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AnLMNcoordinate system for magnetic reconnection events is sometimes determined by definingNas the direction of the gradient across the current sheet andLas the direction of maximum variance of the magnetic field. The third direction,M, is often assumed to be the direction of zero gradient, and thus the orientation of the X line. But when there is a guide field, the X line direction may have a significant component in the L direction defined in this way. For a 2D description, a coordinate system describing such an event would preferably be defined using a different coordinate directionM′ oriented along the X line. Here we use a 3D particle‐in‐cell simulation to show that the X line is oriented approximately along the direction bisecting the asymptotic magnetic field directions on the two sides of the current sheet. We describe two possible ways to determine the orientation of the X line from spacecraft data, one using the minimum gradient direction from Minimum Directional Derivative analysis at distances of the order of the current sheet thickness from the X line, and another using the bisection direction based on the asymptotic magnetic fields outside the current sheet. We discuss conditions for validity of these estimates, and we illustrate these conditions using several Magnetospheric Multiscale (MMS) events. We also show that intersection of a flux rope due to secondary reconnection with the primary X line can destroy invariance along the X line and negate the validity of a two‐dimensional description.

 

The technique to estimate the mass density in the magnetosphere using the physical properties of observed magnetohydrodynamic waves is known as magnetoseismology. This technique is important in magnetospheric research given the difficulty of determining the density using particle experiments. This paper presents a review of magnetoseismic studies based on satellite observations of standing Alfvén waves. The data sources for the studies include AMPTE/CCE, CRRES, GOES, Geotail, THEMIS, Van Allen Probes, and Arase. We describe data analysis and density modeling techniques, major results, and remaining issues in magnetoseismic research. 

We have conducted a statistical study of toroidal mode standing Alfvén waves detected by the Van Allen Probes spacecraft in the dayside inner magnetosphere, with an emphasis on the nodal structure of the fundamental through fifth harmonics. We developed a technique to accurately assign harmonic mode numbers to peaks in the power spectra of the electric (E_ν) and magnetic (B_ϕ) field components of toroidal waves and then determine the spectral intensities ofE_νandB_ϕand the coherence and cross‐phase between these field components for each harmonic. The magnetic latitude (MLAT) dependence of these quantities was statistically examined to determine the location of the nodes. In addition to the equatorial nodes located close to the equator (MLAT = 0), we identified several nodes away from the equator within the MLAT range from −20° to +20°. We found that theE_ν‐B_ϕcross‐phase is very close to ±90° except near the nodes, indicating that the fixed‐end approximation is appropriate in modeling dayside toroidal waves. Noting that the node latitudes depend on the distribution of the mass density (ρ) along the background magnetic field, we inferred the distribution from the nodes observed atL = 4–6. If we adopt a model field line mass density (ρ) distribution of the formρ ∝ (1/r)^α, whereris geocentric distance to the field line andαis a free parameter, the statistically determined node latitudes indicate thatα∼1.5 is appropriate for both the plasmasphere and the plasmatrough.

 

Two‐dimensional hybrid particle‐in‐cell (PIC) simulations are carried out on a constantL‐shell (or drift shell) surface of the dipole magnetic field to investigate the generation process of near‐equatorial fast magnetosonic waves (a.k.a equatorial noise; MSWs hereafter) in the inner magnetosphere. The simulation domain on a constantL‐shell surface adopted here allows wave propagation and growth in the azimuthal direction (as well as along the field line) and is motivated by the observations that MSWs propagate preferentially in the azimuthal direction in the source region. Furthermore, the equatorial ring‐like proton distribution used to drive MSWs in the present study is (realistically) weakly anisotropic. Consequently, the ring‐like velocity distribution projected along the field line by Liouville's theorem extends to rather high latitude, and linear instability analysis using the local plasma conditions predicts substantial MSW growth up to±27° latitude. In the simulations, however, the MSW intensity maximizes near the equator and decreases quasi‐exponentially with latitude. Further analysis reveals that the stronger equatorward refraction at higher latitude due to the larger gradient of the dipole magnetic field strength prevents off‐equatorial MSWs from growing continuously, whereas MSWs of equatorial origin experience little refraction and can fully grow. Furthermore, the simulated MSWs exhibit a rather complex wave field structure varying with latitude, and the scattering of energetic ring‐like protons in response to MSW excitation occurs faster than the bounce period of those protons so that they do not necessarily follow Liouville's theorem during MSW excitation.

 

Recent analysis of an event observed by the Van Allen Probes in the source region outside the plasmapause has shown that fast magnetosonic waves (also referred to as equatorial noise) propagate preferentially in the azimuthal direction, implying that wave amplification should occur during azimuthal propagation. To demonstrate this, we carry out 2‐D particle‐in‐cell simulations of the fast magnetosonic mode at the dipole magnetic equator with the simulation box size, the magnetic field inhomogeneity, and the plasma parameters chosen from the same event recently analyzed. The self‐consistently evolving electric and magnetic field fluctuations are characterized by spectral peaks at harmonics of the local proton cyclotron frequency. The azimuthal component of the electric field fluctuations is larger than the radial component, indicating wave propagation mainly along the azimuthal direction. Because the simulation box is within the source region, this also implies wave amplification mainly during azimuthal propagation. The excellent agreement between the wave polarization properties of the present simulations and the recently reported observations is clear evidence that the main wave amplification occurs during azimuthal propagation in the source region.

 

Recent studies have indicated that fast magnetosonic waves (also referred to as equatorial noise) excited far outside the plasmapause cannot propagate deep into the plasmasphere because of the preferential azimuthal propagation of the waves at the source region. Since conditions in the low‐density plasma trough are typically favorable for the wave excitation, one possible explanation for the magnetosonic wave origin inside the plasmapause is refraction of the waves excited in the plasma trough but close to the plasmapause. In this study, two‐dimensional particle‐in‐cell (PIC) simulations are carried out at the dipole magnetic equator to investigate the self‐consistent excitation and propagation of magnetosonic waves across the steep plasmapause density gradient. The simulations show that the magnetosonic waves grow outside the plasmapause and propagate predominantly in the azimuthal direction. However, the waves excited close to the plasmapause experience refraction toward the density gradient, allowing them to cross the plasmapause and then propagate dominantly toward the Earth. The amount of refraction is in good agreement with a theoretical prediction based on the geometric optic approximation. We find that the refraction at the plasmapause can redirect magnetosonic waves toward the Earth, but an additional mechanism is needed to account for the statistical properties of the wave electric field polarization reported in the plasmasphere.