Igor V. Kubyshkin

There is significant interest in monitoring the instantaneous magnetic configurations and dynamic states of the magnetotail and understanding what controls them. A unique and attractive opportunity is provided by remote sensing of the radial profile of the equatorial magnetic field curvature based on low‐latitude energetic particle measurements of isotropy boundaries (IBs), providing that you can determine the origin of isotropic precipitation. To validate the magnetic field line curvature scattering (FLCS) as the main mechanism of the isotropy boundary formation, we compare coarse energy versus latitude IB profiles (in 3 + 3 energy channels) measured during a few dozen passes of POES and ELFIN spacecraft with the theoretical predictions of the adapted (AM03) magnetospheric model. Two studied intervals in August 2022 include substorm events of various intensities for which good spacecraft coverage in the near magnetotail helps reconstruct the adaptive model in the areas where the IBs are formed. We find a general agreement between the predicted and observed coarse IB profiles' shape and latitude, validating the FLCS hypothesis. Deviations are also observed, and we discuss the factors that can influence identification of the true FLCS profiles in observations and predictions, including limitations of adaptive modeling, non‐monotonic radial structure of the tail magnetic field, and interference of FLCS with other precipitation mechanisms related to wave‐particle interactions. Most can be avoided by improving the sensitivity, energy coverage, and resolution in future instruments.

We thank Lauri Holappa, Jone Peter Reistad and Anders Ohma for their interest in our research and for having published their comments, referred hereafter as HEA2023. Here we present our counterarguments to the points presented in HEA2023. We explain the observed excess of AL values for different polarities of IMF B_y over different IMF B_x polarities by an additional negative IMF B_z, which exist due to the 7.25‐degree tilt of the solar equatorial plane to the ecliptic plane. We emphasize again that the AL index strongly depends on the dipole tilt, so that under the same driving conditions <AL> is more than twice larger during non‐tilted dipole periods than at solstices. The IMF B_x component, depending on its polarity, moves the magnetotail plasma sheet away from or toward the equatorial plane, and thus changes the effective dipole tilt angle. That change may be a cause of the asymmetric response of the AL‐index to positive or negative values of the IMF B_x.

In this work, we question the existing opinion that the interplanetary magnetic field (IMF) Sun‐Earth (Bx) component is of minor importance for the geomagnetic activity and show that both Bx and By, being two principal components of the Parker's spiral, are equally important factors. We show that the asymmetric behavior of activity indices around solstices can be explained as a combination of symmetric (sign‐independent) effect of IMF By and asymmetric (sign‐dependent) effect of Bx, the latter interpreted as a result of the geodipole tilt influence on the magnetotail stability and nightside reconnection. We also show that, due to the 7.5° inclination of the Earth orbital plane to the solar equatorial plane, the geoeffective IMF Bz component may increase or decrease, depending on the IMF sector polarity and season.

The present study is focused on the problem of reconstruction of the magnetic configuration in the magnetic reconnection electron diffusion region (EDR). The problem is addressed in the frame of electron magnetohydrodynamics with kept electron inertia term. We introduce the new reconstruction model independent of divergence of the electron pressure tensor and reconnection electric field. The model is tested on the magnetotail reconnection event of July 11, 2017 observed by the Magnetospheric Multiscale (MMS) spacecraft in the course of crossing the very core part of the reconnection region, the internal EDR. This new model demonstrates considerably better accuracy of the longitudinal electron velocity reconstruction due to the lower sensitivity to the configuration deviation from the two‐dimensional time‐independent model adopted in our study. We suggest also a new technique to estimate the guide field, implementing the reconstruction of magnetic potential of the in‐plane magnetic field and relying on symmetric properties of magnetic reconnection.

The region surrounding the reconnection separatrix consists of many particle and wave transient features (electron, cold and hot ion beams, Hall E&B fields, kinetic Alfvén, LH, etc. waves) whose pattern and parameters may vary depending on the distance from active neutral line. We study nine quick MMS entries into the plasma sheet boundary layer (PSBL) from the tail lobe to address the meso‐scale pattern and other characteristics of phenomena for active separatrix crossings as deduced from particle observations. The outermost thin layer (a fraction of ion inertial scale, d_i) of low‐density plasma consists of accelerated electron beams and lobe cold ions and displays density depletions (EBL region). It is followed by hot proton beam (PBL region) in which the plasma density grows from lobe‐like towards plasma sheet‐like values; the beam energy‐dispersion is used to estimate the distance from the active neutral line. Thin (usually ≤ d_i) region containing intense Hall‐like Ez perturbations (HR) usually overlaps with EBL and PBL regions. It often includes correlated B perturbations suggesting the Alfvén wave‐related transport from the reconnection source; the estimated Alfvénic ratio δE/(V_A δB) varied between 0.3 and 1.3 in studied examples. The HR is associated with profound plasma property changes, including the heating of cold ion beams in its innermost part, it hosts intense structured field‐aligned currents and intense E‐field fluctuations. Surprisingly, most of abovementioned findings are valid for crossings observed at large distances from the reconnection region (exceeding a few tens Re or >100 d_i) except for longer time‐scales and larger spatial scales of the pattern.

The reconstruction problem for steady symmetrical two-dimensional magnetic reconnection is addressed in the frame of a two-fluid approximation with neglected ion current. This approach yields Poisson's equation for the magnetic potential of the in-plane magnetic field, where the right-hand side contains the out-of-plane electron current density with the reversed sign. In the simplest case of uniform electron temperature and number density and neglecting the electron inertia, Poisson's equation turns to the Grad–Shafranov one. With boundary conditions fixed at any unclosed curve (the satellite trajectory), both equations result in an ill-posed problem. Since the magnetic configuration in the reconnection region is highly stretched, one can make use of the boundary layer approximation; hence, the problem becomes well-posed. The described approach is generalized for the case of nonuniform electron temperature and number density. The benchmark reconstruction of the PIC simulations data has shown that the main contribution for inaccuracy arises from replacing Poisson's equation by the equation of Grad–Shafranov. Under this substitution, the reachable cross-size of the reconstructed region is shrinking down to fractions of the proton inertial length. Artificial smoothing, demanded by solving the ill-posed problem, and boundary layer approximation represent two alternative methods of problem regularization. In terms of the reconstruction error, they perform nearly the same; the second method benefits from the comparative simplicity and less restrictions imposed on the boundary shape.

We evaluate the large‐scale energy budget of magnetic reconnection utilizing an analytical time‐dependent impulsive reconnection model and a numerical 2‐D MHD simulation. With the generalization to compressible plasma, we can investigate changes in the thermal, kinetic, and magnetic energies. We study these changes in three different regions: (a) the region defined by the outflowing plasma (outflow region, OR), (b) the region of compressed magnetic fields above/below the OR (traveling compression region, TCR), and (c) the region trailing the OR and TCR (wake). For incompressible plasma, we find that the decrease inside the OR is compensated by the increase in kinetic energy. However, for the general compressible case, the decrease in magnetic energy inside the OR is not sufficient to explain the increase in thermal and kinetic energy. Hence, energy from other regions needs to be considered. We find that the decrease in thermal and magnetic energy in the wake, together with the decrease in magnetic energy inside the OR, is sufficient to feed the increase in kinetic and thermal energies in the OR and the increase in magnetic and thermal energies inside the TCR. That way, the energy budget is balanced, but consequently, not all magnetic energy is converted into kinetic and thermal energies of the OR. Instead, a certain fraction gets transfered into the TCR. As an upper limit of the efficiency of reconnection (magnetic energy kinetic energy) we find η_eff=1/2. A numerical simulation is used to include a finite thickness of the current sheet, which shows the importance of the pressure gradient inside the OR for the conversion of kinetic energy into thermal energy.