Magnetic reconnection is an important fundamental process that occurs in the magnetosphere and is responsible for phenomena on multiple scales, including geomagnetic storms, aurora, and radiation belt enhancement. However, detailed knowledge of precisely when, where, and how it occurs has challenged the research community since the dawn of the space age. The largest scale reconnection occurs between solar wind and the Earth’s magnetic field. This interaction is theorized to occur on the dayside magnetopause from where energetic particles precipitate to the northern and southern cusps (Reiff et al., 1977; Burch et al., 1982).

The most direct method of studying magnetopause reconnection in the magnetosphere is accomplished by flying appropriately instrumented spacecraft through the daysidemagnetopause, as performed many times during the Magnetospheric Multiscale (MMS) Mission era (Burch et al., 2016a; Burch et al., 2016b) and with the previous missions such as Cluster (Escoubet et al., 2001; Retinò et al., 2006; Pitout and Bogdanova, 2021), THEMIS (Sibeck and Angelopoulos, 2008), Geotail (Nishida, 1994), and ISEE (Paschmann et al., 1979; Sonnerup et al., 1981). The catalog of events collected through this approach is notable but limited, owing to the long orbital period (with scales of days to a week) required to visit the magnetopause. Furthermore, there is a low probability that reconnection occurs within the proximity to a spacecraft rapidly crossing the magnetopause. Furthermore, most missions designed to sample the dayside magnetopause are highly elliptical and undergo orbital precession during the year, leading to seasons when the spacecraft does not sample the dayside magnetosphere at all. Major missions subject to this precession effect include MMS (Fuselier et al., 2016) and Time History of Events and Macroscale Interactions during Substorms (THEMIS) (Frey et al., 2008). To begin answering questions regarding when, where, and how often different types of magnetopause reconnection scenarios occur through a statistical analysis, it is desirable to use a method with more frequent observation opportunities to prepare event catalogs.

Russell and Elphic (1978); Dunlop et al. (2011); Lockwood and Smith, (1989); Lockwood and Smith, (1994), (Frank and Craven, 1988; Frey et al., 2019).

We direct our attention to a signature of magnetopause reconnection, which can be encountered in low Earth orbits (LEOs), and can be measured approximately 1–2 times every 90–100 min. We call this signature ion-energy dispersion in the cusp or simply a “dispersion event” (Basinska et al., 1992; Lavraud and Trattner, 2021). In this paper, we discuss two different types of dispersion, single dispersion and double dispersion, with double dispersion being rarer and the main focus of this paper. We will start by describing the features common to both.

The lifetime of dispersion events starts at the reconnection site, as shown in Figure 1. At the reconnection site, particles are accelerated by a reconnection electric field, and ions and electrons are moved along the cusp field line. As these particles move down the magnetic field lines at speed v _‖(t), the field lines also move as part of the global magnetic reconfiguration process (Lockwood and Smith, 1992). Some particles will mirror before reaching the LEO cusp, and some will not. Those that do not mirror prior to those points are then available to be detected by a spacecraft flying through the LEO cusp. We note that in LEO, the thermosphere and exosphere are sparse enough that particle loss due to absorption into the atmosphere occurs at a zero to negligible rate.

Previous studies of dispersion events established the groundwork for the analysis of the dispersion structure. In Lockwood and Smith (1992), it was shown that the slope of the dispersion in the spectrogram could be related to the upstream reconnection rate at the magnetopause. Wing et al. (2001) utilized modeling techniques to show that the double cusp structure can be predicted as a result of the differences in the E ⃗ × B ⃗ structure during strongly duskward/dawnward and weakly southward IMFs. Later in Trattner et al. (2015), dispersion signatures were used to distinguish between pulsed and continuous reconnections at the dayside magnetopause.

Cusp ion dispersions sometimes show overlapping signatures (Trattner et al. 1998; Trattner et al. 2012a). The leading interpretation has since become that multiple reconnection sites formed during the reconnection process generate this effect, wherein each simultaneous reconnection is responsible for a single injection (Lockwood, 1995). This is particularly because, in overlapping dispersion, the delay between each injection happens on a timescale understood to be significantly shorter than the accepted cadence of magnetically disjointed individual injections. This warrants a link to multiple reconnections, wherein the two injections are magnetically coupled, originating from the same global phenomenon and creating double injections very close to each other in time. Observationally, this is supported by direct measurements from the MMS era, which linked multiple reconnections to flux transfer events and the subsequent detection of overlapping dispersion in the cusp using MMS (Fuselier et al., 2018). More recently, direct measurements reported in Fuselier et al. (2022) observed multiple reconnection sites on the magnetopause with MMS and then, several hours later (during similar IMF conditions), double dispersion at the northern cusp with the Twin Rocket Investigation of Cusp Electrodynamics-2 (TRICE-2) rocket experiment.

Figure 2 shows an example of overlapping dispersion signatures in LEO (specifically 840–860 km) taken from the F-16 Satellite of the Defense Meteorological Satellite Program (DMSP) (Dickinson, 1974; Redmann, 1985). During this time, the satellite observes two plasma populations, where each of them displays energy dispersions (sorted over space by energy). This takes place between 10:13:00 UTC and 10:14:30 UTC. The key feature of this plot is that the central energy of each population decreases in energy with the increasing magnetic latitude. The satellite crosses the cusp region at a magnetic local time (MLT) of approximately 13.5 and magnetic latitudes (MLAT) between 74° and 77°.

The contributions of this paper include extensions to the existing methodology and the use of these new techniques to observe statistical correlations. When we apply the methodology, we produce quantitative statistics of double dispersion in the dayside northern cusp during southward IMF. In the methodology section, we extend the algorithm developed in da Silva et al. (2022), originally for the automatic detection of single dispersion events. The algorithm is extended to detect double dispersion using the same general approach. We apply our new algorithm to the time period between January 2011 and August 2022. We report the number of detected double dispersion events with respect to the month of the year, the three IMF components (B _x , B _y , and B _z ), and the IMF clock and cone angles. The relevant background to place each relationship in the proper context is reviewed, and the different ways to interpret the data are discussed.

In Section 2, we describe the DMSP mission, its associated instrument used to measure particle precipitation, and the OMNI dataset used for IMF measurements. In Section 3, we describe the new features implemented in our previously established single dispersion algorithm to enable double dispersion detection. Section 4 describes the preparation and hand review process conducted to remove false positives and curate the dataset quality. In Section 5, we present the findings of the rate with respect to the aforementioned variables. Finally, in Section 6, we review the contributions of this work and the progress made toward understanding double dispersion.

In this study, we utilize data from the F-16 satellite of the DMSP mission (Dickinson, 1974; Redmann, 1985). Overall, the DMSP mission provides four decades of coverage of precipitating plasma data, acquired by multiple spacecraft in flight at any given time. DMSP utilizes a mission design wherein multiple spacecraft are placed in different LEOs and Sun-synchronous orbits, and a replacement strategy is used to ensure continuous coverage when a satellite reaches its end-of-life. We utilize data from the F-16 satellite (launched in 2003) because we found that the F-16 satellite provides more distinct dispersed cusp particle precipitation signatures. The F-16 satellite has an orbital period of 101 min, an inclination of 98.9°, and a nominal local time of ascending/descending nodes of 19:54/07:54.

The DMSP spacecraft includes top-facing electron and ion instruments with a 90° field of view, known as Special Sensor J (SSJ) instruments (Redmon et al., 2017). Because they are top-facing, the spectrograms measure only downward precipitating particles, excluding particles traveling upward due to the bounce motion. The SSJ instrument used in this study is of the fifth generation, known as SSJ/5, and comprises 16 log-spaced energies between 30 eV and 30 keV (similar to the previous generation SSJ/4, described in Hardy (1984)). In this study, we utilize the ion and electron differential energy flux data in units of eVcm⁻²s⁻¹sr⁻¹eV⁻¹.

In addition to the ion and electron differential energy flux data from SSJ/5, we also utilize estimates of IMF at the bow shock provided by the OMNI dataset (Papitashvili et al., 2014). OMNI provides high-resolution (1-min cadence) estimates of the IMF vector, solar wind velocity, and solar wind density. These variables are measured in situ at L ₁ and are subsequently propagated to the bow shock during post-processing for magnetospheric applications (Chiu et al., 1998; Ogilvie et al., 1995;Ogilvie and Desch, 1997).

The methodology for automatically detecting double dispersion is built upon the previous work to detect single dispersion (da Silva et al., 2022). Here, we define a numerical criterion which is used to detect events. We begin with modeling the criteria around single dispersion events and then generalizing them to double dispersion events.

The modeling approach focuses on simplifying a spectrogram problem into a time series problem. This is carried out by characterizing an entire energy spread into a single time series variable E _p (t), where the variable’s value is located at the energy of peak flux (“p” stands for peak). Through this simplification, the problem of identifying a single dispersion curve becomes about characterizing patterns in one variable.

Our approach moves a sliding window through time, calculating an instantaneous score at each point in time. When the total score over a window is above a threshold, we mark that window as having an event. The equation for the selection criteria for single dispersion is then generally written as follows: ∫ window D t d t > τ , (1) where D(t) is the instantaneous scoring function and τ is the threshold. The threshold τ is itself a type of sensitivity, wherein lower thresholds are stricter and select fewer events. The scoring function is given by the following expression: D t = − sgn d | M L A T | d t d L o g E smoothed d t b south t e t g t , (2) where MLAT is the magnetic latitude, b _south (t) has a value of 1 when B _z <0 (zero otherwise), e(t) has a value of 1 on the dayside (zero otherwise), and g(t) has a value of 1 when MLAT >50° (zero otherwise). The term d [ L o g E ] smoothed d t is used to tie the score to log-scale changes in E(t). The term − sgn d | M L A T | d t is used to tie this change to the north–south vs. south–north path of the satellite, and overall produces a positive score when the pattern is indicative of southward IMF dispersion on the dayside. The variable [LogE] _smoothed is obtained by smoothing E(t) using a box-car averaging scheme with five points on each side. A window size of 60 s is used.

To generalize it to double dispersion, we use dual peak-finding methods to find two nominal energy curves, E _p1(t) and E _p2(t). A bimodal energy curve is illustrated in Figure 3. The criteria in Equation 1 are then generalized to the following: ∫ window D p 1 t d t > τ and ∫ window D p 2 t d t > τ , (3) where D _p1(t) corresponds to E _p1(t) and D _p2(t) corresponds to E _p2(t). Details of the peak-finding and peak-labeling processes are subtle and complex; the full details are disclosed for those interested in the Appendix.

Because double dispersion events are much rarer, finding a large set of hand-picked examples to validate against was not feasible. Four events were hand-picked from a study of the 20 December 2015 storm, and the algorithm was tuned until it was able to autonomously select all of them.

The automated double dispersion detection algorithm was run over the period of January 2011 and August 2022 using the DMSP F-16 satellite, with the intention of covering approximately one solar cycle. As outlined in Section 3, our search is confined to the northern cusp on the dayside and B _z <0. Following the automated selection of events, the detections were individually reviewed by hand and detections identified as double dispersions that were not real events (false positives) were filtered out. After this review process, the final collection resulted in a total of 138 events.

In particular, during the review process, we searched for events that met the following qualitative criteria:

1) The event showed two clear populations dispersed in ion energy over the magnetic latitude.

In this collection of events, we discard those cases with double injections that (a) do not show dispersion features or (b) do not present an overlap. Non-overlapping injections are more consistent with the double cusp model developed in Wing et al. (2001), where E ⃗ × B ⃗ drift causes particles to arrive at two distinct locations.

Figure 4 shows the coverage of the satellite in magnetic coordinates over the time period studied. We identify two features which should be considered in the subsequent statistical report: (a) the coverage in the magnetic local time is not symmetric across noon, and the regions closer to dusk are more sampled than those close to dawn, and (b) the magnetic latitudes under 60° are similarly sampled closer to dusk. According to the cusp location model of Petrinec et al. (2023), compiled from published studies and applied to the recent TRICE-2 campaign of cusp region observations during southward IMF, the cusp is (a) centered at 12.6 h when B _y = 0, (b) moves duskward with increasing B _y (by a MLT factor of approximately 0.120 h/nT), (c) has a full extent of 6 h, and (d) has a magnetic latitude extent of 21.7 exp (0.1 B _z ) + 58.2 + ψ/15 ± 1.00°, where ψ is the dipole tilt in degrees.

The selected events are made available as both plots and a list of start/stop times in a computer-readable comma-separated value (CSV) format. Readers who wish to compare their understanding of the aforementioned criteria with the final selections may download the events to find the examples. The software application is also made available to repeat the initial search, with the option available to modify parameters, thresholds, and the core algorithm itself. Links to these can be found at the end of this paper.

The results collected from the previous section were organized to compare the detected event distributions as a function of various parameters. In particular, we focused on the detection rate with respect to the month of the year; the IMF components B _x , B _y , and B _z as provided by OMNI; and the IMF clock and cone angles.

In this work, we presented the first statistical report of double dispersion, a term used here to mean overlapping double-injection ion-energy dispersion events in the cusps. An algorithm previously established in the literature for single-injection dispersion was extended to automatically detect double dispersion, and the extensions were documented, justified, and applied here. We used an algorithm to narrow the number of events, which were also reviewed by hand according to the criteria stated in Section 4 to ensure scientific integrity.

Using our collection of events, we reported the statistics on relationships between the number of detected events and several other variables. The distributions explored include binning by the month of the year (seasonally) (5.1), the three IMF components (5.2), and the IMF clock and cone angles (5.3). The seasonal distribution indicated that the events were found much more during the summer months when the dipole was tilted toward the Sun, a finding that can be linked to the reconnection geometry. The distribution of three IMF components and the IMF clock angle indicated a preference for detection in response to a more positive B _y value, but we cannot say this conclusively due to the orbit of the DMSP F-16 satellite.

In this study, we looked at the northern cusp. This limitation was due to the orbit of the DMSP F-16 satellite we used. However, important questions relating to the seasonal bias reported here can be elevated by repeating the analysis for the southern cusp as well. Overall, the signature of double dispersion in the cusp presents a 2D picture (over energy and time) of the global reconnection process, which is necessarily 7D (over space, velocity, and time) in nature. The statistics reported in this paper are made possible due to the long lifetime of the DMSP F-16 satellite and the accessibility (in terms of the revisit rate) for cusp crossings in the low Earth orbit. As investigations into magnetic reconnection in the magnetosphere continue, double dispersion continues to provide us with a powerful perspective to understand these phenomena.