Magnetic Pressure Gradient Force Research Articles

Outflows Driven from a Magnetic Pseudodisk

Outflows play a pivotal role in star formation as one of its most visible markers and a means of transporting mass, momentum, and angular momentum from the infalling gas into the surrounding molecular cloud. Their wide reach (at least thousands of astrnomical units) is a contrast to typical disk sizes (∼10–100 au). We employ high-resolution three-dimensional nested-grid nonideal magnetohydrodynamic (MHD) simulations to study outflow properties in the Class 0 phase. We find that no disk wind is driven from the extended centrifugal disk that has weak magnetic coupling. The low-velocity winds emerge instead from the infalling magnetic pseudodisk. Much of the disk actually experiences an infall of matter rather than outflowing gas. Some of the pseudodisk wind (PD-wind) moves inward to regions above the disk and either falls onto the disk or proceeds upward. The upward flow gives the impression of a disk wind above a certain height even if the gas is originally emerging from the pseudodisk. The PD-wind has the strongest flow coming from a disk interaction zone that lies just outside the disk and is an interface between the inwardly advected magnetic field of the pseudodisk and the outwardly diffusing magnetic field of the disk. The low-velocity wind exhibits the features of a flow driven by the magnetic pressure gradient force in some regions and those of a magnetocentrifugal wind in other regions. We interpret the structure and dynamics of the outflow zone in terms of the basic physics of gravity, angular momentum, magnetic fields, and nonideal MHD.

Statistical Survey of Magnetic Forces Associated With Earthward Bursty Bulk Flows Measured by MMS 2017–2021

AbstractWe investigate the magnetic forces (the magnetic pressure gradient force, the curvature force, and their sum the j × B‐force) associated with earthward bursty bulk flows (BBFs) using Magnetospheric Multiscale (MMS) data from five tail seasons (2017–2021). For the first time, the magnetic forces are inferred downtail of XGSM = −20 RE and in the GSM XY and YZ planes. The results suggest that BBFs tend to be accelerated earthward by the magnetic pressure gradient force tailward of ∼19 RE and decelerated closer to that distance in the 2017–2018 data. The force magnitudes increase with distance. This is in accordance with earlier Cluster results. In the 2019–2021 data, the pressure gradient force magnitudes are generally smaller and no clear distance for the acceleration reversal can be determined. The curvature forces for both 2017–2018 and 2019–2021 BBFs indicate earthward acceleration independent of distance, consistent with the Cluster measurements. The sum, the j × B‐force, suggests for the 2017–2018 BBFs earthward acceleration tailward of XGSM ∼15 RE and deceleration within that distance, also consistent with Cluster. In contrast, the 2019–2021 BBFs show general earthward acceleration by j × B independent of distance. In the GSM XY plane, the average (j × B)xy vectors are earthward, and in the premidnight and postmidnight dawnward for the 2017–2018 BBFs. For 2019–2021, the average (j × B)xy vectors have components toward the tail center. In the GSM YZ plane, the average (j × B)yz vectors are toward the neutral sheet.

The force density in electrical machines modeled as tension and pressure gradients of magnetic field lines

This paper shows how to model the force density in electrical machines based on the field lines of the magnetic flux density. The force density is written as two vector components: the magnetic tension force and the magnetic pressure gradient force. This approach has been applied in physics but never to forces in engineering problems. The magnetic tension force acts to straighten bent field lines, based on the curvature of the flux density. The magnetic pressure gradient force acts from regions of high flux density to regions of low flux density. Both force densities are derived from the Lorentz force using the tnb-frame of Frenet–Serret formulas and shown to be equivalent to the divergence of the Maxwell stress tensor. It is shown how the force density could describe the forces in a synchronous machine, including both the angular torque of the load and the radial forces between the rotor and the stator. It could also be linked to the power flow and thereby to the energy flux of Poynting’s vector. The force densities could be used to improve the understanding of the Maxwell stress tensor, since they are easier to illustrate as vectors compared to the matrix form of the Maxwell stress tensor. It also shows the location of the force density, which could improve the use of enclosing volumes when calculating the force based on the divergence theorem with the Maxwell stress tensor.

Density filamentation nonlinearly driven by the Weibel instability in relativistic beam plasmas

Density filamentation has been observed in many beam-plasma simulations and experiments. Because current filamentation is a pure transverse mode, charge density filamentation cannot be produced directly by the current filamentation process. To explain this phenomenon, several mechanisms are proposed such as the coupling of the Weibel instability to the two-stream instability, coupling to the Langmuir wave, differences in thermal velocities between the beam and return currents, the magnetic pressure gradient force, etc. In this paper, it is shown that the gradient of the Lorentz factor can, in fact, represent the nonlinear behavior of a plasma fluid and further that the nonuniform Lorentz factor distribution can give rise to electrostatic fields and density filaments. Simulation results together with theoretical analyses are presented.

The Causes of Peripheral Coronal Loop Contraction and Disappearance Revealed in a Magnetohydrodynamic Simulation of Solar Eruption

Abstract The phenomenon of peripheral coronal loop contraction during solar flares and eruptions, recently discovered in observations, has gradually drawn the attention of solar physicists. However, its underlying physical mechanism is still uncertain. One possible mechanism is Hudson’s implosion conjecture, which attributes the contraction of peripheral coronal loops to magnetic pressure reduction in the magnetic energy liberation core, while other researchers proposed alternative explanations. In previous observational studies we also note the disappearance of peripheral shrinking loops in the late phase, of which there is a lack of investigation and interpretation. In this paper, we exploit a full MHD simulation of solar eruption to study the causes of the two phenomena. It is found that the loop motion in the periphery is well correlated with magnetic energy accumulation and dissipation in the core, and the loop shrinkage is caused by a more significant reduction in magnetic pressure gradient force than in magnetic tension force, consistent with the implosion conjecture. The peripheral contracting loops in the late phase act as inflow to reconnect with central erupting structures, which destroys their identities and naturally explains their disappearance. We also propose a positive feedback between the peripheral magnetic reconnection and the central eruption.

Ion‐Scale Flux Rope Observed inside a Hot Flow Anomaly

AbstractWe report an earthward moving ion‐scale flux rope embedded within the trailing edge of a hot flow anomaly (HFA) observed by the Magnetospheric Multiscale satellite constellation on 17 December 2016 upstream of Earth's quasi‐parallel bow shock. The driver of the HFA, a tangential discontinuity, was observed by the Wind spacecraft without flux rope signatures around it in the solar wind. This suggests that the earthward moving flux rope was generated inside the HFA. This ion‐scale flux rope is not a force free structure and expands due to a strong magnetic pressure gradient force. Solar wind ions are decelerated inside the flux rope by the static electric field likely caused by the charge separation of solar wind particles. Our observations imply that magnetic reconnection may have occurred inside the HFA. Reconnection and flux ropes may play a role in particle acceleration/heating inside foreshock transients.

A Statistical Study of the Force Balance and Structure in the Flux Ropes in Mercury's Magnetotail

AbstractThis study presents a statistical investigation of the force balance and structures in the flux ropes in Mercury's magnetotail plasma sheet by using the measurements of MErcury Surface, Space ENviroment, GEochemistry, and Ranging (MESSENGER). One hundred sixty‐eight flux ropes were identified from the 14 hot seasons of MESSENGER from 11 March 2011 to 30 April 2015, and 143 of them show clear magnetic field enhancements with the core field being ≥20% higher than the background magnetic field. The investigation on the force balance of these 143 flux ropes shows that magnetic pressure gradient force cannot be solely balanced by magnetic tension force, implying that thermal plasma pressure gradient force cannot be neglected in the flux ropes. We employ a non‐force‐free model considering the contribution of thermal pressure to resolve the physical properties of flux ropes in Mercury's magnetotail. Twenty‐eight flux ropes are obtained through the fitting to the non‐force‐free model. The flux ropes are found to be consistent with the flattened structures, in which the mean semimajor is ∼851 km and semiminor is ∼333 km, both are several times the local proton inertial length. The average core field is estimated to be ∼57.5 nT, and flux content is ∼0.019 MWb, much larger than the previous results obtained from force‐free flux rope model. The importance of thermal pressure gradient in the force balance of the flux ropes and the flattened structure indicates that the flux ropes in Mercury's magnetotail plasma sheet are mostly in early stage of the evolution, and still contain enough plasma to affect their magnetic structures.

Solar Cycle Variation of the Heliospheric Plasma Sheet Thickness

Past independent studies of the heliospheric plasma sheet (HPS) have shown that the thickness is highly variable, ranging from \(\approx 3.8 \times 10^{5}\) to \(8.9 \times 10^{6}\) km. Here we conduct a survey of the previous results and find a solar cycle dependence – where the HPS tends to be wider during solar-minimum years and narrower during solar-maximum years. The HPS is thicker near solar minimum than near solar maximum by a factor of 1.6 (in Solar Cycle 23) and 8 (in Solar Cycle 24). We also found that the average HPS thickness in 2007 (near the minimum of Solar Cycle 23/24) was almost ten times larger than that in 1995 (near minimum of Solar Cycle 22/23), and it was associated with a weak polar magnetic field in 2007. Based on the solar-surface-field measurements, we found that the average solar magnetic-field strength [\(| \boldsymbol{B}|\)] at 2.5 solar radii [R⊙] was \(\approx 40\)% larger in 1995 than in 2007 (0.22 gauss versus 0.16 gauss). We also found a larger (\(\approx 27 \)%) magnetic pressure-gradient force in 1995 than in 2007. Because this magnetic gradient force points toward the Equator in the corona (which is probably also true farther out), a wider HPS is expected to occur in 2007 than in 1995, at least close to the Sun. This result supports the so-called heliospheric plasma-sheet inflation hypothesis, i.e. the HPS is wider if the Sun’s polar field is weaker and narrower if the Sun’s polar field is stronger.

Numerical study of the propagation characteristics of coronal mass ejections in a structured ambient solar wind

AbstractUsing a three‐dimensional (3‐D) magnetohydrodynamics (MHD) model, we analyze and study the propagation characteristics of coronal mass ejections (CMEs) launched at different positions in a realistic structured ambient solar wind. Here the ambient solar wind structure during the Carrington rotation 2095 is selected, which is the characteristics of activity rising phase. CMEs with a simple spherical plasmoid structure are initiated at different solar latitudes with respect to the heliospheric current sheet (HCS) and the Earth in the same ambient solar wind. Then, we numerically obtained the evolution process of the CMEs from the Sun to the interplanetary space. When the Earth and the CME launch position are located on the same side of the HCS, the arrival time of the shock at the Earth is faster than that when the Earth and the CME launch position are located on the opposite side of the HCS. The disturbance amplitudes for the same side event are also larger than those for the opposite side event. This may be due to the fact that the HCS between the CME and the Earth for the opposite side event hinders its propagation and weaken it. The CMEs tend to deflect toward the HCS in the latitudinal direction near the corona and then propagate almost parallel to the HCS in the interplanetary space. This deflecting tendency may be caused by the dynamic action of near‐Sun magnetic pressure gradient force on the ejected coronal plasma.

Particle-in-cell simulation study of a lower-hybrid shock

The expansion of a magnetized high-pressure plasma into a low-pressure ambient medium is examined with particle-in-cell simulations. The magnetic field points perpendicular to the plasma's expansion direction and binary collisions between particles are absent. The expanding plasma steepens into a quasi-electrostatic shock that is sustained by the lower-hybrid (LH) wave. The ambipolar electric field points in the expansion direction and it induces together with the background magnetic field a fast E cross B drift of electrons. The drifting electrons modify the background magnetic field, resulting in its pile-up by the LH shock. The magnetic pressure gradient force accelerates the ambient ions ahead of the LH shock, reducing the relative velocity between the ambient plasma and the LH shock to about the phase speed of the shocked LH wave, transforming the LH shock into a nonlinear LH wave. The oscillations of the electrostatic potential have a larger amplitude and wavelength in the magnetized plasma than in an unmagnetized one with otherwise identical conditions. The energy loss to the drifting electrons leads to a noticeable slowdown of the LH shock compared to that in an unmagnetized plasma.

INSTABILITY OF NON-UNIFORM TOROIDAL MAGNETIC FIELDS IN ACCRETION DISKS

ABSTRACT We present a new type of instability that is expected to drive magnetohydrodynamic (MHD) turbulence from a purely toroidal magnetic field in an accretion disk. It is already known that in a differentially rotating system, the uniform toroidal magnetic field is unstable due to magnetorotational instability (MRI) under a non-axisymmetric and vertical perturbation, while it is stable under a purely vertical perturbation. Contrary to the previous study, this paper proposes an unstable mode completely confined to the equatorial plane, driven by the expansive nature of the magnetic pressure gradient force under a non-uniform toroidal field. The basic nature of this growing eigenmode, which we name “magneto-gradient driven instability,” is studied using linear analysis, and the corresponding nonlinear evolution is then investigated using two-dimensional ideal MHD simulations. Although a single localized magnetic field channel alone cannot provide sufficient Maxwell stress to contribute significantly to the angular momentum transport, we find that the mode coupling between neighboring toroidal fields under multiple localized magnetic field channels drastically generates a highly turbulent state and leads to the enhanced transport of angular momentum, which is comparable to the efficiency seen in previous studies on MRIs. This horizontally confined mode may play an important role in the saturation of an MRI through complementray growth with the toroidal MRIs and coupling with magnetic reconnection.

Stochastic non-circular motion and outflows driven by magnetic activity in the Galactic bulge region

By performing a global magneto-hydrodynamical simulation for the Milky Way with an axisymmetric gravitational potential, we propose that spatially dependent amplification of magnetic fields possibly explains the observed noncircular motion of the gas in the Galactic center region. The radial distribution of the rotation frequency in the bulge region is not monotonic in general. The amplification of the magnetic field is enhanced in regions with stronger differential rotation, because magnetorotational instability and field-line stretching are more effective. The strength of the amplified magnetic field reaches >~ 0.5 mG, and radial flows of the gas are excited by the inhomogeneous transport of angular momentum through turbulent magnetic field that is amplified in a spatially dependent manner. In addition, the magnetic pressure-gradient force also drives radial flows in a similar manner. As a result, the simulated position-velocity diagram exhibits a time-dependent asymmetric parallelogram-shape owing to the intermittency of the magnetic turbulence; the present model provides a viable alternative to the bar-potential-driven model for the parallelogram-shape of the central molecular zone. This is a natural extension into the central few 100 pc of the magnetic activity, which is observed as molecular loops at radii from a few 100 pc to 1 kpc. Furthermore, the time-averaged net gas flow is directed outward, whereas the flows are highly time-dependent, which we discuss from a viewpoint of the outflow from the bulge.

Electric field generation by the electron beam filamentation instability: filament size effects

The filamentation instability (FI) of counter-propagating beams of electrons is modelled with a particle-in-cell simulation in one spatial dimension and with a high statistical plasma representation. The simulation direction is orthogonal to the beam velocity vector. Both electron beams have initially equal densities, temperatures and moduli of their non-relativistic mean velocities. The FI is electromagnetic in this case. A previous study of a small filament demonstrated that the magnetic pressure gradient force (MPGF) results in a nonlinearly driven electrostatic field. The probably small contribution of the thermal pressure gradient to the force balance implied that the electrostatic field performed undamped oscillations around a background electric field. Here, we consider larger filaments, which reach a stronger electrostatic potential when they saturate. The electron heating is enhanced and electrostatic electron phase space holes form. The competition of several smaller filaments, which grow simultaneously with the large filament, also perturbs the balance between the electrostatic and magnetic fields. The oscillations are damped but the final electric field amplitude is still determined by the MPGF.

One-dimensional particle simulation of the filamentation instability: Electrostatic field driven by the magnetic pressure gradient force

Two counterpropagating cool and equally dense electron beams are modeled with particle-in-cell simulations. The electron beam filamentation instability is examined in one spatial dimension, which is an approximation for a quasiplanar filament boundary. It is confirmed that the force on the electrons imposed by the electrostatic field, which develops during the nonlinear stage of the instability, oscillates around a mean value that equals the magnetic pressure gradient force. The forces acting on the electrons due to the electrostatic and the magnetic field have a similar strength. The electrostatic field reduces the confining force close to the stable equilibrium of each filament and increases it farther away, limiting the peak density. The confining time-averaged total potential permits an overlap of current filaments with an opposite flow direction.

Simulation study of the filamentation of counter-streaming beams of the electrons and positrons in plasmas

The filamentation instability (FI) driven by two spatially uniform and counter-streaming beams of charged particles in plasmas is modelled by a particle-in-cell simulation. Each beam consists of electrons and positrons. The four species are equally dense and have the same temperature. The one-dimensional simulation direction is orthogonal to the beam velocity vector. The magnetic field grows spontaneously and rearranges the particles in space, such that the distributions of the electrons of one beam and the positrons of the second beam match. The simulation demonstrates that as a result no electrostatic field is generated by the magnetic field through its magnetic pressure gradient prior to its saturation. This electrostatic field would be repulsive at the centres of the filaments and limit the maximum charge and current density. The filaments of electrons and positrons in this simulation reach higher charge and current densities than in one with no positrons. The oscillations of the magnetic field strength induced by the magnetically trapped particles result in an oscillatory magnetic pressure gradient force. The latter interplays with the statistical fluctuations in the particle density and it probably enforces a charge separation, by which electrostatic waves grow after the FI has saturated.

High‐ and Low‐Velocity Magnetized Outflows in the Star Formation Process in a Gravitationally Collapsing Cloud

The driving mechanisms of low- and high-velocity outflows in star formation processes are studied using three-dimensional resistive MHD simulations. Starting with a Bonnor-Ebert isothermal cloud rotating in a uniform magnetic field, we calculate cloud evolution from the molecular cloud core (nc = 104 cm −3) to the stellar core (nc = 1022 cm −3), where nc denotes the central density. In the collapsing cloud core, we found two distinct flows: low-velocity flows (~5 km s−1) with a wide opening angle, driven from the adiabatic core when the central density exceeds nc 1012 cm −3; and high-velocity flows (~30 km s−1) with good collimation, driven from the protostar when the central density exceeds nc 1021 cm −3. High-velocity flows are enclosed by low-velocity flows after protostar formation. The difference in the degree of collimation between the two flows is caused by the strength of the magnetic field and configuration of the magnetic field lines. The magnetic field around an adiabatic core is strong and has an hourglass configuration; therefore, flows from the adiabatic core are driven mainly by the magnetocentrifugal mechanism and guided by the hourglass-like field lines. In contrast, the magnetic field around the protostar is weak and has a straight configuration owing to ohmic dissipation in the high-density gas region. Therefore, flows from the protostar are driven mainly by the magnetic pressure gradient force and guided by straight field lines. Differing depth of the gravitational potential between the adiabatic core and the protostar causes the difference of flow speed. Low-velocity flows may correspond to the observed molecular outflows, while high-velocity flows may correspond to the observed optical jets. We suggest that the protostellar outflow and the jet are driven by different cores, rather than the outflow being entrained by the jet.

Current Sheets and Prominence Formation in the Solar Atmosphere

If magnetic field lines in opposite directions expand toward each other to squeeze out the field between them, they come into contact to form an abrupt field reversal (tangential discontinuity) which supports a current sheet. Field line expansion can be caused by the combined pressure gradient and gravity force, the magnetic field pressure gradient force, magnetic fields merging toward each other, or a combination of these effects. In this paper we show that in a quadrupolar magnetic field geometry magnetohydrostatic (MHS) equilibria without null point can be deformed into equilibrium field configurations containing current sheets by changes in forces associated with thermodynamic properties or field line footpoint displacement. The shape of current sheets depends on the pressure distributions and footpoint displacement profiles. These MHS equilibria containing current sheets can evolve into different prominence magnetic field configurations via resistive magnetic reconnection processes to support a higher plasma density at the reconnection site than its surrounding. Examples are given to demonstrate these physical processes. If the plasma pressure (or density) on the photospheric boundary is higher in the lower flux tubes than in the higher tubes in each bipolar arcade, the combined pressure gradient and gravity force pushes magnetic field lines outward from the center of each bipolar arcade. When the plasma temperature increases above a critical value, the enhanced expansion of these arcade fields results in the formation of a current sheet between these two arcades along a separatrix line. Similarly, if the field line footpoints undergo a spatially continuous shearing motion so that the outward gradient force of the sheared magnetic field pressure pushes the field lines of each bipolar arcade into contact, a current sheet of the same shape is formed when the amount of shear is above a critical value. This field configuration can be deformed into a configuration with an X-point through resistive magnetic reconnection. It is expected that an inverse polarity prominence can stably reside above the X-point. If the plasma pressure (or density) on the photospheric boundary is lower in the lower flux tubes than in the higher tubes in each bipolar arcade, the combined pressure gradient and gravity force which pushes down magnetic field lines is reduced when the atmosphere is cooled. When the temperature is decreased below a critical value, the subsequent expansion of field lines due to the magnetic tension force creates a new current sheet configuration with a sharp downward-pointing tip hanging at a distance above the bottom boundary. Resistive magnetic reconnection in this type of current sheet results in a Malville-type field configuration with a magnetic island wrapped in dipped field lines. It is expected that an inverse polarity prominence can stably reside within the magnetic island. Our results suggest that the formation of MHS equilibria containing current sheets and their evolution into prominence magnetic field configurations must be a general process in the solar atmosphere.

The Dynamics and Radiative Properties of Clouds in Magnetized Accretion Disk Outflows in AGNs

AbstractWe have embarked on a general analysis of multi-component outflows from magnetized accretion disks in AGNs. In this scenario, dense diamagnetic clouds are embedded in a centrifugally driven wind and are uplifted from the disk surface by the dynamical drag of the wind as well as by the “melon seed” magnetic pressure gradient force. We follow the motion of the clouds above the disc surface, taking account of the radiation pressure force exerted by the central continuum for different spectral energy distributions and emission patterns. We study the evolution of the clouds as they accelerate through the wind, considering possible sources of confinement and estimating the cloud lifetimes against various disruptive processes. We then examine the spectral signatures of accelerated clouds in the context of this dynamical scheme and compute absorption line profiles as a function of viewing angle through the wind. We apply our results to the interpretation of the observed optical/UV spectra from BALQSOs and of the broad EUV and X-ray absorption features detected in a number of BL Lac objects, as well as to other AGNs in which radiative acceleration of clouds has been inferred (e.g., “warm absorbers”).

Latitudinal dependence of the radial IMF component: Coronal imprint

Measurements by Ulysses have confirmed that there is no significant gradient with respect to heliomagnetic latitude in the radial component, Br, of the interplanetary magnetic field. In the corona, the plasma β is ≪ 1, except directly above streamers, so longitudinal and latitudinal gradients in field strength will relax due to the transverse magnetic pressure gradient force as the solar wind carries magnetic flux away from the Sun. This happens quickly enough so that the field is essentially uniform by 5–10 R⊙, apparently remaining so as it is carried to beyond 1 AU. Here, we illustrate the coronal relaxation with a qualitative physical argument and by reference to a detailed MHD simulation.

One‐dimensional hybrid simulations of the diamagnetic cavity boundary region of comet Halley

A one‐dimensional hybrid technique (particle ions and fluid electrons) is used to study the cometary diamagnetic cavity surface (CS). This hybrid study is unique in that it includes the effects of binary ion‐ion Coulomb collisions, an important process in the dense inner coma. The equilibrium location of the CS is maintained by a force balance mainly between the ion‐neutral drag force and the magnetic pressure gradient force. However, the detailed structure of the CS layer also depends on properties of the plasma such as the thermal pressure. Significant variations of the ion density, ion flow speed, and magnetic field strength take place across the CS boundary layer. Our hybrid code description of the CS structure compares favorably with the data from experiments onboard the Giotto spacecraft. When compared to the magnetohydrodynamical (fluid) results of Cravens (1989), there is good agreement on the "core" width of the plasma density enhancement and on the width of the current layer associated with the magnetic field gradient, but a large discrepancy exists in the width of the ion flow speed transition because of the failure of the fluid model to discern particle effects. Related to this, the hybrid code ion density enhancement is not symmetric as a result of a magnetically reflected, backstreaming ion population within the cavity. The core width of this enhancement (Δn) is highly dependent upon the dissociative recombination rate coefficient, and the hybrid results agree to within 20 percent with the fluid model results of Cravens (1989). The width of the velocity transition (Δν), or the "tail" of the density enhancement, is determined by the collision time for the backstreaming ions. The effect of Coulomb collisions is to decrease (Δν) by a factor of 2. The magnetic field transition has a width (ΔB) that is of the order of a few ion gyroradii. Disrupting the ion gyration by including the effects of binary ion‐ion Coulomb collisions alters the role of the ions as the dominant current carriers within the current layer and slightly reduces ΔB.