In this paper we suggest a simple modification of the dipole magnetic field which introduces field-aligned currents and torsion to the field lines. The resulting field lines are not contained in the meridional planes and have resemblance to the geomagnetic field lines in the dawn and dusk flanks of the magnetosphere. We analyze polarization of the guided standing Shear Alfv & eacute;n Waves (SAWs) in this background field. The resulting polarization is mixed, and pure toroidal and poloidal waves appear only in the limit of exactly dipole background magnetic field. We show that even a small amount of torsion of the background field lines leads to significant deviations from the pure toroidal and poloidal polarization. In contrast, the frequency of the standing waves is much less sensitive to small deviations from the dipole field. In our study the deviation of the wave polarization from either toroidal or poloidal is attributable entirely to the topology of the background magnetic field, as both the magnetic field strength and the plasma density are constrained to be axisymmetric.

It is well established that a sufficiently large gradient of the electric field causes instability of the motion of charged particles in mutually perpendicular electric and magnetic fields. This instability leads to an effective energization of the particles by electrostatic electric fields. The minimum value of the electric field gradient required for this instability to occur for non-relativistic particles depends on the strength of the magnetic field but is independent of both the particle velocity and the local electric field strength. This paper describes an instability caused by non-uniformity of the electric field for relativistic particles and demonstrates that its threshold in the relativistic case depends, in addition to the magnetic field intensity, on the speed of the particle and the local strength of the electric field. Larger particle speeds and larger electric fields reduce the gradient of the electric field required to make the particle motion unstable. (c) 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercialNoDerivs 4.0 International (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/). https://doi.org/10.1063/5.0220994

This paper analyzes the two-dimensional motion of a charged particle in constant mutually perpendicular electric and magnetic fields. The magnetic field is assumed to be uniform, and the electric field components are assumed to be linear functions of the Cartesian coordinates. Under these assumptions, the equations of particle motion can be solved analytically. This solution is used to study the stability of particle motion and to assess the accuracy of the guiding center approximation in the presence of electric field gradients. It is well known that if the gradient of a one-dimensional electric field is sufficiently large, the motion of the charged particles becomes unstable and the particles are effectively energized by the electric field. This paper, however, demonstrates that the instability threshold depends on the spatial derivatives of both electric field components and is, under certain conditions, very sensitive to both. The analytical solution is averaged over the gyroperiod to derive simple expressions for the drift speed and the position of the gyrocenter, which explicitly account for the electric field gradient. The results of this averaging are used to develop equations for tracing the particle gyrocenter location, which incorporate the effects of non-uniformity of the electric field. These equations are shown to be noticeably more accurate than those based on the standard E × B drift velocity, which is exact only for uniform electric and magnetic fields. Simple expressions for the local errors in the E × B drift velocity are also derived, which arise from the electric field gradients.

Using global magnetohydrodynamic simulations, we construct a 3D parametric model of the Martian magnetic pileup boundary (MPB). This model employs a modified parabola function defined by four parameters. The effects of the solar wind dynamic pressure, the solar wind densities and velocities, and the intensity and orientation of the interplanetary magnetic field (IMF) are examined using 267 simulation cases. The results from our parametric model show that (1) the MPB moves closer to Mars when the upstream solar wind dynamic pressure (Pd) increases, the subsolar standoff distance decreases and the flaring degree of the Martian MPB increases with an increasing Pd according to the power-law relations. For the same Pd, a higher solar wind velocity (a lower density) leads to a farther location of the MPB from Mars, along with a larger flaring degree, which is explained by the higher solar wind convection electric fields and a stronger magnetic pileup process under these conditions. (2) Larger Y or Z components of the IMF, BY or BZ, result in a thicker pileup region and a farther MPB location from Mars, as well as a decrease in the flaring degree. The radial IMF component, BX, has little effect on the geometry of the MPB. (3) In most of the simulations used to derive the current parametric model, the strongest Martian crustal magnetic field is located on the dayside. However, for a larger value of the southward IMF, the Martian MPB is located farther away in the northern hemisphere instead of the southern hemisphere. The north-south asymmetry of the Martian MPB with the southern hemisphere being farther away is observed for other IMF directions. We suggest that the magnetic reconnection of the southward IMF with the crustal field that occurs at middle latitudes of the southern hemisphere results in different magnetic field topologies and the closer location of the MPB under these conditions. Our model results show a relatively good agreement with the previous empirical and theoretical models.

A global MHD model is used to study the energy transfer from solar wind to magnetosphere through magnetopause under radial interplanetary magnetic fields (IMFs). We use the streamline method to determine the smooth surface of the magnetopause by searching the inner boundary of the solar-wind streamline and discuss the roles of magnetic reconnection and viscous interaction under radial IMFs, which we compare with cases of north–south IMFs. We find that (1) the energy transfer across the magnetopause is asymmetric between the northern and southern hemispheres due to different reconnection locations, particularly for electromagnetic energy; (2) for sunward IMF, the most significant area of the net input of mechanical energy occurs on the day side and near-Earth magnetotail, and the electromagnetic energy input in the northern hemisphere is much larger than in the southern hemisphere on the night side; (3) the mechanical and electromagnetic energy-transfer distribution in the northern (southern) hemisphere for earthward IMF is the same as that in the southern (northern) hemisphere for sunward IMF; (4) the electromagnetic energy input for radial IMF is two times larger than for northward IMF, but three times smaller than for southward IMF, the viscous effect is smaller than for northward IMF but comparable to that for southward IMF, the rate of energy transfer is 2.22% for radial IMF, which is lower than 4.95% for southward IMF, but higher than 1.7% for northward IMF; and (5) the Akasofu-type energy-coupling formula, ϵ , is not suitable for the solar-wind events dominated by IMF B x .

This paper presents the calculation of the adiabatic invariant for the motion of a charged particle in a two-dimensional magnetic field with a constant gradient. Magnetic field intensity is equal to zero along the neutral line for this field model. The mathematical expression for the invariant depends upon whether the particle crosses the neutral line. For trajectories that do not cross the neutral line, the adiabatic invariant reduces to the familiar expression for the magnetic moment, μ0=v2/B, for small values of the magnetic field gradient. The two expressions for the adiabatic invariant can be matched continuously across the change in the type of trajectory. When the magnetic field parameters smoothly change in time, the adiabatic invariant is conserved exponentially well as long as the type of the particle trajectory remains the same. If, however, the trajectory of a particle initially crosses the neutral line but after the magnetic field evolution stops crossing it (or vice versa), the adiabatic invariant is not conserved.

Using a 3D multispecies magnetohydrodynamic model, we investigated the effect of the solar wind dynamic pressure ( P d ) with different densities and velocities on the subsolar standoff distance ( r 0 ) of the Martian magnetic pileup boundary (MPB). We fixed the solar maximum condition, the strongest crustal field located in the dayside region, and the Parker spiral interplanetary magnetic field at Mars. We simulated 35 cases with a P d range of 0.1494 to 7.323 nPa (solar wind number density n ∈ [1, 9] cm −3 , and solar wind velocity V ∈ [−258, −1344] km s −1 ). The main results are as follows. (1) r 0 decreases with increasing P d according to the power-law relations. For the same P d , a higher solar wind velocity (lower density) results in a larger r 0 of the Martian MPB. (2) A higher solar wind density leads to a lower ratio of the compressed magnetic field strength to the crustal field strength and a larger plasma β under the same P d . This indicates that the thermal pressure at the Martian MPB plays a significant role for the compressed magnetic field. Because the magnetic pileup process is stronger for a higher solar wind velocity, the magnetic pressure at the Martian MPB is increased. As a result, the thermal pressure decreases and r 0 of the Martian MPB increases. (3) We present a new formula of r 0 with the parameters of the solar wind dynamic pressure, number density, and velocity.

In studies of physical processes near planetary bow shocks, empirical models of the latter are usually used. While computational magneto‐hydrodynamics (MHD) or kinetic models of bow shocks are often more accurate, their computationally extensive nature limits their applicability to routine analysis of large volumes of data. We suggest an analytical model of the bow shock position based on MHD calculations and accurate analytical solutions. The analytical expressions for the bow shock position and shape include the following parameters: The distance of the bow shock nose point from the planet, radii of curvature and bluntnesses of the shock surface at this point and a parameter describing the transition to the asymptotic downstream slope of the shock. It is shown that for an analytical description of the surface of the shock, it is sufficient to approximate its radius of curvature and bluntness in two perpendicular planes. Another parameter used in this model is the bow shock skewing angle, appearing when the interplanetary magnetic field directed at an angle with respect to the solar wind velocity. This parameter naturally vanishes when the magnetic field of the solar wind is directed either parallel or perpendicular to the velocity vector. The exact analytical solution for the asymptotic downstream slope of the MHD Mach cone is modified to take into account the skewing angle of the bow shock.

Study of physical processes in plasma near planets often requires knowledge of the position and shape of the planetary bow shock. Empirical models are usually used since theoretical MHD and kinetic models consume too much computer time and cannot be used to track fast processes. M.I. Verigin proposed a semi-empirical approach based on the use of exact theoretical expressions with a small number of parameters, which have a clear physical meaning. These parameters are estimated by fitting experimental data or detailed MHD calculations. A model of the bow shock near an arbitrary-shaped obstacle has previously been developed for a gas-dynamic flow. This model can be applied to any sonic Mach numbers and large values of the Alfven Mach number. In addition, the asymptotic Mach cone - the angle of inclination of the shock wave at an infinite distance from the planet - has been calculated analytically in the MHD approximation. In this paper, we propose a model of the bow shock for any direction of the magnetic field with respect to the upcoming flow and for any Mach numbers. Parameters of the model are the distance of the nose point from the obstacle, radius of curvature and bluntness of the bow shock at the nose point, a parameter related to the transition to the asymptotic downstream slope of the shock, and a skewing angle appearing when the interplanetary magnetic field is directed at an angle to the solar wind velocity.

The frozen-in interplanetary magnetic field (IMF) in the solar wind is one of the most important parameters affecting the Earth's space weather. In the early studies of the IMF's influence on space weather, significant effects of the north-south component of the IMF B-Z were emphasized, while the radial component of the IMF B-X was largely ignored. However, the IMF near the Earth is not always dominated by the north-south component of the IMF B-Z, and the radial component of the IMF B-X also plays an important role. However, while the effects of the IMF B-X (cone angle) on the magnetopause have been studied in recent years, there has been much less effort to quantify the B-X (cone angle) effects on the bow shock. In this paper, using the bow shock crossing data from multiple satellites, we investigate the IMF cone angle effect on the dayside and nightside of the bow shock. Our results show that under the radial IMF condition, the dayside of the bow shock is located closer to the Earth than the average. At the same time, on the nightside, the bow shock is farther away from the Earth than the average. The mechanism explaining the bow shock location under the radial IMF is not completely understood. We believe that the magnetosonic Mach number and unusual conditions of the magnetosheath, especially for low dynamic pressure, play an important role. In the future, more work is needed to describe the reactions of the Earth's magnetosphere to different IMF orientations, especially to the radial IMF.

An analytical semiempirical model of the bow shock based on theoretical MGD calculations, accurate analytical solutions, and experimental data continues to be developed. The model parameters have a clear physical meaning. For cases in which the magnetic field of the solar wind is directed along its velocity or is perpendicular to the velocity vector, analytical expressions that allow calculating the parameters of the bow shock-the distance to the subsolar point, the radius of the curvature, and the bluntness at the subsolar point-are obtained via renormalization of the previously developed detailed gas-dynamic model. For the case in which the magnetic field vector is perpendicular to the solar wind velocity vector, it is shown that it is sufficient for an analytical description of the bow shock surface to approximate its parameters in two perpendicular planes.

This paper discusses the calculation of the adiabatic invariant of a charged particle moving in an axisymmetric magnetic field with straight field lines. This calculation can be reduced to quadratures, and in several cases, the exact analytical results can be obtained. In particular, an exact expression is obtained for the charged particle motion in the equatorial field of a magnetic dipole, which can have important applications to the high-order guiding center theory for the particles in the terrestrial radiation belts. Another closed-form analytical result corresponds to magnetic field intensity which is inversely proportional to the radius. The results represent an extension of the classical series expansions of Kruskal for these specific magnetic fields.

Using the bow shock crossing events from four spacecraft: IMP 8, Geotail, Magion-4, and Cluster 1, a new three-dimensional asymmetric bow shock model is constructed. The model is parameterized by the solar wind dynamic pressure, the interplanetary magnetic field, magnetosonic Mach number, solar wind beta, and the Earth's dipole tilt angle. It is shown that the shape and size of bow shock are both affected by the dipole tilt angle. The dipole tilt angle causes asymmetries in the meridional plane: (1) the bow shock subsolar standoff distance and the north-south asymmetry increase with the dipole tilt angle; (2) as the dipole tilt angle increases, the shock flaring angle in the equatorial plane is slightly reduced, while in the meridional plane the flaring angle obviously decreases in Southern Hemisphere and keeps almost unchanged in the Northern Hemisphere. The flaring angle in the Northern Hemisphere is larger than in the Southern Hemisphere; (3) the effects of negative dipole tilt angle on shock flaring are just the opposite of those for positive tilt, and the effects of dipole tilt angle on the shape of the bow shock are north-south symmetric. The model results are also validated by comparing with one previous empirical model and with observational crossings, and it is demonstrated that the new model is able to predict the observed crossings more accurately and can better describe the rotational asymmetry and north-south asymmetry of the Earth's bow shock.

A plane‐polarized electromagnetic wave that propagates through a plasma, (anti)parallel to a magnetic field, experiences a gradual rotation of its plane of polarization called Faraday rotation (FR). The FR angle depends on the integrated product of the electron density and the strength of the parallel magnetic field projection to the radio wave propagation direction. The integral is taken along the radio wave propagation direction over the entire path length. Therefore, accurate measurements or a suitable model for both the electron density and the magnetic field as well as the propagation trajectory are required for the interpretation of FR measurements. Many authors use the average value of the parallel magnetic field for estimation of FR from ionospheric total electron content measurements. Although it is known that the strength of Earth's geomagnetic field varies slowly at ionospheric altitudes, a reference height characteristic value or mean value may not always be appropriate. This work considers alternative methods to establish a characteristic value for the average parallel component of the magnetic field, particularly when independent FR and total electron content measurements are available.

In this paper we discuss conditions under which charged particles are confined by an axisymmetric longitudinal magnetic field with power law dependence on the radius. We derive a transcendental equation for the critical speed corresponding to the threshold between bounded and unbounded trajectories of the particles. This threshold speed shows strong dependence on the direction, and this dependence becomes more prominent as the exponent of the power law increases. The equation for threshold speed can be solved exactly for several specific values of the power exponent, but in general it requires a numerical treatment. Remarkably, if the magnetic field magnitude decreases more slowly than the inverse of the radius, charged particles remain confined no matter how large their energies may be.

In this study we use the bow shock crossings contained in the Space Physics Data Facility database, collected by four spacecraft (IMP 8, Geotail, Magion-4, and Cluster1) to analyze the effect of the interplanetary magnetic field (IMF) B-y component on the bow shock position and shape. Although the IMF B-z component is usually considered much more geoeffective than B-y, we find that the dayside bow shock is more responsive to the eastward component of the IMF than the north-south one. We believe that the explanation lies in the changes that the B-z component induces on the magnetopause location and shape, which largely compensate the corresponding changes in the dayside bow shock location. In the tail, we find that the bow shock cross section is elongated roughly in the direction perpendicular to the IMF direction, which agrees with earlier modeling studies.

Magnetotail dipolarizations, often associated with substorms, produce significant energetic particle enhancements in the nighttime magnetosphere. In this paper, we apply our recently developed magnetotail dipolarization model to the problem of energizing electrons and ions. Our model is two-dimensional in the meridional plane and is characterized by the ability to precisely control the location of the transition from the dipole-like to tail-like magnetic fields. Both magnetic and electric fields are calculated, self-consistently, as the transition zone retreats farther into the tail and the area around the Earth occupied by dipole-like lines increases in size. These fields are used to calculate the motion of electrons and ions and changes in their energies. We consider the energizing effects of the fields restricted to +/- 15 degrees and +/- 30 degrees sectors around the midnight meridian, as well the axisymmetric case. Energies of some electrons increase by a factor of 25, which is more than enough to produce observable ionospheric signatures. Electrons are treated using the Guiding Center approximation, while protons and heavier particles generally require description based on the Lorentz equations.

Radio waves propagating through plasma in the Earth's ambient magnetic field experience Faraday rotation; the plane of the electric field of a linearly polarized wave changes as a function of the distance travelled through a plasma. Linearly polarized radio waves at 1090MHz frequency are emitted by Automatic Dependent Surveillance Broadcast (ADS-B) devices that are installed on most commercial aircraft. These radio waves can be detected by satellites in low Earth orbits, and the change of the polarization angle caused by propagation through the terrestrial ionosphere can be measured. In this manuscript we discuss how these measurements can be used to characterize the ionospheric conditions. In the present study, we compute the amount of Faraday rotation from a prescribed total electron content value and two of the profile parameters of the NeQuick ionospheric model.