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We have developed a new automated small-scale magnetic flux rope (SSMFR) detection algorithm based on the Grad-Shafranov (GS) reconstruction technique. We have applied this detection algorithm to the Wind spacecraft in-situ measurements during 1996 - 2016, covering two solar cycles, and successfully detected a total number of 74,241 small-scale magnetic flux rope events with duration from 9 to 361 minutes. This large number of small-scale magnetic flux ropes has not been discovered by any other previous studies through this unique approach. We perform statistical analysis of the small-scale magnetic flux rope events based on our newly developed database, and summarize the main findings as follows. (1) The occurrence of small-scale flux ropes has strong solar cycle dependency with a rate of a few hundreds per month on average. (2) The small-scale magnetic flux ropes in the ecliptic plane tend to align along the Parker spiral. (3) In low speed ($<$ 400 km/s) solar wind, the flux ropes tend to have lower proton temperature and higher proton number density, while in high speed ($\ge$ 400 km/s) solar wind, they tend to have higher proton temperature and lower proton number density. (4) Both the duration and scale size distributions of the small-scale magnetic flux ropes obey a power law. (5) The waiting time distribution of small-scale magnetic flux ropes can be fitted by an exponential function (for shorter waiting times) and a power law function (for longer waiting times). (6) The wall-to-wall time distribution obeys double power laws with the break point at 60 minutes (corresponding to the correlation length). (7) The small-scale magnetic flux ropes tend to accumulate near the heliospheric current sheet (HCS). The entire database is available at \url{http://fluxrope.info} and in machine readable format in this article., Comment: ApJS, in press; containing electronic spreadsheet of the database

We present unique {and additional} observational evidence for the self-generation of small-scale coherent magnetic flux rope structures in the solar wind. Such structures with durations between 9 and 361 minutes are identified from Wind in-situ spacecraft measurements through the Grad-Shafranov (GS) reconstruction approach. The event occurrence counts are on the order of 3,500 per year on average and have a clear solar cycle dependence. We build a database of small-scale magnetic flux ropes from twenty-year worth of Wind spacecraft data. We show a power-law distribution of the wall-to-wall time corresponding well to the inertial range turbulence, which agrees with relevant observations and numerical simulation results. We also provide the axial current density distribution from the GS-based observational analysis, which yields a non-Gaussian probability density function consistent with numerical simulation results., Comment: To appear in ApJL

Hydromagnetic waves, especially those of frequencies in the range of a few milli-Hz to a few Hz observed in the Earth's magnetosphere, are categorized as Ultra Low Frequency (ULF) waves or pulsations. They have been extensively studied due to their importance in the interaction with radiation belt particles and in probing the structures of the magnetosphere. We developed an approach in examining the toroidal standing Aflv\'{e}n waves in a background magnetic field by recasting the wave equation into a Klein-Gordon (KG) form along individual field lines. The eigenvalue solutions to the system are characteristic of a propagation type when the corresponding eigen-frequency is greater than a cut-off frequency and an evanescent type otherwise. We apply the approach to a compressed dipole magnetic field model of the inner magnetosphere, and obtain the spatial profiles of relevant parameters and the spatial wave forms of harmonic oscillations. We further extend the approach to poloidal mode standing Alfv\'{e}n waves along field lines. In particular, we present a quantitative comparison with a recent spacecraft observation of a poloidal standing Alfv\'{e}n wave in the Earth's magnetosphere. Our analysis based on KG equation yields consistent results which agree with the spacecraft measurements of the wave period and the amplitude ratio between the magnetic field and electric field perturbations. We also present computational results of eigenvalue solutions to the compressional poloidal mode waves in the compressed dipole magnetic field geometry., Comment: submitted to JASTP