cases.

The Magnetic Mechanism for Hotspot Reversals in Hot Jupiter Atmospheres

Abstract Magnetically driven hotspot variations (which are tied to atmospheric wind variations) in hot Jupiters are studied using nonlinear numerical simulations of a shallow-water magnetohydrodynamic (SWMHD) system and a linear analysis of equatorial SWMHD waves. In hydrodynamic models, mid-to-high-latitude geostrophic circulations are known to cause a net west-to-east equatorial thermal energy transfer, which drives hotspot offsets eastward. We find that a strong toroidal magnetic field can obstruct these energy transporting circulations. This results in winds aligning with the magnetic field and generates westward Lorentz force accelerations in hotspot regions, ultimately causing westward hotspot offsets. In the subsequent linear analysis we find that this reversal mechanism has an equatorial wave analogy in terms of the planetary-scale equatorial magneto-Rossby waves. We compare our findings to three-dimensional MHD simulations, both quantitatively and qualitatively, identifying the link between the mechanics of magnetically driven hotspot and wind reversals. We use the developed theory to identify physically motivated reversal criteria, which can be used to place constraints on the magnetic fields of ultra-hot Jupiters with observed westward hotspots.

Nonlinear MHD simulation of core plasma collapse events in Wendelstein 7-X

Three-dimensional nonlinear MHD simulations study the core collapse events observed in a stellarator experiment, Wendelstein 7-X. In the low magnetic shear configuration like the Wendelstein 7-X, the rotational transform profile is very sensitive to the toroidal current density. The 3D equilibrium with localized toroidal current density is studied. If the toroidal current density follows locally in the middle of the minor radius, the rotational transform is also changed locally. Sometimes, the magnetic topology changes due to appearing the magnetic island. A full three-dimensional nonlinear MHD code studies the nonlinear behaviors of the MHD instability. It was found that the following sequence. At first, the high-n ballooning-type mode structure appears in the plasma core, and then the mode linearly grows. The high-n ballooning modes nonlinearly couple and saturate. The mode structure changes to the low-n mode. The magnetic field structure becomes strongly stochastic into the plasma core due to the nonlinear coupling in that phase. Finally, the plasma pressure diffuses along the stochastic field lines, and then the core plasma pressure drops. This is a crucial result to interpret the core collapse event by strong nonlinear coupling.

Gravitational wave signature of proto-neutron star convection: I. MHD numerical simulations

ABSTRACT Gravitational waves provide a unique and powerful opportunity to constrain the dynamics in the interior of proto-neutron stars during core collapse supernovae. Convective motions play an important role in generating neutron stars magnetic fields, which could explain magnetar formation in the presence of fast rotation. We compute the gravitational wave emission from proto-neutron star convection and its associated dynamo, by post-processing three-dimensional MHD simulations of a model restricted to the convective zone in the anelastic approximation. We consider two different proto-neutron star structures representative of early times (with a convective layer) and late times (when the star is almost entirely convective). In the slow rotation regime, the gravitational wave emission follows a broad spectrum peaking at about three times the turnover frequency. In this regime, the inclusion of magnetic fields slightly decreases the amplitude without changing the spectrum significantly compared to a non-magnetized simulation. Fast rotation changes both the amplitude and spectrum dramatically. The amplitude is increased by a factor of up to a few thousands. The spectrum is characterized by several peaks associated with inertial modes, whose frequency scales with the rotation frequency. Using simple physical arguments, we derive scalings that reproduce quantitatively several aspects of these numerical results. We also observe an excess of low-frequency gravitational waves, which appears at the transition to a strong field dynamo characterized by a strong axisymmetric toroidal magnetic field. This signature of dynamo action could be used to constrain the dynamo efficiency in a proto-neutron star with future gravitational wave detections.

Configurations of Earth’s magnetosphere in response to variations in z component Solar-wind flow during the southward IMF

Based on the compressible resistive MHD models, the Earth’s dipole magnetic field is employed to investigate magnetic reconnection driven by the solar wind with southward interplanetary magnetic field. By including the z-component solar wind velocity vswz in a three-dimensional compressible global resistive MHD simulation with uniform resistivity, we found that vswz does not affect the location of magnetic reconnection on the dayside magnetopause in the interaction of southward magnetic field of the solar wind with the Earth’s dipole field. However, significant deviation of the central plasma sheet in the magnetotail from equatorial plane can occur. Detailed study also shows that vswz promotes magnetic reconnection at the dayside magnetopause, and the reconnection rate and deviation of magnetotail current sheet both increase with vswz. In particular, the deviation angle increases linearly with vswz. The results here can be useful for understanding observed substorm behavior in the magnetosphere.

Coronal Mass Ejection Effect on Envelopes of Hot Jupiters

Abstract—Currently, hot Jupiters have extended gaseous (ionospheric) envelopes extending far beyond the Roche lobe. The envelopes are loosely bound to the planet and are subject to a strong influence by stellar wind fluctuations. Since hot Jupiters are close to the parent star, the magnetic field of the stellar wind is an important factor which defines the structure of their magnetospheres. For a typical hot Jupiter, the velocity of stellar wind plasma flowing around the atmosphere is close to the Alfven velocity. Thus, fluctuations of the stellar wind parameters (density, velocity, magnetic field) can affect conditions for the formation of the bow shock around a hot Jupiter, such as transforming the flow from sub-Alfven to super-Alfven regime and back. The study results of three-dimensional numerical MHD simulations confirm that, in a hot Jupiter’s envelope located near the Alfven point of the stellar wind, both the disappearance and appearance of a detached shock can occur under the influence of a coronal mass ejection. The study also shows that this process can affect the observational manifestations of a hot Jupiter, including the radiation flux in the spectrum’s hard region.

Recurrent CME-like Eruptions in Emerging Flux Regions. II. Scaling of Energy and Collision of Successive Eruptions

Abstract We present results of three-dimensional MHD simulations of recurrent eruptions in emerging flux regions. The initial numerical setup is the same as that in the work by Syntelis et al. Here, we perform a parametric study on the magnetic field strength (B 0) of the emerging field. The kinetic energy of the produced ejective eruptions in the emerging flux region ranges from 1026 to 1028 erg, reaching up to the energies of small coronal mass ejections. The kinetic and magnetic energies of the eruptions scale linearly in a logarithmic plot. We find that the eruptions are triggered earlier for higher B 0 and that B 0 is not directly correlated to the frequency of occurrence of the eruptions. Using large numerical domains, we show the initial stage of the partial merging of two colliding erupting fields. The partial merging occurs partly by the reconnection between the field lines of the following and the leading eruption at the interface between them. We also find that tether-cutting reconnection of the field lines of the leading eruption underneath the following eruption magnetically links the two eruptions. Shocks develop inside the leading eruption during the collision.

The Crab nebula in the light of three-dimensional relativistic MHD simulations

Pulsar wind nebulae inside young supernova remnants, and in particular the Crab nebula, are probably the best laboratories for high-energy astrophysics and relativistic plasma physics. They have been modeled numerically for more than a decade through multi-dimensional relativistic MHD simulations, relying on axial symmetry until a few years ago while currently using full three-dimensional simulations employing adaptive meshes. Here, we discuss the most recent findings, especially those obtained by our Arcetri group, focusing on the problem of magnetic field dissipation inside the nebula.

Three-dimensional MHD simulation of the 2008 December 12 coronal mass ejection: from the Sun to Interplanetary space

A three-dimensional time-dependent, numerical magnetohydrodynamic simulation is performed to investigate the propagation of a coronal mass ejection that occurred on 12 December 2008. The background solar wind is obtained by using a splitting finite-volume scheme based on a six-component grid system in spherical coordinate, with Parker’s one-dimensional solar wind solution and measured photospheric magnetic fields as the initial values. A spherical plasmoid is superposed on the realistic ambient solar wind to study the 12 December 2008 coronal mass ejection event. The plasmoid is assumed to have a spheromak magnetic structure with a high-density, high-velocity, and high-pressure near the Sun. The dynamical interaction between the coronal mass ejection and the background solar wind flow is then investigated. We compared the model results with observations, and the model provide a relatively satisfactory comparison with the Wind spacecraft observations at 1 AU. We also investigated the numerical results assuming different parameters of the CME, we find that initial magnetic fields in the CME have a larger influence on the solar wind parameters at the Earth.

Three-dimensional MHD Simulation of Solar Wind Using a New Boundary Treatment: Comparison with In Situ Data at Earth

Abstract Three-dimensional magnetohydrodynamics (MHD) numerical simulation is an important tool in the prediction of solar wind parameters. In this study, we improve our corona interplanetary total variation diminishing MHD model by using a new boundary applicable to all phases of solar cycles. This model uses synoptic magnetogram maps from the Global Oscillation Network Group as the input data. The empirical Wang–Sheeley–Arge relation is used to assign solar wind speed at the lower boundary, while temperature is specified accordingly based on its empirical relation with the solar wind speed. Magnetic field intensity and solar wind density at the boundary are obtained from observational data in the immediate past Carrington rotations, permitting the persistence of these two parameters in a short time period. The boundary conditions depend on only five tunable parameters when simulating the solar wind for different phases of the solar cycle. We apply this model to simulate the background solar wind from 2007 to 2017 and compare the modeled results with the observational data in the OMNI database. Visual inspection shows that our model can capture the time patterns of solar wind parameters well at most times. Statistical analysis shows that the simulated solar wind parameters are all in good agreement with the observations. This study demonstrates that the improved interplanetary total variation diminishing model can be used for predicting all solar wind parameters near the Earth.

The Steady Global Corona and Solar Wind: A Three-dimensional MHD Simulation with Turbulence Transport and Heating

Abstract We present a fully three-dimensional magnetohydrodynamic model of the solar corona and solar wind with turbulence transport and heating. The model is based on Reynolds-averaged solar wind equations coupled with transport equations for turbulence energy, cross helicity, and correlation scale. The model includes separate energy equations for protons and electrons and accounts for the effects of electron heat conduction, radiative cooling, Coulomb collisions, Reynolds stresses, eddy viscosity, and turbulent heating of protons and electrons. The computational domain extends from the coronal base to 5 au and is divided into two regions: the inner (coronal) region, 1–30 R ☉, and the outer (solar wind) region, 30 R ☉–5 au. Numerical steady-state solutions in both regions are constructed by time relaxation in the frame of reference corotating with the Sun. Inner boundary conditions are specified using either a tilted-dipole approximation or synoptic solar magnetograms. The strength of solar dipole is adjusted, and a scaling factor for magnetograms is estimated by comparison with Ulysses observations. Except for electron temperature, the model shows reasonable agreement with Ulysses data during its first and third fast latitude transits. We also derive a formula for the loss of angular momentum caused by the outflowing plasma. The formula takes into account the effects of turbulence. The simulation results show that turbulence can notably affect the Sun’s loss of angular momentum.

On the Sensitivity of Magnetic Cycles in Global Simulations of Solar-like Stars

Abstract The periods of magnetic activity cycles in the Sun and solar-type stars do not exhibit a simple or even single trend with respect to rotation rate or luminosity. Dynamo models can be used to interpret this diversity and can ultimately help us understand why some solar-like stars do not exhibit a magnetic cycle, whereas some do, and for the latter what physical mechanisms set their magnetic cycle period. Three-dimensional nonlinear MHD simulations present the advantage of having only a small number of tunable parameters, and produce in a dynamically self-consistent manner the flows and the dynamo magnetic fields pervading stellar interiors. We conduct a series of such simulations within the EULAG-MHD framework, varying the rotation rate and luminosity of the modeled solar-like convective envelopes. We find decadal magnetic cycles when the Rossby number near the base of the convection zone is moderate (typically between 0.25 and 1). Secondary, shorter cycles located at the top of the convective envelope close to the equator are also observed in our numerical experiments, when the local Rossby number is lower than 1. The deep-seated dynamo sustained in these numerical experiments is fundamentally nonlinear, in that it is the feedback of the large-scale magnetic field on the large-scale differential rotation that sets the magnetic cycle period. The cycle period is found to decrease with the Rossby number, which offers an alternative theoretical explanation to the variety of activity cycles observed in solar-like stars.

AGN and Star Formation Feedback in Galaxy Outflows

AbstractLarge-scale, broad outflows are common in active galaxies. In systems where star formation coexists with an AGN, it is unclear yet the role that both play on driving the outflows. In this work we present three-dimensional radiative-cooling MHD simulations of the formation of these outflows, considering the feedback from both the AGN and supernovae-driven winds. We find that a large-opening-angle AGN wind develops fountain structures that make the expanding gas to fallback. Furthermore, it exhausts the gas near the nuclear region, extinguishing star formation and accretion within a few 100.000 yr, which establishes the duty cycle of these outflows. The AGN wind accounts for the highest speed features in the outflow with velocities around 10.000 km s−1 (as observed in UFOs), but these are not as cold and dense as required by observations of molecular outflows. The SNe-driven wind is the main responsible for the observed mass-loading of the outflows.

Periodic shearing motions in the Jovian magnetosphere causing a localized peak in the main auroral emission close to noon

Recently, a transient localized brightness enhancement has been observed in Jupiter's main auroral emission close to noon by Palmaerts et al. (2014). We use results from three-dimensional global MHD simulations to understand what is causing this localized peak in the main emission. In the simulations, the peak occurs every rotation period and is due to shearing motions in the magnetodisk. These shearing motions are caused by heavy flux-tubes being accelerated to large azimuthal speeds at dawn. The centrifugal force acting on these flux-tubes is then so high that they rapidly move away from the planet. When they reach noon, their azimuthal velocity decreases, thus reducing the centrifugal force, and allowing the flux-tubes to move back closer to Jupiter. The shearing motions associated with this periodic phenomenon locally increase the field aligned currents in the simulations, thus causing a transient brightness enhancement in the main auroral emission, similar to the one observed by Palmaerts et al. (2014).

Three-dimensional MHD Simulations of Solar Prominence Oscillations in a Magnetic Flux Rope

Abstract Solar prominences are subject to all kinds of perturbations during their lifetime, and frequently demonstrate oscillations. The study of prominence oscillations provides an alternative way to investigate their internal magnetic and thermal structures because the characteristics of the oscillations depend on their interplay with the solar corona. Prominence oscillations can be classified into longitudinal and transverse types. We perform three-dimensional ideal magnetohydrodynamic simulations of prominence oscillations along a magnetic flux rope, with the aim of comparing the oscillation periods with those predicted by various simplified models and examining the restoring force. We find that the longitudinal oscillation has a period of about 49 minutes, which is in accordance with the pendulum model where the field-aligned component of gravity serves as the restoring force. In contrast, the horizontal transverse oscillation has a period of about 10 minutes and the vertical transverse oscillation has a period of about 14 minutes, and both of them can be nicely fitted with a two-dimensional slab model. We also find that the magnetic tension force dominates most of the time in transverse oscillations, except for the first minute when magnetic pressure overwhelms it.

Time-varying Heliospheric Distance to the Heliopause

Using a three-dimensional MHD simulation, we examine the time-varying outer heliospheric structure and distance to the heliopause. Voyager 2 (V2) solar-wind observations show that a global merged interaction region (GMIR) with a ram-pressure of the order of several nPa normalized at 1 au enters the distant solar wind at an average rate of about one per year. This series of GMIRs adds an additional perturbative increase to the solar-wind ram-pressure in the inner heliosheath, and it also reduces the surrounding interstellar medium pressure acting on the heliopause; consequently, our simulation results in the distance to the heliopause being ~14 au larger when compared to the case when a series of GMIRs is not taken into account. In addition, OMNI data show that the solar-wind ram-pressure near the Earth increases from ~1.3 nPA in 2010 and before to 1.7–2.4 nPa after that until the present time. These variations in the overall ram-pressure of the solar wind are also included in our simulation. The inclusion of the time variable solar-wind ram-pressure and the series of GMIRs allows us to illustrate how the realistic distance to the heliopause varies in response to both long- and short time variability in solar activity. This simulation study also explains the puzzle of why V2 has not yet crossed the heliopause, although it is now almost 5 years since Voyager 1 crossed the heliopause in 2012.

High Speed Solar Wind Forecast Model from the Solar Surface to 1AU Using Global 3D MHD Simulation

AbstractEmanating from coronals holes (CHs), high speed streams (HSSs) cause recurrent geomagnetic disturbances in the Earth’s magnetosphere. For this reason being able to predict the occurrence and timing of the high speed solar wind is one of the more important issues in space weather forecasting. Currently, it is still difficult to estimate the effect of a CH in case that it extends from high latitudes to lower ones. To monitor the global solar wind condition we have therefore developed a three-dimensional MHD simulation code, the REProduce Plasma Universe (REPPU) code, that is driven by the solar magnetic field from the solar surface to 1AU. The connectivity of magnetic field lines from CHs to Earth’s orbit via HSSs has been investigated. Simulation results are presented and the usefulness of our model is discussed.