Pressure Balance Condition Research Articles

The Dependence of the Location and Pressure Variations of the Martian Magnetic Pileup Boundary on the Interplanetary Magnetic Field: An MHD Simulation Study

Abstract In this paper, using a three-dimensional multispecies MHD model, we study the effect of the interplanetary magnetic field (IMF) intensity and orientation on the subsolar standoff distance of the Martian magnetic pileup boundary (r 0) and the pressure balance across it. The results show that: (1) with the increasing magnitude of the Y- or Z-component of the IMF, B Y or B Z , r 0 increases, while the radial IMF component, B X , has little effect. With the increasing magnitude of B Y or B Z , the compression degree of the magnetic field (f) increases, while the solar wind pressure coefficient (k) remains unchanged, resulting in the enhancement of r 0. (2) Under the same IMF intensity, B t , the impact of the IMF cone angle on r 0 and f is controlled by the ratio of the IMF Y- and Z-components to B t , B Y 2 + B Z 2 / B t . When the ratio is enhanced, both r 0 and f increase, while k generally remains unchanged. Compared with the IMF cone angle, the influence of the IMF clock angle is relatively less. We suggest that the stronger magnetic pileup process controlled by the perpendicular IMFs (B Y or B Z ) causes the larger r 0, while the weaker magnetic pileup under the radial IMF leads to the smaller r 0. The difference in the IMF effect on the size of the Martian magnetic pileup boundary and the terrestrial magnetopause reveals different solar wind interactions with a magnetized and unmagnetized planet. Last, the location of the intense crustal field can also affect r 0 and the pressure balance condition, and the specific impact needs to be further studied.

A semi-analytical solution to the forward–reverse shock hydrodynamics of the gamma-ray burst afterglow

ABSTRACT We extend the standard model of forward–reverse shock (FS–RS) for gamma-ray burst (GRB) afterglow to more general cases. On one hand, we derive the analytical solution to the hydrodynamics of the shocks in two limiting cases, i.e. an ultrarelativistic reverse shock case and a Newtonian reverse shock case. Based on the asymptotic solutions in these two limiting cases, we constitute a semi-analytical solution for the hydrodynamics of the shocks in the generic case, covering the mildly relativistic reverse shock case. On the other hand, we derive the evolution of the system taking into account the condition of energy conservation which is not satisfied in the standard FS–RS model. A generic solution of semi-analytical expressions is also given. In both the extended standard FS–RS model (satisfying pressure balance condition) and the model satisfying energy conservation, we find that the results in the ultrarelativistic reverse shock case and in the early stage of the Newtonian reverse shock case are different from those in the standard FS–RS model by only a factor that close to one while the same initial conditions adopted. However, the asymptotic solutions in the limiting cases are not good approximations to those in the intermediate case. Our semi-analytical results agree well with the numerical results for a large range of model parameters, and hence can be easily employed to diagnose the physical quantities of the GRB shell and circumburst environment.

Metal evaporation flux across Knudsen layer in laser keyhole welding of Al–Mg alloys with pressure balance condition method

This study aims to calculate the metal evaporation flux across the Knudsen layer inside the keyhole in laser welding of Al–Mg alloys. The pressure balance at the keyhole wall was analysed and used as the boundary condition in the calculation. Based on the extracted keyhole shape parameters from high-speed images, the surface temperature and gas pressure inside the keyhole were calculated, and the evaporation fluxes for both Al and Mg were acquired. The results show that the front wall of the keyhole absorbs more laser energy than the rear wall. The gas pressure inside the keyhole increases and the evaporation flux decreases with increasing keyhole depth. In addition, the evaporation flux of Mg is much higher than that of the base element Al, which can result in the loss of Mg inside the melt pool. The distribution of the Mg evaporation flux inside the keyhole agrees with the measured Mg loss in the welded section of the Al–Mg alloy. Thus, the calculation method of the metal evaporation flux inside the keyhole can be applied in future simulations of element loss in laser keyhole welding.

Pressure Control of High Pressure Tubing

This article focuses on how to control the pressure in the high-pressure tubing. First, an overall analysis of the system is performed to determine the pressure balance conditions of the high-pressure fuel pipe; that is, the mass of fuel flowing out of the high-pressure fuel pipe is equal to the mass of fuel flowing in. This article uses Excel to fit and organize the data in all data processing. When solving differential equations of pressure and density, the fourth-order Runge-Kutta formula is used, and the numerical solution is obtained by MATLAB2017a.

A Self‐Regulating Equilibrium Magnetopause Model With Applications to Saturn

AbstractWe describe a new method of constructing an equilibrium magnetopause surface based on the pressure balance between external and internal pressure sources. Details are given for every step of the procedure, including the initial pressure balance condition (which determines magnetopause morphology), the related underlying assumptions, and the final optimized magnetopause surface. Our method produces a final equilibrium magnetopause surface that satisfies the local balance between the solar wind dynamic pressure and planetary magnetic pressure with an error no greater than 1%. We also discuss the contribution of hot plasma pressure and equatorial ring currents and their effects on magnetopause morphology. For each optimized magnetopause boundary, we give coefficients for fitted polynomial approximations to allow simple and accurate reproductions for practical applications. We specifically discuss the potential application to the modeling of Saturn's magnetopause and describe how the equilibrium magnetopause model can be used to estimate the compressibility of the boundary.

Halo coronal mass ejections during Solar Cycle 24: reconstruction of the global scenario and geoeffectiveness

Coronal mass ejections (CMEs), in particular Earth-directed ones, are regarded as the main drivers of geomagnetic activity. In this study, we present a statistical analysis of a set of 53 fast (V ≥ 1000 km·s−1) Earth-directed halo CMEs observed by the SOHO/LASCO instrument during the period Jan. 2009–Sep. 2015, and we then use this CME sample to test the forecasting capabilities of a new Sun-to-Earth prediction scheme for the geoeffectiveness of Earth-directed halo CMEs. First, we investigate the CME association with other solar activity features such as solar flares, active regions, and others, by means of multi-instrument observations of the solar magnetic and plasma properties, with the final aim of identifying recurrent peculiar features that can be used as precursors of CME-driven geomagnetic storms. Second, using coronagraphic images to derive the CME kinematical properties at 0.1 AU, we propagate the events to 1 AU by means of 3D global MHD simulations. In particular, we use the WSA-ENLIL+Cone model to reconstruct the propagation and global evolution of each event up to their arrival at Earth, where simulation results are compared with interplanetary CME (ICME) in-situ signatures. We then use simulation outputs upstream of Earth to predict their impact on geospace. By applying the pressure balance condition at the magnetopause and the coupling function proposed by Newell et al. [J Geophys Res: Space Phys 113 (2008)] to link upstream solar wind properties to the global Kp index, we estimate the expected magnetospheric compression and geomagnetic activity level, and compare our predictions with global data records. The analysis indicates that 82% of the fast Earth-directed halo CMEs arrived at Earth within the next 4 days. Almost the totality of them compressed the magnetopause below geosynchronous orbits and triggered a minor or major geomagnetic storm afterwards. Among them, complex sunspot-rich active regions associated with X- and M-class flares are the most favourable configurations from which geoeffective CMEs originate. The analysis of related Solar Energetic Particle (SEP) events shows that 74% of the CMEs associated with major SEPs were geoeffective, i.e. they triggered a minor to intense geomagnetic storm (Kp ≥ 5). Moreover, the SEP production is enhanced in the case of fast and interacting CMEs. In this work we present a first attempt at applying a Sun-to-Earth geoeffectiveness prediction scheme − based on 3D simulations and solar wind-geomagnetic activity coupling functions − to a statistical set of fast Earth-directed, potentially geoeffective halo CMEs. The results of the prediction scheme are promising and in good agreement with the actual data records for geomagnetic activity. However, we point out the need for future studies performing a fine-tuning of the prediction scheme, in particular in terms of the evaluation of the CME input parameters and the modelling of their internal magnetic structure.

Effect of stellar wind induced magnetic fields on planetary obstacles of non-magnetized hot Jupiters

We investigate the interaction between the magnetized stellar wind plasma and the partially ionized hydrodynamic hydrogen outflow from the escaping upper atmosphere of non- or weakly magnetized hot Jupiters. We use the well-studied hot Jupiter HD 209458b as an example for similar exoplanets, assuming a negligible intrinsic magnetic moment. For this planet, the stellar wind plasma interaction forms an obstacle in the planet's upper atmosphere, in which the position of the magnetopause is determined by the condition of pressure balance between the stellar wind and the expanded atmosphere, heated by the stellar extreme ultraviolet (EUV) radiation. We show that the neutral atmospheric atoms penetrate into the region dominated by the stellar wind, where they are ionized by photo-ionization and charge exchange, and then mixed with the stellar wind flow. Using a 3D magnetohydrodynamic (MHD) model, we show that an induced magnetic field forms in front of the planetary obstacle, which appears to be much stronger compared to those produced by the solar wind interaction with Venus and Mars. Depending on the stellar wind parameters, because of the induced magnetic field, the planetary obstacle can move up to ~0.5-1 planetary radii closer to the planet. Finally, we discuss how estimations of the intrinsic magnetic moment of hot Jupiters can be inferred by coupling hydrodynamic upper planetary atmosphere and MHD stellar wind interaction models together with UV observations. In particular, we find that HD 209458b should likely have an intrinsic magnetic moment of 10-20% that of Jupiter.

Magnetotail magnetic flux monitoring based on simultaneous solar wind and magnetotail observations

AbstractThe magnetotail magnetic flux (MTF) is an important global variable to describe the magnetospheric state and dynamics. Existing methods of MTF estimation on the basis of the polar cap area, inferred from observations of global auroras and field‐aligned currents, do not allow benchmarking due to the absence of a gauge for comparison; besides, they rarely allow a systematic nearly real time MTF monitoring. We describe three modifications (F0, F1, and F2) of the method to calculate the MTF, based on simultaneous spacecraft observations in the magnetotail and in the solar wind, suitable for real‐time MTF monitoring. The MTF dependence on the solar wind parameters and the observed tail lobe magnetic field is derived from the pressure balance conditions. An essential part of this study is the calibration of our approximate method against global 3‐D MHD simulations and the empirical T14 magnetospheric field model. The calibration procedure provides all variables required to evaluate F0, F1, and F2 quantities and, at the same time, computes the reference MTF value through any tail cross section. It allowed us to extend the method to be used in the near tail, investigate its errors, and define the applicability domain. The method was applied to Cluster and THEMIS measurements and compared with methods of polar cap area calculation based on IMAGE and AMPERE observations. We also discuss possible applications and some recent results based on the proposed method.

Role of finite ion temperature in the generation of field swelling instability

Field swelling instability is one of the most important instabilities in plasmas in which electrons are hotter than ions. In contrast to diamagnetic (mirror) instability belonging to the branch of slow magnetosonic waves, field swelling instability corresponds to the branch of fast magnetosonic waves. The theory of this instability was developed by (Basu and Coppi, 1982, 1984) in the early 1980s in the idealized zero ion temperature limit in the context of the magnetohydrodynamic model. To make the model more realistic, it is necessary to complete it with finite ion temperature effects. In addition, we consider the field swelling theory in the context of a more instructive quasihydrodynamic approach which showed a good performance on examination of the mirror instability. Here, it appears to be necessary to use only the transverse plasma pressure balance condition and Liouville theorem for calculating the transverse pressure variation. This consideration is simpler and clearer and makes it possible to understand in more detail the physical nature of the instability and to prepare the necessary basis for interpreting observational data.

STOCHASTIC ACCELERATION OF SUPRATHERMAL PARTICLES UNDER PRESSURE BALANCE CONDITIONS

The acceleration of suprathermal charged particles in the heliosphere under pressure balance conditions including for the first time the radial spatial particle diffusion and convection in the solar wind is investigated. The physical conditions are derived for which the stationary phase space distribution of suprathermal particles approaches the power-law distribution f∝p –5, which is often seen in spacecraft observations. For separable source distributions in momentum and position we analytically solve the stationary particle transport equation for a radially constant solar wind speed V 0 and a momentum-independent radial spatial diffusion coefficient. The resulting stationary solution at any position within the finite heliosphere is the superposition of an infinite sum of power laws in momentum below and above the (assumed mono-momentum) injection momentum pI . The smallest spatial eigenvalue determines the flattest power law, to which the full stationary solution approaches at large and small enough momenta. Only for the case of a reflecting inner and a free-escape outer spatial boundary, does one small eigenvalue exist, yielding the power-law distribution f∝p –5 at sufficiently large momentum values. The other three spatial boundary conditions imply steeper momentum spectra. Momentum spectra and radial profiles of suprathermal particles are calculated by adopting a uniform outer ring spatial source distribution.

Pressure balance on the magnetopause near the subsolar point according to observational data of the THEMIS project satellites

An analysis of the pressure balance on the magnetopause near the subsolar point has been made for 18 crossings of the magnetopause by the THEMIS project satellites under magneto-quiet conditions. Dynamic and static pressures of plasma are determined, as well as magnetic pressure in the magnetosheath, and magnetic and plasma static pressure inside the magnetosphere. Variations of the total pressure have been studied in the case when one satellite is located inside the magnetosphere and another one stays in the magnetosheath near the magnetopause. It is demonstrated that for 18 investigated events the condition of pressure balance at the subsolar point is valid on average with an accuracy of 7%, within measurement errors and under applicability of the approximation of anisotropic magnetic hydrodynamics to collisionless plasma of the magnetosheath and magnetosphere.

The separation of immiscible liquid slugs within plastic microchannels using a metallic hydrophilic sidestream

This paper describes experiments and related modelling on a new method for separating aqueous phase slugs from the surrounding organic matrix phase in segmented two phase flow in a plastic microcapillary film (MCF). Kerosene or paraffin oil was metered through a plastic capillary of 630 microns diameter and aqueous phase slugs were generated within the capillary by the continuous sidestream injection of water. It was found that the resulting aqueous phase slugs formed in the MCF could be subsequently easily separated from the organic phase by piercing the downstream sidewall of the plastic capillary with a hydrophilic metal hypodermic needle to draw off an aqueous sidestream. Optical scrutiny of the phase separation process indicated that two distinct disengagement mechanisms are involved, in which the metal needle tip either remains submerged in the aqueous phase or becomes periodically exposed to the organic phase at certain stages of the segregation process. The separation efficiency, i.e. the degree of residual phase cross-contamination, was determined as a function of both the sidestream needle angle and the depth of needle penetration into the capillary for a given flow rate and phase ratio. It was established that the separation efficiency was very sensitive to the downstream pressure balance between the organic mainstream flow in the plastic capillary and the aqueous sidestream flow through the needle. A mathematical model for the pressure balance conditions was developed by making certain simplifying assumptions and taking the Laplace interfacial pressure into account. The model predictions agreed surprisingly well with the experimental findings, thus providing circumstantial evidence for the validity of the insights into the phase separation mechanism.

On the reconstruction of magnetospheric plasma pressure distributions from empirical geomagnetic field models

Four data‐based models of the magnetospheric magnetic field were tested for the degree of their consistency with a static balance between the magnetic and plasma stresses. To that end, best fit distributions of the plasma sheet pressure and its anisotropy were derived in the midnight meridian plane, using two specific forms of the particle distribution function. The tailward limit of the modeling region was placed at R = 20 RE, where the condition of pressure balance with the tail lobe field was used to avoid the multiplicity of solutions of the force balance equation. Best fit solutions were derived by minimizing the rms difference between the magnetic and plasma stress vectors over a set of points within the model plasma sheet at distances 5 ≤ R ≤ 20 RE. The obtained equatorial profiles of P⊥ and P∥ demonstrate a steep decrease of both pressures from the inner to outer boundary and a strong overall increase from quiet to disturbed conditions. The anisotropy ratio β = P∥/P⊥ was found to significantly deviate from unity in the case of TU82 and T87 models, with progressively higher values of β at larger tailward distances. By contrast, more recent T89 and T96 models yielded more realistic results with nearly isotropic pressure in the tail and a moderate pancake‐type anisotropy in the inner magnetosphere, consistent with observations.

Mirror instability in space plasmas: Solitons and cnoidal waves

The nonlinear theory of magnetic mirror instability (MI) in space plasmas is revisited. The nonlinear dynamics of the MI is analyzed using the perpendicular plasma pressure balance condition and the drift kinetic equation for the ion distribution function as the starting point. In contrast with previous studies we do not rely on the reductive perturbation method and kinetic effects have been included in the model at all stages. It is shown that the MI initially produces a depression in the magnetic field that has an explosive behavior as was predicted previously. However, this process rapidly terminates and reaches finally saturation with the formation of stationary solutions in the form of either soliton type magnetic holes, cnoidal waves, or linear oscillations.

Rankine–Hugoniot relations for shocks with demagnetized ions

AbstractThe width of a quasi-perpendicular collisionless shock front is smaller than the convective ion gyroradius so that ions become demagnetized in the ramp. An approach is proposed for derivation of approximate expressions for the magnetic compression ratio and cross-shock potential from the analysis of the ion motion across the ramp and pressure balance condition, without making assumptions about the ion equation of state. The cross-shock potential and magnetic compression ratio are found as functions of the Mach number for low-Mach-number perpendicular shocks.

Nonlinear analysis of the equilibrium shape of a charged drop in the tornado funnel wall

From the pressure balance condition on the free surface of a conducting liquid charged drop, an expression is derived for the equilibrium shape of the drop placed in the field of centrifugal forces acting in the tornado wall. The analysis is carried out in an approximation quadratic in small parameter (the ratio of the deformation amplitude to the radius of the initially spherical drop). In the linear approximation, the drop is a spheroid oblate in the direction normal to the tornado axis. The eccentricity of the spheroid squared is proportional to the angular velocity squared and the radius of the drop cubed. In the quadratic approximation, the equilibrium shape of the drop is other than spheroidal.

Nonlinear analysis of the equilibrium shape of a charged drop rotating around its symmetry axis

From the condition of pressure balance on the free surface of a charged rotating conducting-liquid drop, an analytical expression for the equilibrium shape of the drop is derived in the second-order approximation in a small parameter, the ratio of the deformation amplitude to the radius of the initial spherical shape. It is found that, in the linear approximation in the small parameter, the drop takes the form of an oblate spheroid, while in the quadratic approximation, the equilibrium shape of the drop differs from the spheroidal one.

Magnetostatic penumbra models with field-free gaps

We present numerical 2D magnetostatic models for sunspot penumbrae consisting of radially aligned field-free gaps in a potential magnetic field, as proposed by Spruit and Scharmer (2006). The shape of the gaps and the field configurations around them are computed consistently from the condition of magnetostatic pressure balance between the gap and the magnetic field. The results show that field-free gaps in the {\it inner} penumbra are cusp-shaped and bounded by a magnetic field inclined by about $70^\circ$ from the vertical. Here, the magnetic component has a Wilson depression on the order 200--300 km relative to the top of the field-free gap; the gaps should thus appear as noticeably elevated features. This structure explains the large variations in field strength in the inner penumbra inferred from magnetograms and two-component inversions, and the varying appearance of the inner penumbra with viewing angle. In the {\it outer} penumbra, on the other hand, the gaps are flat-topped with a horizontal magnetic field above the middle of the gap. The magnetic field has large inclination variations horizontally, but only small fluctuations in field strength, in agreement with observations.

A proxy for determining solar wind dynamic pressure at Mars using Mars Global Surveyor data

We develop a method to infer the upstream solar wind pressure at Mars using data from the Mars Global Surveyor (MGS) magnetometer instrument. The method assumes magnetic field pressure in the magnetic pileup region balances the incident solar wind dynamic pressure. Newtonian pressure balance conditions are imposed for positions off of the subflow point. Proof of concept exists from the mapping phase of the spacecraft mission, when the orbital geometry at a constant altitude allows fits to magnetic field data as a function of solar zenith angle. During the elliptical orbit phase of MGS, when the spacecraft passes through a large range of altitudes, such fits are not possible. However, the measured magnetic pressure in the magnetic pileup region is scaled by the same means as derived for the mapping orbits and reasonable upstream solar wind pressure is obtained. We compare the distribution of solar wind pressure calculated using MGS data with the solar wind pressure measured upstream of the Earth during the same time period and find good agreement, further supporting this algorithm as a valid proxy for the incident solar wind pressure. The response of the position of the Magnetic Pileup Boundary to the inferred solar wind pressure also validates the method. High solar wind ram pressure depresses the altitude of the Magnetic Pileup Boundary.

On the Bowshocks Associated with the Orion Proplyds

We investigate the global stellar wind dynamics of the exciting star of the Orion Nebula by using the “proplyds” and their bowshocks as probes of the ram pressure balance conditions in the nebula. This careful analysis is only possible if high resolution data are available, since the proplyds are so small and the bowshocks are so faint.