Correction: Calculation of the dayside reconnection rate from cusp ion-energy dispersion

INTRODUCTION Magnetic reconnection is a fundamental process between the Earth's magnetosphere and solar wind material ejected from the sun. It is the primary method through which solar wind material and associated energy enter the magnetosphere, leading to the most notable magnetospheric phenomena and the domain of near-Earth space weather. The reconnection process is well established to occur for both southward and northward IMF. The reconnection electric field is the out-of-plane electric field at the point where field lines break and reconnect. A stronger reconnection electric field leads to faster energy release. The global rate of dayside magnetopause is given by the integral of the parallel electric field over the dayside x-line (the magnetic field line corresponding to the intersection of the magnetic separatrix surfaces). In a quasi-steady reconnection scenario, the parallel electric field at a point on the x-line is roughly the same as the perpendicular electric just outside the reconnection diffusion region. This perpendicular electric field is thus often taken as a proxy for the reconnection rate. Accelerated ions streaming away from the reconnection site along newly reconnected field lines (Fuselier et al., 1991, 2000; Trattner et al., 2005a), leave a signature in the cusp region of the magnetosphere. This work will focus on dayside reconnection during southward IMF. Dispersed ion-energy precipitation in the cusp is the spreading of particles by energy over magnetic latitude due to a mix of convection and varying time-of-flight effects associated with the reconnection that causes higher-energy particles to precipitate at lower magnetic latitudes during southward IMF (Lockwood and Smith, 1989; Basinska et al., 1992; Connor et al., 2012, 2015; Trattner et al., 2015). The precise structure of this dispersion is shaped by the reconnection rate and magnetic and electric field structures of the dayside magnetosphere. This manuscript builds upon the work of Lockwood and Smith (1992), which derives a formula to calculate the dayside magnetopause reconnection rate from structure within the dispersed ion-energy spectrogram measured somewhere in either the low altitude or high altitude cusp. In that work, the ion spectrogram is characterized as a time series Eic(t) (ion cutoff energy), defined as the nominally the energy whose flux is 10% of the peak flux over the entire energy spectra. The Eic(t) and dEic/dt variables are used as key indicators of upstream dynamics. The Lockwood and Smith (1992) formulation is designed around a mostly 2-dimensional picture of reconnection, with several free parameters such as (a) the angle between the reconnection path and the spacecraft trajectory, (b) the method for calculating the ion cutoff energy, and (c) the length of the virtual path between the spacecraft and the reconnection site. The reconnection rate calculation applies to a spacecraft traversing the cusp that measures precipitating ion dispersion. One such set of spacecraft is the Defense Meteorological Satellite Program (DMSP) with their Special Sensor J (SSJ) precipitating plasma payload (Hardy et al., 1979; Redmon et al., 2017). The DMSP orbits vary between satellites but are all sun-synchronous and primarily survey the northern cusp on the dayside post-noon sector. Because DMSP spacecraft have been carrying similar space environment sensors since the 1970s, they provide a powerful historical record of precipitating plasma in the cusp. An advantage of using DMSP over high-altitude missions such as Cluster is that the revisit rate per cusp, defined by the orbital period, is much shorter for DMSP than Cluster (101 minutes vs 54 hours), leading to more substantial potential for statistical and long-term studies (da Silva et al., 2024). However, a limitation of the methodology presented in this manuscript as applied to DMSP involves the space-time ambiguity. It is impossible to use one satellite to distinguish whether the change in energy over time is caused by a time-varying process coinciding with the satellite pass (a temporal structure), or spatial variation in continuous particle streams that are not time-varying (a spatial structure). The algorithm presented here assumes that the observed dispersion is a temporal structure, but because each DMSP satellite crosses at different local times, it is impossible to use DMSP to distinguish spatial and temporal structures. Furthermore, with DMSP, the orbits include both east-west and north-south components around the cusp, which, for some events, makes it difficult to distinguish whether the dispersion is over magnetic latitude or longitude. Examples of temporal and spatial structures observed in the cusp and more details on the differences can be found in Trattner et al. (1999, 2002, 2005b). In 2025, the Tandem Reconnection and Cusp Electrodynamics Reconnaissance Satellites (TRACERS) satellites will launch with state-of-the-art instrumentation for measuring plasma and fields in the low altitude cusp (Kletzing, 2019). These issues around the space-time ambiguity will be addressed by TRACERS, which includes two satellites spaced 2-minutes apart in an orbit centered around noon. Among the science objectives of the 1-year TRACERS mission is to determine how the reconnection rate evolves, and hence, computing the reconnection rate from cusp dispersion is essential. In preparation for the TRACERS mission and to apply the method to DMSP data outside the TRACERS mission lifetime, in this work, we study the calculation using data from DMSP, with the assumption that the observed dispersions are temporal in nature, to advance the state of the art. Discoveries from the TRACERS mission, such as when and where temporal versus spatial structures emerge based on IMF, could relieve this issue with DMSP and allow for long-term statistical studies by filtering out possible spatial structures using this knowledge. In the Data section, we review the modern DMSP SSJ sensor and the related instruments we will use. In the Observations section, we calculate the reconnection rate for seven instances of ion-energy cusp dispersion made with the DMSP F18 satellite in the northern cusp. These occur over seven subsequent passes during the March 23-24, 2023 geomagnetic storm when the IMF Bz is steadily southward. The ion and electron spectrograms and the numerically stable ranges of the reconnection rates are compared against each other, and the related IMF conditions are discussed. In the Calculation Review section, we review how the calculation is performed. In Calculation Analysis we discuss limitations, significant sources of uncertainty, and caveats in applying the methodology. In the Comparison to v×B Baseline section, we verify that the calculation is on the same order of magnitude by comparing it to an alternate method using an in-situ |E| ≈|v × B| as an approximation (DMSP satellites do not carry electric field instrumentation). Finally, in the Conclusion we summarize the paper's results and anticipate future work. In the Appendix, we provide additional information on the OMNI IMF Parameters and Dst index during the March 23-24 storm and plots of associated ionospheric electric field models for further contextualization of the storm. DATA In this work, data from three DMSP satellites F16, F17, and F18 is used. Each satellite is in a sun-synchronous orbit with an altitude between 840 and 860 km. The orbits of each satellite are designed to work in unison, and they vary by the longitudinal point of the equatorial crossing. Each satellite carries identical instrumentation. In this work, we utilize data from the SSJ instrument (Special Sensor J) for the results presented in the Observations, Calculation Review, and Calculation Analysis sections. In the later section titled Comparison to v×B Baseline, we also use data from the SSM (Special Sensor Magnetometer) and SSIES (Special Sensor for Ion and Electron Scintillation) instruments. The SSJ instruments collect particles traveling towards Earth with an aperture of 4◦× 90◦, binning particles in 16 log-spaced energies between 30 eV and 30,000 eV (Redmon et al., 2017). The instrument is positioned such that the 90◦FOV spans the ram direction to zenith; an informative diagram illustrating how this influences pitch angle coverage can be found in Redmon et al. (2017), Figure 1. Implications of this FOV on the calculation will be discussed in the Calculation Analysis section. This work uses the ion and differential energy flux data in the released units of 1/(cm2 ∗s ∗sr). The SSM instruments are standard triaxial fluxgate magnetometers widely used in space weather (Torbert et al., 2016; Balogh et al., 1997), having a magnetic field vector resolution of 2 nT (Alken et al., 2014). From the DMSP SSIES instrument, we use data from the Ion Drift Meter (IDM), which measures the ion drift velocity by tracking the incoming angles of ions (Kihn et al., 2006). All data used in this study from DMSP is at the time resolution of one second. The DMSP SSJ instrument is sensitive to particles in a small range for each channel. This is smaller than the spacing between energy channels, and no particle flux data is measured between these sensitive regions. This constrains the precision that the lower energy cutoff can reasonably measure. Quantifying this uncertainty and propagating through the Lockwood formula shall be considered in the Calculation Analysis section. Because of the DMSP inclined orbits, most of their dayside time is spent in the northern hemisphere and most of the nightside time in the southern hemisphere (Oliveira and Zesta, 2024). Therefore, for this study, we are restricted to the northern cusp for our analysis of dayside precipitation. To connect DMSP observations to the upstream solar wind, we use the OMNI dataset at a one-minute cadence (King and Papitashvili, 2020). OMNI is a calculated measurement of the interplanetary magnetic field (IMF), solar wind density, and pressure at Earth's bow shock derived from L1 of these OMNI these from the L1 point to Earth's bow shock using to provide a derived for magnetospheric data OMNI uses data from two the et al., and and et al., In Figure we the ion and electron spectrograms from the DMSP SSJ instrument on F18 for seven passes of the northern cusp. Each is a pass spaced minutes as defined by the orbital each subsequent dispersion is in the ion and an electron with the ion dispersion. The are not to dispersion on the same time as the ions (da Silva et al., that the peak flux in each dispersion structure is between and 1/(cm2 ∗s but by an order of magnitude between differences in the of to ions in the upstream 1. OMNI IMF and during each in units of IMF are in Bz 2 Figure 1. ion-energy dispersion made with DMSP F18 during the March 23-24, 2023 with their calculated reconnection Reconnection rates are to the range of where they are most are to with the calculation using dEic/dt a of uncertainty in dEic/dt (Lockwood and Smith, IMF and during each can be found in 1. It is that each of these passes by reconnection by with the cusp The more is that continuous reconnection this period, with during times, with the satellite an often reconnection have been established through of the et al., and analysis of cusp dispersion et al., 2015). this we also observed dispersion from DMSP and F17, similar to in additional on the IMF and Dst Figure DMSP satellite F17, and orbit in magnetic during the with where dispersion The cusp can be to be around the region. index during this and for the ionospheric potential and The spatial of the dispersion are presented in a of the northern hemisphere in Figure The precise magnetic local time and magnetic latitude of the dispersion structures vary between passes as a of the IMF et al., and solar wind The ion dispersion in between and between and These are with of where the cusp be from and are also in Figure 2 for It is that and than F18 because their orbits further from In the of each dispersion in Figure a calculation of the reconnection rate is for of The is a free of the calculation be the to the to for parallel electric field Because this is a free we three for the range that in and 30 The calculated reconnection rates within the with some These occur when the of the in the which causes the calculation to numerically due to a this we to these from the plots to The details of the calculation will be in the section. are using the method from Lockwood and Smith This which uncertainty in dEic/dt is by the calculation with dEic/dt by with to the dEic/dt in the this results in the from Figure that the stable are within 2 This range is with in work, such as and where an reconnection rate of calculated from reconnection using observations from the et al., It is also similar to the range of for the storm using observations in et al., The range of within a can in a be considered a of uncertainty associated with the we will discuss how we the of the calculated but not the will discuss how the reconnection rate The methodology for calculating the reconnection rate in Lockwood and Smith (1992), and is The calculation assumes that the dispersion is a temporal structure et al., caused by the of newly field a of ions at the the time at which the the field line can be as where is with (ion cutoff the lower energy of the the of an and the virtual for parallel In this for the of the of a in the low altitude of the spacecraft where is along the path of newly field lines and is perpendicular to it such that is away from Earth Lockwood and Smith (1992) Figure for a we can the of the newly field line path by the satellite orbit where is the time in the satellite is the of the and is the angle between the spacecraft and each the at The change in this with to the rate at which flux is in an is where is the magnetic field at the is the electric field at the is the reconnection and is the length of the flux in the direction to the of the The the spatial of the flux at the magnetopause to smaller at the satellite all these the for the reconnection rate Reconnection from 2 2 The calculation in Calculation Review variables to a dayside reconnection the variables are variables such as and are In this section, we summarize and discuss these variables and their related sources of we the FOV of DMSP SSJ The FOV spans a 4◦× and is not field which Each instrument is such that the the ram direction to and the is the of the on the and direction of the spacecraft this leads to of pitch angle space when is outside the and when is the The data compared with the instrument FOV for the two for which The pitch angle coverage by calculating the angle between and the vector both of the (the ram direction and the The pitch angle coverage calculated this the and a with variation in these than an that this is to the are for the calculation presented because the is during an and not change the structure of the used to the reconnection rate. The ion energy cutoff is a significant of uncertainty with Lockwood and Smith (1992) using the energy that 10% of the peak flux in the energy in this is to In Figure we a set of energy from a dispersed ion have a line at the of 10% of the peak In several of these time we point out that calculating the cutoff energy this is difficult due to issues out of low energy or the that that energy and and found that they results are more to out of low energy that work on the cusp calculated the ion energy cutoff by a to the where the parallel velocity and is the the peak energy as the et al., However, this method is when using DMSP due to the of In Figure we the Eic(t) time series using a of to the effects of as in Silva et al. the between of flux Lockwood and Smith (1992) of upstream and the magnetic field and comparing the to magnetic where and are the magnetic through the magnetopause and satellite altitude of the flux In this Figure of a of uncertainty in calculating the reconnection rate with DMSP, which is the (ion cutoff the where is the magnetic field at the and is the magnetic field at the satellite The upstream magnetopause magnetic field is difficult to a a of nT for the satellite and nT for the magnetopause are This a of However, for the three in Figure for which the range of at the satellite between 30,000 and In the of it is to from the where is the of the magnetic field at the magnetic is the of the is the spacecraft altitude 840 and is the magnetic measured from the magnetic The between the with parallel is primarily by varying of dayside from the solar wind pressure and the of the parallel electric field the work that parallel electric fields occur the dayside during magnetic reconnection et al., the to for This is to vary between and 30 (Lockwood and Smith, on solar wind pressure and the corresponding of the dayside magnetosphere. The angle between the spacecraft and the direction at which field lines are is by southward reconnection with an x-line the magnetic is the angle between the spacecraft velocity and the line of However, this is the and for reconnection such as when a substantial is The of in the can be with the of includes the of the x-line such as through an analysis of the magnetic between the and the magnetosphere. A magnetic analysis for our is presented in Figure In this the Magnetic et al., 2017). Figure plots the magnetic the magnetopause in the and plots the x-line as a In this the magnetic field is calculated using an based on upstream made by and the magnetospheric magnetic field is with the often as and the magnetic is the angle between the Each is calculated using the to the corresponding we to in passes where the of the x-line longitudinal field line In these in the of ion drift and as a angle such as more than the we will that using × and the spacecraft velocity vector with this for pass is to pass To study the of we between and of the reconnection rate using a 90◦, the calculation since no dispersion is The of this can be in Figure that leads to the reconnection with the Figure Magnetic between the and magnetospheric magnetic field as calculated using the Magnetic et al., 2017). The passes in the of each to in Figure 1. between a of and the also that in Figure the of used using field line in a magnetic field through a The to the between the satellite and the three as by the Magnetic of found this between and for this storm. a field line through the satellite this field line not the the to the field line that The taken as the point on that field line between the satellite and the a point of we that the calculation is A eV minutes to a To this Figure of the effects of varying the angle between the spacecraft and the direction of newly field on the reconnection rate This be measured by DMSP, and for the of using DMSP it is a free in the a for the reconnection rate from ion-energy dispersion a process on the time of minutes each of the reconnection rate time series in Figure 1. v×B In this section, we the calculation results from the using an alternate The made in this section will the order of because of the limitations, it more in the reconnection rate The method we as a SSM and the SSIES ion drift the we calculate |E| at the satellite using the approximation that × a similar methodology to the Lockwood we apply the flux to the magnetopause reconnection rate from the ionospheric electric The formula Reconnection from × Baseline Figure Comparison between the Lockwood and the v×B the reconnection rate by the v×B method some differences in structure with the by the Lockwood they is the same order of The reconnection rate from the Lockwood method here uses the observed × B| where is identical to that used in the Lockwood is the ion drift is the and is the magnetopause reconnection rate. In Figure we the reconnection rate from the Lockwood method with that of the for passes and In both the reconnection rate by the × method and the Lockwood method on order of structure is not From this we that the calculated reconnection rate using the Lockwood method is the order of to and the flux also the observed calculated as the angle between the defined and the spacecraft The DMSP SSM and SSIES instruments use a where is in the is in the direction of the spacecraft and the to the of the we as the between a angle and the angle between and the satellite velocity both the and the satellite velocity are perpendicular in the this for passes with and In Figure we use a of the where no data is The in Figure uses these to calculate the reconnection rate. The this is pass and for pass This with our that based on the magnetic in Figure for pass be the In this work, we applied the Lockwood and Smith (1992) method to calculate the dayside reconnection rate using dispersion ion-energy cusp observed by the DMSP dispersion in seven passes during a time of continuous southward IMF reconnection in the March 23-24, geomagnetic we the of applying DMSP SSJ data to study reconnection rates and found a reconnection rate during the of the March 23-24, geomagnetic storm. that a limitation of using DMSP for the calculation here around the space-time ambiguity. The Lockwood method assumes a temporal structure causes the but it is impossible to distinguish between temporal and spatial structures with This work is presented in the that results from instrumentation on the TRACERS mission and will provide on the and rate of temporal versus cusp structures. information such as how one is compared to the change the of applying the methodology. it is that temporal structures in orbit at a rate more than spatial for space weather the of applying the methodology the of some In future work, this methodology could be to spacecraft or with such as the et al., et al., have been used to the ionospheric electric field and calculate the dayside reconnection et al., et al., 2006). spacecraft in orbits, such as also the high altitude cusp 2 and ion-energy dispersion et al., 2024). The advantage of Cluster compared to DMSP is that of the to provide velocity the is the orbital period, which the of cusp during a geomagnetic storm. results the calculated reconnection rates with DMSP during this storm between and 2 when are This range of is similar to of the reconnection rates during geomagnetic using in-situ observations and et al., In this we the in the on uncertainty sources for the Lockwood such as the of the ion cutoff energy the angle between the reconnection path and the spacecraft and the virtual to the site these sources of uncertainty, our to a method that a of the reconnection rate using |E| × B| to the local electric field that our results are on the order of to the flux for both This work the potential for long-term statistical studies of the reconnection using the DMSP we to a point where the assumption of temporal structure can be on a to such as that which will with the TRACERS mission, will provide an to further the Lockwood An for future work during the TRACERS is the study of with more in the reconnection rate during the OMNI Parameters and Dst during March 23-24, 2023 This section the observed dispersion during the March 23-24 geomagnetic storm. In Figure the the IMF magnetic field at the bow with when a dispersion from either of the F16, F17, or F18 Figure OMNI IMF solar wind pressure and the associated Dst index during the March 23-24, 2023 The dispersion during the of the storm when Bz southward and this period, from to with dispersion observed in both The dispersion primarily during the of the storm. The the pressure of the solar wind, a substantial in pressure at the of the storm when Bz not stable southward and no dispersion during the a in pressure during stable southward Bz that with the dispersion and In Figure we the ionospheric potential and magnetic field using the The is at the In this we that the is on the dayside at local where DMSP the cusp. The ionospheric potential in this also calculated with the also at the which similar structure but Because both models similar structure, we the structure that the angle between the electric field and the the with the electric field in most around Figure and as by the