There is not currently a consensus on the process responsible for producing the waiting time distribution of solar flares. This study presents an information theoretical approach to determining whether solar flare data are significantly distinguishable from a nonstationary Poisson process. A study of solar flares stronger than C1 class detected by the Geostationary Operational Environmental Satellite from 1975 to 2017 was performed. A sequence of waiting times (time elapsed between adjacent X-ray flare peaks) was constructed from the data. Surrogate waiting time sequences were produced using a time-varying Poisson firing rate from the Bayesian block procedure. Utilizing Shannon entropy, the mutual information of time-lagged waiting time distributions was computed for both the original data and the surrogates using a method of discretization by binning. When the entire period is considered, we see that when compared to carefully constructed surrogates, there is a significant elevation of mutual information on a timescale of approximately 30 hr, demonstrating that flares are confidently related to subsequent flares, contradicting the null hypothesis that flares are produced by a nonstationary Poisson process. When only 4 yr subsets of the data are considered, we see that at relatively small timescales (on the order of 10–30 hr), solar flare waiting times have a significant impact on subsequent flares. When corrected for the number of points in each considered time window, there is no correlation between the magnitude of significance and position in the solar cycle.

Magnetosphere-ionosphere coupling is a particularly important process that regulates and controls magnetospheric dynamics such as storms and substorms. However, in order to understand magnetosphere-ionosphere coupling it is necessary to understand how regions of the magnetosphere are connected to the ionosphere. It has been proposed that this connection may be established by firing electron beams from satellites that can reach an ionospheric footpoint creating detectable emissions. This type of experiment would greatly aid in identifying the relationship between convection processes in the magnetotail and the ionosphere and how the plasma sheet current layer evolves during the growth phase preceding substorms. For practical purposes, the use of relativistic electron beams with kinetic energy on the order of 1 MeV would be ideal for detectability. However, Porazik et al. (2014) has shown that, for relativistic particles, higher order terms of the magnetic moment are necessary for consideration of the ionospheric accessibility of the beams. These higher order terms are related to gradients and curvature in the magnetic field and are typically unimportant unless the beam is injected along the magnetic field direction, such that the zero order magnetic moment is small. In this article, we address two important consequences related to these higher order terms. First, we investigate the consequences for satellites positioned in regions subject to magnetotail stretching and demonstrate systematically how curvature affects accessibility. We find that curvature can reduce accessibility for beams injected from the current sheet, but can increase accessibility for beams injected just above the current sheet. Second, we investigate how detectability of ionospheric precipitation of variable energy field-aligned electron beams could be used as a constraint on field-line curvature, which would be valuable for field-line reconstruction and/or stability analysis.

Using electron beam accelerators attached to satellites in Earth orbit, it may be possible to measure arc length and curvature of field-lines in the inner magnetosphere if the accelerator is designed with the capability to vary the beam energy. In combination with additional information, these measurements would be very useful in modeling the magnetic field of the inner magnetosphere. For this purpose, a three step data assimilation modeling approach is discussed. The first step in the procedure would be to use prior information to obtain an initial forecast of the inner magnetosphere. Then, a family of curves would be defined that satisfies the observed geometric attributes measured by the experiments, and the prior forecast would then be used to optimize the curve with respect to the allowed degrees of freedom. Finally, this approximation of the field-line would be used to improve the initial forecast of the inner magnetosphere, resulting in a description of the system that is optimally consistent with both the prior information and the measured curvature and arc length. This article details the method by which a family of possible approximations of the field-line may be defined via a numerical procedure, which is central to the three step approach. This method serves effectively as a pre-conditioner for parameter estimation problems using field-line curvature and arc length measurements in combination with other measurements.