Formation of the bow shock indentation: MHD simulation results

Simulation results from a global magnetohydrodynamic(MHD)model are used to examine whether the bow shock has an indentation and characterize its formation conditions,as well as its physical mechanism.The bow shock is identified by an increase in plasma density of the solar wind,and the indentation of the bow shock is determined by the shock flaring angle.It is shown that when the interplanetary magnetic field(IMF)is southward and the Alfvén Mach number(Mα)of solar wind is high(>5),the bow shock indentation can be clearly determined.The reason is that the outflow region of magnetic reconnection(MR)that occurs in the low latitude area under southward IMF blocks the original flow in the magnetosheath around the magnetopause,forming a high-speed zone and a low-speed zone that are upstream and downstream of each other.This structure hinders the surrounding flow in the magnetosheath,and the bow shock behind the structure widens and forms an indentation.When Mαis low,the magnetosheath is thicker and the disturbing effect of the MR outflow region is less obvious.Under northward IMF,MR occurs at high latitudes,and the outflow region formed by reconnection does not block the flow inside the magnetosheath,thus the indentation is harder to form.The study of the conditions and formation process of the bow shock indentation will help to improve the accuracy of bow shock models.

Analytical studies on the evolution processes of rarefied deuterium plasma shell Z-pinch by PIC and MHD simulations

In this paper, we analytically explore the magnetic field and mass density evolutions obtained in particle-in-cell（PIC）and magnetohydrodynamics（MHD） simulations of a rarefied deuterium shell Z-pinch and compare those results, and also we study the effects of artificially increased Spitzer resistivity on the magnetic field evolution and Z-pinch dynamic process in the MHD simulation. There are significant differences between the profiles of mass density in the PIC and MHD simulations before 45 ns of the Z-pinch in this study. However, after the shock formation in the PIC simulation,the mass density profile is similar to that in the MHD simulation in the case of using multiplier 2 to modify the Spitzer resistivity. Compared with the magnetic field profiles of the PIC simulation of the shell, the magnetic field diffusion has still not been sufficiently revealed in the MHD simulation even though their convergence ratios become the same by using larger multipliers in the resistivity. The MHD simulation results suggest that the magnetic field diffusion is greatly enhanced by increasing the Spitzer resistivity used, which, however, causes the implosion characteristic to change from shock compression to weak shock, even shockless evolution, and expedites the expansion of the shell. Too large a multiplier is not suggested to be used to modify the resistivity in some Z-pinch applications, such as the Z-pinch driven inertial confinement fusion（ICF） in a dynamic hohlraum. Two-fluid or Hall MHD model, even the PIC/fluid hybrid simulation would be considered as a suitable physical model when there exist the plasma regions with very low density in the simulated domain.

Application of ADER Scheme in MHD Simulation

The Arbitrary accuracy Derivatives Riemann problem method(ADER) scheme is a new high order numerical scheme based on the concept of finite volume integration,and it is very easy to be extended up to any order of space and time accuracy by using a Taylor time expansion at the cell interface position.So far the approach has been applied successfully to flow mechanics problems.Our objective here is to carry out the extension of multidimensional ADER schemes to multidimensional MHD systems of conservation laws by calculating several MHD problems in one and two dimensions: (ⅰ) Brio-Wu shock tube problem,(ⅱ) Dai-Woodward shock tube problem,(ⅲ) Orszag-Tang MHD vortex problem.The numerical results prove that the ADER scheme possesses the ability to solve MHD problem,remains high order accuracy both in space and time,keeps precise in capturing the shock.Meanwhile,the compared tests show that the ADER scheme can restrain the oscillation and obtain the high order non-oscillatory result.

Modeling the Jovian magnetosphere under an antiparallel interplanetary magnetic field from a global MHD simulation

We present preliminary results of a new global Magnetohydrodynamics(MHD) simulation model of the Jovian magnetosphere.The model incorporates mass loading from Jupiter's satellite Io, the planet's fast corotation, and electrostatic coupling between its magnetosphere and ionosphere(M-I coupling). The basic configuration of the Jovian magnetosphere including the equatorial plasma flow pattern, the corotation enforcement current system, and the field aligned currents(FACs) in the ionosphere are presented under an antiparallel interplanetary magnetic field(IMF) condition. The simulation model results for equatorial density and pressure profiles are consistent with results from data-based empirical models. It is also found that there are similarities between the FACs distribution in the ionosphere and the observed aurora features, showing the potential application of the simple ionospheric model to the complicated M-I coupling. This model will help deepen our understanding of the global dynamics of the Jovian magnetosphere.

Energetics characteristics of the super magnetic storm on November 20,2003 based on 3D global MHD simulation

The three-dimensional global magnetohydrodynamic model(PPM-LR MHD)is employed to investigate the energy budget in the solar wind-magnetosphere system during the super magnetic storm on November 20,2003,one of the biggest storms during the last decade with Dst^-500 n T.During this event,about 23%solar wind kinetic energy is transferred into the magnetosphere.The total energy input is estimated to be about 9.50×1017 J,about 14 times of a moderate storm.The energy dissipation via the inner magnetosphere is less than the energy input with the coupling efficiency of^63.3%.The energy dissipated via ring current injection is less than that via high-latitude ionosphere at the initial stage of the super storm.Furthermore,both the simulation results and the empirical results indicate that the ratio of ring current injection to the total energy output increases with the enhancement of the magnetospheric activity level.These are consistent with the statistical results we have got before.The empirical equations underestimate the solar wind kinetic energy,the energy input,and the energy dissipation via high-latitude ionosphere compared with the simulation results;however,the coupling efficiency of the high-latitude ionosphere(23.4%)is close to the simulation result(23.1%)during the entire storm time period.

Three-dimensional MHD simulation of the lunar wake

We study the interaction between the Moon and the solar wind through a three-dimensional MHD simulation.Three cases have been discussed in which the interplanetary magnetic field lies at 90,180,and 135 to the solar wind flow,respectively.A wake with low density and low pressure can always be formed behind the Moon.The plasma temperature and magnetic field are enhanced in the central wake,but the field strength is reduced in the surrounding region.A Mach cone is formed by rarefaction waves emanating from the limb.These rarefaction waves propagate via the fast magnetosonic mode with different velocities in different directions relative to the magnetic field.When the interplanetary magnetic field is not parallel to the solar wind flow,the wake shows some asymmetries,with an acceleration region turning up at the center.Finally,the results are compared with the observations by WIND spacecraft.Our calculations agree reasonably well with the observed values.

Numerical Simulation of the 12 May 1997 CME Event

Our newly developed CESE MHD model is used to simulate sun-earth connection event with the well-studied 12 May 1997 CME event as an example. The main features and approximations of our numerical model are as follows： （1） The modifed conservation element and solution element （CESE） numerical scheme in spherical geometry is implemented in our code. （2） The background solar wind is derived from a 3D time-dependent numerical MHD model by input measured photospheric magnetic fields. （3） Transient disturbances are derived from solar surface by introducing a mass flow of hot plasma. The numerical simulation has enabled us to predict the arrival of the interplanetary shock and provided us with a relatively satisfactory comparison with the WIND spacecraft observations.

Magnetohydrodynamics (MHD) numerical simulations on the interaction of the solar wind with the magnetosphere: A review

The magnetosphere is the outermost layer of the geospace, and the interaction of the solar wind with the magnetosphere is the key element of the space weather cause-and-effect chain process from the Sun to Earth, which is one of the most challenging scientific problems in the geospace weather study. The nonlinearity, multiple component, and time-dependent nature of the geospace make it very difficult to describe the physical process in geospace using traditional analytic analysis approach. Numerical simulations, a new research tool developed in recent decades, have a deep impact on the theory and application of the geospace. MHD simulations started at the end of the 1970s, and the initial study was limited to two-dimensional (2D) cases. Due to the intrinsic three-dimensional (3D) characteristics of the geospace, 3D MHD simulations emerged in the 1980s, in an attempt to model the large-scale structures and fundamental physical processes in the magnetosphere. They started to combine with the space exploration missions in the 1990s and make comparisons with observations. Physics-based space weather forecast models started to be developed in the 21st century. Currently only a few space-power countries such as USA and Japan have developed 3D magnetospheric MHD models. With the rapid advance of space science in China, we have developed a new global MHD model, namely PPMLR-MHD, which has high order spatial accuracy and low numerical dissipation. In this review, we will briefly introduce the global 3D MHD modeling, especially the PPMLR-MHD code, and summarize our recent work based on the PPMLR-MHD model, with an emphasis on the interaction of interplanetary shocks with the magnetosphere, large-scale current systems, reconnection voltage and transpolar potential drop, and Kelvin-Helmholtz (K-H) instability at the magnetopause.

Effects of a dipole-like crustal field on solar wind interaction with Mars

A three-dimensional four species multi-fluid magnetohydrodynamic (MHD) model was constructed to simulate the solar wind global interaction with Mars. The model was augmented to consider production and loss of the significant ion species in the Martian ionosphere, i.e., H^+, O2^+, O^+, CO^+2, associated with chemical reactions among all species. An ideal dipole-like local crustal field model was used to simplify the empirically measured Martian crustal field. Results of this simulation suggest that the magnetic pile-up region (MPR) and the velocity profile in the meridian plane are asymmetric, which is due to the nature of the multi-fluid model to decouple individual ion velocity resulting in occurrence of plume flow in the northern Martian magnetotail. In the presence of dipole magnetic field model, boundary layers, such as bow shock (BS) and magnetic pile-up boundary (MPB), become protuberant. Moreover, the crustal field has an inhibiting effect on the flux of ions escaping from Mars, an effect that occurs primarily in the region between the terminator (SZA 90°) and the Sun Mars line of the magnetotail (SZA 180°), partially around the terminator region. In contrast, near the tailward central line the crustal field has no significant impact on the escaping flux.

The Energy Balance of Plasma in a Coaxial Plasma Opening Switch

The two-dimensional energy balance in a coaxial plasma opening switch （POS） is studied based on the single-fluid magnetohydrodynarnic （MHD） equations coupled with the generalized Ohm＇s law. The energy transfers between the plasma and the magnetic field are considered during the penetration of the magnetic field as the Ohmic heating is included in the energy-balance equation. The focus is on the energy partition between the magnetic-field energy and the dissipated magnetic-field energy in a high-density POS with different rise-in-time electric currents at the generator boundary. The simulation code is tested in two cases： the constant-in-time current case and the linear rise-in-time current case. For the sinusoidally rise-in-time current similar to that of the experiments, it is shown that at the end of the conduction phase the dissipated magnetic-field energy is 36.5% of the input electromagnetic energy, which is consistent with the experimental results.

Influence of Downstream Flow on Conduction Phase of Coaxial Plasma Opening Switch

Plasma behaviour and the scaling relations in a coaxial plasma opening switch （POS） using hydrogen plasma are studied self-consistently based on the two-dimensional magnetohydrodynamic （MHD） equations in conjunction with the generalized Ohm＇s law. The vacuum region on the right of POS is included in the model and the influence of downstream flow on the conduction characteristics is discussed. It is found that with the penetration of magnetic field, the pure hydrogen plasma is pushed downstream significantly; and POS still conducts current after the magnetic field arrives at the load edge of POS, which is different from the previous experimental results in a multispecies POS. It is because that the noticeable downstream plasma in the pure hydrogen POS may continue to conduct the current, while in the multispecies POS, the downstream plasma is unimportant so that the conduction phase ends soon after the magnetic field reaches the load edge. The scaling relation obtained from the simulations including the downstream region is consistent with the experimental results.

Fuel compression in the magnetized cylindrical implosion driven by a gold tube heated by heavy ion beams

A magnetized cylindrical target composed of a gold tube filled with deuterium-tritium fuel plasma at low density is studied numerically in the present paper.A shock wave is produced when a heavy ion beam heats the gold along the direction of the magnetic field.The density peak of the shock wave increases with the increase in time and it propagates in the-r direction in the cylindrical tube.It seems that this wave is the supermagnetosonic wave.It is found that the Mach number M is between 6.96 and 19.19.The density peak of the shock wave increases as the intensity of the heavy ion beam increases.Furthermore,the density peak of the shock wave increases as the external magnetic field increases.

Effects of thermophoresis particle deposition and of the thermal conductivity in a porous plate with dissipative heat and mass transfer

Network simulation method（NSM） is used to solve the laminar heat and mass transfer of an electricallyconducting,heat generating/absorbing fluid past a perforated horizontal surface in the presence of viscous and Joule heating problem. The governing partial differential equations are non-dimensionalized and transformed into a system of nonlinear ordinary differential similarity equations,in a single independent variable,畏. The resulting coupled,nonlinear equations are solved under appropriate transformed boundary conditions. Computations are performed for a wide range of the governing flow parameters,viz Prandtl number,thermophoretic coeffcient（a function of Knudsen number）,thermal conductivity parameter,wall transpiration parameter and Schmidt number. The numerical details are discussed with relevant applications. The present problem finds applications in optical fiber fabrication,aerosol filter precipitators,particle deposition on hydronautical blades,semiconductor wafer design,thermo-electronics and problems including nuclear reactor safety.

Large scale current systems developed from substorm onset:Global MHD results

We investigate the large-scale substorm current systems developed from its onset in an idealized substorm event simulated by global magnetohydrodynamic(MHD) models. Mainly three current systems(loops) are revealed:(1) the classical substorm current wedge, which is composed by the disputed cross-tail current in the magnetotail, the nightside westward electrojet in the high-latitude ionosphere and a pair of region 1 field-aligned currents(FAC);(2) the partial-ring current system, which is braced by two region 2 FACs; and(3) the meridional current system, which is formed by an equatorial radial current(outward/inward in the morning/evening sector), and region 1 and region 2 FACs at its two ends. The region 2 FAC connects with region 1 FAC by a latitudinal horizontal current at each morning/evening ionosphere to complete Loops 2 and 3. A quantitative study shows the significant enhancement of these current systems during the substorm expansion phase, while Loop 1 dominates, which can reach a magnitude of ~1 MA. Empirical relations among the ionospheric currents and the related magnetotail currents are established based on the simulation results, implying that the substonn current systems are not evolved locally or separately, but must be viewed from a global perspective. This knowledge of large-scale substorm current system would deepen our understanding of the substorm development and could be validated by observations in the future.

Effects of the interplanetary magnetic field clock angle on the shape of bow shock

Using the global magnetohydrodynamics(MHD) simulation model, we investigated the effects of the interplanetary magnetic field(IMF) clock angle on the shape of bow shock, including its rotational asymmetry and subsolar point. For general northward IMF( z component Bz > 0), the rotational symmetry of the bow shock is broken by the effects of fast magnetosonic Mach number(Mms), and the cross-sectional line of the bow shock is an ellipse with the semi-major axis along the direction perpendicular to the IMF. The ratio or D-value between semi-major and semi-minor axis can be used to illustrate the extent of asymmetry of the bow shock. On the basis of the multiple parameters fitting, we obtain the changing relationship of both semi-axes with the clock angle and the distance away from the Earth. For general southward IMF(Bz < 0), the cross sectional line of the bow shock is highly asymmetrical under the multiple effects of magnetopause and Mms. The effects of IMF clock angle on subsolar point depend mainly on the changing subsolar point of magnetopause as an obstacle. The distance of subsolar point of bow shock from the Earth increases with the increasing IMF clock angle for Bz > 0, and decreases with the increasing IMF clock angle for Bz < 0.

A computational study on the optical shaping of gas targets via blast wave collisions for magnetic vortex acceleration

This research work emphasizes the capability of delivering optically shaped targets through the interaction of nanosecond laser pulses with high-density gas-jet profiles,and explores proton acceleration in the near-critical density regime via magnetic vortex acceleration(MVA).Multiple blast waves(BWs)are generated by laser pulses that compress the gas-jet into near-critical steep gradient slabs of a few micrometres thickness.Geometrical alternatives for delivering the laser pulses into the gas target are explored to efficiently control the characteristics of the density profile.The shock front collisions of the generated BWs are computationally studied by 3D magnetohydrodynamic simulations.The efficiency of the proposed target shaping method for MVA is demonstrated for TW-class lasers by a particle-in-cell simulation.

Ion acceleration at dipolarization fronts associated with the interchange instability in Earth's magnetotail

It has been confirmed that dipolarization fronts(DFs)are the result of the interchange instability in the Earth's magnetotail.In this paper,we use a Hall MHD model to simulate the evolution of the interchange instability that produces DFs along the leading edge.A test particle simulation is performed to study the physical phenomenon of ion acceleration at the DF.The numerical simulation indicates that almost all particles move earthward and dawnward and then drift to the tail.The DF-reflected ion population at the duskside appears earlier as a consequence of the asymmetric Hall electric field.Ions that are distributed in a dawn-dusk asymmetric semicircle behind the DF tend to be accelerated to higher energies(>13.5 keV).These high-energy particles eventually concentrate in the dawnside.Ions experience effective acceleration by the dawnward electric field,while they drift through the dawn flank at the front,toward the tail.

Numerical research on the interaction between coronal mass ejection and streamer

By proposing a two-dimensional triggering model with concentrically circular closed magnetic field line structure,numerical research is made on the asymmetric propagation feature of coronal mass ejection (CME) in two cases emerging at the solar northern latitudes 10° and 45° respectively.The numerical results can qualitatively explain some features of CME event observed by the spacecraft SOHO and show that:(i) In these two cases,the triggering model can initiate CME with an asymmetric closed magnetic field structure.(ii) Closed magnetic structure of CME event will keep deflecting to the current sheet when it propagates away from the sun and this deflecting effect mostly happens within tens of solar radii before CME travels finally along the current sheet.(iii) The triggering model emerging at different locations can introduce CME events with different magnetic shapes.This shape happens to be circular and crescent when the triggering model emerges at the northern latitudes 10° and 45°,respectively.