# Numerical Simulations for Optimizing Small Satellite Constellations for TGF Studies

Melody Pallu, Sebastien Celestin, Philippe Laurent

► To cite this version:

Melody Pallu, Sebastien Celestin, Philippe Laurent. Numerical Simulations for Optimizing Small Satellite Constellations for TGF Studies. Journal of Geophysical Research: Atmospheres, 2025, 130, 10.1029/2024JD042528. insu-05057849

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Distributed under a Creative Commons Attribution 4.0 International License
**Key Points:**

* We perform simulations of Terrestrial Gamma ray Flash (TGF) observations by a small satellite constellation

* We present the impact of orbit and detector parameters on TGF detection, multi-detection and number of photon received by satellites

* We present minimum detection surfaces for TGF detection depending on TGF fluence

**Correspondence to:**

M. Pallu,
pallu@apc.in2p3.fr

**Citation:**

Pallu, M., Celestin, S., & Laurent, P. (2025). Numerical simulations for optimizing small satellite constellations for TGF studies. *Journal of Geophysical Research: Atmospheres*, 130, e2024JD042528. https://doi.org/10.1029/2024JD042528

Received 22 SEP 2024
Accepted 16 APR 2025

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# Numerical Simulations for Optimizing Small Satellite Constellations for TGF Studies

Melody Pallu¹,² ID, Sebastien Celestin³ ID, and Philippe Laurent⁴ ID

¹Universite Paris Cite, CNRS, Astroparticule et Cosmologie, Paris, France, ²CNES, Toulouse, France, ³LPC2E, University of Orleans, CNRS, Orleans, France, ⁴Departement d'Astrophysique, CEA, CNRS, AIM, Universite Paris Cite, Universite Paris-Saclay, Gif-sur-Yvette, France

**Abstract** The detection of Terrestrial Gamma ray Flashes (TGFs) from space is mostly made by astrophysics satellites, which only provide single-point measurements. Future TGF missions could consist in performing simultaneous detection by a detector array in space. In order to prepare such a scientific objective, we simulate the detection of TGFs by a nanosatellite, or small satellite, constellation. The objective is to quantify the impact of six parameters defining such a constellation, in order to maximize the scientific return of the mission. The parameters characterized in this work are the number of satellites, their relative distance, their altitude, their orbital configuration, the effective detection surface, and their orbital inclination. We use a Monte Carlo simulation code to propagate photons in the atmosphere and simulate the satellite positions and photons hits on satellites. Finally, we quantify the number of TGFs detected by the fleet, multi-detected, the number of photons received, and draw conclusions about the impact of each parameter.

**Plain Language Summary** Terrestrial Gamma ray Flashes are brief and intense events producing gamma rays in thunderstorms. Their detection is usually performed using scintillators in space, providing only single-point measurements of these events. In order to prepare future missions that could be planned to improve the understanding of these events, we simulate their detection by a small satellite constellation. These simulations, associating a Monte Carlo code and a code calculating satellite positions, allow us to study several parameters and determine what the best configuration depending on the scientific objectives is. We present the results of our simulations, and give an open conclusion in order that the reader can adapt to its different scientific objectives and constraints.

## 1. Introduction

Terrestrial Gamma ray Flashes (TGFs) are bursts of gamma rays produced in thunderstorms, observed for the first time by Fishman et al. (1994). They are made of ~$10^{17}$-$10^{18}$ high-energy photons at the source, for TGFs observed from space (e.g., Gjesteland et al., 2015; Mailyan et al., 2016), in ~100 µs (Fishman et al., 2011; Marisaldi et al., 2015), part of which will reach Low Earth Orbit (LEO) satellites. For 30 years and up to now, the great majority of TGF observations are single-point detections by space-based instruments, such as BATSE on the Compton Gamma Ray Observatory (Fishman et al., 1994), GBM on Fermi (Roberts et al., 2018), RHESSI (Smith et al., 2005), AGILE (Marisaldi et al., 2010), or the Atmosphere-Space Interactions Monitor (ASIM) onboard the International Space Station (Østgaard et al., 2019); the latter being the only instrument specifically built for TGF detection. Those detections have allowed to determine and understand a lot about physical processes involved in producing TGFs, especially the Relativistic Runaway Electron Avalanches (RREAs) (e.g., Dwyer & Smith, 2005) process, where electrons are accelerated in the strong electric fields present in thunderstorms, generating gamma rays by bremsstrahlung. However, single-point measurements cannot bring information about geometrical features of TGFs such as the geometry of the gamma ray beam or the position of the source. This is a key limitation on our understanding of TGFs as the inference of source spectra from satellite observations depends on these geometrical features. In fact, with a single spacecraft, even much larger effective areas than currently available on ASIM cannot constrain better the source parameter space (Lindanger et al., 2021). Even if recent advances in this field have been achieved through the use of aircraft rather than satellites (Marisaldi et al., 2024; Østgaard et al., 2024), which revealed an unexpected population of low-energy TGFs too weak to be observed from space (Bjørge-Engeland et al., 2024), simultaneous detection by an array of satellite detectors, called in this paper "multi-point satellite detections" is one of the next steps in the development of instrumentation for the
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Reproduction from Pallu et al. (2023). Terrestrial Gamma ray Flash (TGF) density map calculated from Fermi's TGF first catalog (Roberts et al., 2018), used to generate TGF below 25° latitude on Earth.</figcaption></figure>

atmospheric electricity research field. Satellite (or nanosatellite) constellations in formation flight, is a way to perform such observations.

It is worth mentioning that multi-point detections of TGFs have already been performed (downward-TGFs in that case) with the Telescope array in Utah (e.g., Abbasi et al., 2023; Belz et al., 2020). As a ground detector, it allows a higher number of detectors, a larger detection surface, a bigger amount of data possible to record, and continuous measurements on longer periods, compared to a satellite constellation (Berge & Celestin, 2019). However, a satellite constellation would perform measurements all over the world, for different climate conditions (depending on the inclination), would detect upward TGFs, and have a larger field of view.

In order to prepare such future space missions and maximize their scientific return for TGF study, we propose in this work to quantify the number of TGF detections, multi-detections and the number of photons received by the satellites, as a function of the different flight configurations. The number of photons received by the satellites is very important, as the reader can use it to identify which configuration allows it to reach its scientific objectives. For that, we vary several parameters such as the number of satellites, their relative positions, their relative distance, their altitude, the effective detection area of the instrument, and the orbit inclination of the satellites. In Section 2, we present the methodology of this work. We present the results in Section 3 and discuss them in Section 4.

## 2. Method

In order to simulate the detection of TGFs by a satellite constellation, two simulation codes are used. The main code consists in randomly producing TGFs following a TGF density map, and calculating the position of a satellite constellation, to check when a TGF is detected by one or several satellites. The different parts of this code are presented in Sections 2.1 and 2.3. The second code is used to determine the distribution of photons per unit area as a function of the distance to the TGF. This part is presented in Section 2.2. The coupling between both codes is explained in Section 2.4.

### 2.1. TGF Production

A TGF density map has been calculated and presented in Pallu et al. (2023), using Fermi/GBM first catalog (Roberts et al., 2018). It is shown in Figure 1. In this work, we randomly pick the positions where TGFs are simulated, following this TGF density map. We consider a global rate of 388,000 TGFs/year, also calculated in Pallu et al. (2023). The production times of TGFs are randomly but uniformly distributed over the whole period simulated (discussed in Section 2.7). It is worth mentioning that TGF occurrence is not uniformly distributed in time on Earth, as it follows lightning activity yearly modulation, but this does not have a significant impact on the results under the assumption of a mission lasting years.

This TGF density map is representative of TGFs detectable from space, that is to say quite strong >10¹⁷ photons-TGFs. In this work, we decided to choose our reference case to be TGFs with a number of photons at the source of 10¹⁸. Even though weaker TGFs have recently been observed by aircraft (Bjørge-Engeland et al., 2024), and from
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Number of photons as a function of the radial distance propagated up to 400 km, with a source at 15 km and at 12 km, using the Monte Carlo code described in the text. Values for distances <10 km are non significant due to the lack of statistics in the results of the code, but this is resolved by using models shown in green lines.</figcaption></figure>

space (Gjesteland et al., 2015), the source fluence can be easily scaled in the results presenting the number of photons received, as it is a linear effect.

## 2.2. Photons Propagation up to Satellite Altitudes

We use a Monte Carlo code presented in Pallu et al. (2021), and based on Østgaard et al. (2008). It propagates photons in the atmosphere from a TGF production altitude to satellite altitude, fixed to 15 and 400 km respectively for the reference case. We assume 10¹⁸ photons produced at the source. The energy distribution is in agreement with the RREA phenomenon, which produces a 7.3 MeV cut-off in the primary electron spectrum. Three electromagnetic processes are taken into account for the photons: photoelectric absorption, Compton scattering, and electron-positron pair production. Initial velocities of photons are uniformly distributed into a 45°-cone, and directed upward.

Using the cylindrical symmetry of the system (for purely vertical TGFs), we determine the number of photons that reached the satellite altitude as a function of the radial distance. We use photons with energies greater than 10 keV. In other words, we assume that the gamma ray spectrometer in this work has a low-energy threshold of 10 keV. This number of photons as a function of the radial distance will be used in the main simulation code. The results of two different configurations are presented in Figure 2, a TGF source at 15 km and a TGF source at 12 km. The satellite altitude is set to 400 km for both. A manual adjustment (in green) is used for small radial distances, as statistics are missing. In fact, the TGF count at low radial distance is constant, as it is uniform in the center of the photon beam. The fits is going up to ~800 km, as the TGF counts fall below 10⁻²/cm² for larger radial distances, and would not imply a detection on the detector.

This Monte Carlo code also allows to calculate the distribution of propagation time up to the satellite altitude as a function of the radial distance. We use it to determine the arrival time of each photon at each satellite (explained in Section 2.4).

In this Monte Carlo simulation, we assume that the Earth atmosphere is flat (non curved) to simplify the calculations. Assuming a 6,800 km distance from the earth center to the satellite at 400 km, the difference between the flat approximation and the radial approximation for 400 km radial distance is only 11 km. We consider therefore that our assumption is acceptable, as the path of TGF photons, that are at the edge of the beam, is only <2% different from what it would have with a curved atmosphere.

TGFs simulated in this work are assumed to be instantaneous. This assumption does not impact our results, as we do not account for instrumental temporal limitations such as dead-time and pile-up in this work. The timing is only used for the TGF detection, that is to say for the arrival time. The detection time bin used is 1 ms.
<figure><img src="image_5.png" /><figcaption>Figure 3. The three different satellite configurations studied in this work.</figcaption></figure>

## 2.3. Satellite Constellation

The satellite constellation is defined by a number of satellites, their relative positions, their relative distances, their altitude, and the inclination of their orbit. The positions of all the satellites are then calculated with Matlab code `Orbit3D` (Version 1.4.0.0) written by Ennio Condoleo.

The number of satellites in this study varies from 3 to 20. Their relative positions vary following 3 different configurations, shown in Figure 3. All the configurations require the whole fleet of satellites to be at the same altitude, as it is technically difficult to stay in formation flight while changing altitude

(different altitudes imply spending energy to stay in formation). We set this altitude to 400 km. Config. 1 corresponds to all the satellites being on the same orbit (one line of satellites). Config. 2 consists in distributing the satellites on the same orbit but with two different phases (two lines of satellites). Config. 3 consists in distributing the satellites on the same orbit but with three different phases (three lines of satellites)

The inclination of the orbit for the reference case has been chosen to be 25°. The distances between satellites in this study vary from 0.5° to 10°. For information, 1° at 400 km of altitude corresponds to ~118 km.

## 2.4. TGF Photon Hits

For each satellite, the radial distance to the TGF is calculated. In order to speed up the simulation, we use a field of view of 1,000 km around the TGF axis. In other words, if at least one satellite is at less than 1,000 km from the TGF axis, we consider that the detector might potentially have detected one photon, and thus the determination of the number of photons detected is performed. The determination of the number of photons is done using results of the Monte Carlo simulation code (shown in Figure 2). For each satellite, we determine the number of photons received by the detector (= TGF photon hits), calculated by the distribution of photon fluxes as a function of the radial distance, and the effective detection surface. At the same time, the Monte Carlo code gives the distribution of the propagation duration of photons, as a function of the radial distance. Thus, we determine the arrival time of each photon received with a random draw based on this distribution. This arrival time is used here by the TGF detection algorithm explained in the following Section. To simplify the calculations, the detection surface of the detector considered here is assumed to be the effective area of the detector. It is also considered to be satellite-attitude independent.

## 2.5. TGF Detection Algorithm

Threshold to detect TGFs in data is defined considering the gamma ray background radiation and using the Poisson law. We make the assumption that the gamma ray background is Poissonian, even if it is not strictly Poissonian. In fact, a cluster of counts can occur when a high-energy cosmic directly interacts with a satellite. With a constellation, these events can be discarded as they will appear in only one satellite, so a further analysis has to be performed on the ground.

We fix the threshold to limit the number of false positives detected by the triggering system to one false positive per unit time (here is <1/month). For a Poisson distribution of counts, the probability to have a number of counts k over a time bin of duration τ is:

$$P(X = k) = e^{-\lambda} \frac{\lambda^k}{k!} \quad (1)$$

where $\lambda = R\tau$ is the mean number of particles detected over a duration $\tau$ and R is the mean number of particles detected per second (due to the radiation background). The probability to obtain more than k counts from the background over a time $\tau$ is then:

$$P(X \geq k) = \sum_{n \geq k} e^{-\lambda} \frac{\lambda^n}{n!} = 1 - \sum_{n < k} e^{-\lambda} \frac{\lambda^n}{n!} \quad (2)$$
The likelihood of any number of detected particles caused by the radiation background is quantified in both these equations. When the number of counts by the background is greater than the threshold k, we refer to it as a false positive event. The duration between two false positive events is then:

$$ \Delta t = \frac{\tau}{p} \qquad (3) $$

Here, we choose to limit the false positive events to one per month, that is to say: $\Delta t = 1$ month. The gamma ray radiation background is difficult to estimate at LEO, therefore we used the work of Cumani et al. (2019), which gives a gamma ray radiation background to be around ~40 cts/s/cm² for energies between 10 keV and 30 MeV. For comparison, we can estimate the gamma ray background with Fermi/GBM to be ~10 cts/s/cm² in BGO detectors (Fitzpatrick et al., 2012). We have taken into account cosmic and albedo photons, that are given for a LEO at 550 km, with a low inclination and a medium solar activity.

$\tau$ is the detection time bin, chosen to be ~1 ms since TGFs lasts $\leqslant 1$ ms (Fishman et al., 2011; Marisaldi et al., 2015). It is worth mentioning that AGILE and ASIM have obtained their best results with a time bin of 300 µs.

In this study, the detection strategy is to fix a threshold on each satellite separately to detect TGFs, and then when a satellite triggers a TGF, all the data from all the satellites, around that detection time, are collected and can be analyzed on the ground. Of course, a more efficient detection algorithm can be developed, but we decided to present the absolute number of photon hits in order to give hints to determine the best detection algorithm to use.

The effective surface detection per satellite for the reference case is 100 cm². The detection time bin is fixed to 1 ms in order to take into account the duration of the TGF and the propagation delay between a satellite in the center of the field of view, and a satellite near the limit of the field of view (~500 km of radial distance). The threshold is defined only depending on the detection area on each satellite, defining the background count rate. To limit to one false positive per month, the threshold is defined as 22 cts/ms per satellite. TGFs for which the number of photon hits exceeds this threshold are called “detected TGFs” (or “triggered TGFs”) in the following.

## 2.6. Monitored Variables

We use several variables to quantify the optimized flight configuration for the satellite fleet. We quantify the number of TGFs triggered (also called “detected TGF”) by the TGF detection algorithm (presented in Section 2.5). The mean number of satellites hit by at least one photon, by fleet, is presented. The mean number of TGF photon hits by satellite of the fleet, is also quantified and presented. In each fleet and for each TGF, the satellite receiving the greater number of photons is considered as the “main satellite.” The number of TGF photon hits on an average on the main satellite, for TGF that has got at least one photon hit on a satellite, is illustrated. Finally, we present the mean distribution of the TGF photon hits per satellite in the fleet, depending on the distance between satellites and the different configurations. A satellite's number corresponds to the rank of the satellite in terms of photons received. The term TGFs simulated, used in Section 3, correspond to the total number of TGFs produced in the simulation, triggered or not.

## 2.7. Duration of the Flight Simulation

To estimate the optimal duration of the total simulation to get enough statistics to avoid an initial satellites position dependency in the results, but also to limit the computing time when the simulation results have reached a stationary state, we have performed the same simulation 20 times, with 20 different initial positions for the satellites. We keep track of the proportion of TGF detected as a function of time. A stationary state, independent of the initial position, is reached around 50 days of flight. Therefore, we decided for this study to set the simulation duration to 100 days.

# 3. Results

In this paper, we show the impact of each parameter of the system on TGF observations to determine the best configuration for future TGF missions focused on multi-detection. For that, we vary the following parameters: the satellite altitude, the orbital configuration, the detection area, and the orbit inclination. We also try different TGF
production altitudes: 15 km (reference case) and 12 km. We use a reference case, presented in Section 3.1. Then we will present the impact of each parameter on TGF detection.

In Figure 4, all the results are presented, the eight lines (from A to H) correspond to the eight configurations used, and for each line, five panels are shown, presenting the monitored variables listed in Section 2.6.

For each case, on panel (a), the colorbar represents the proportion of detected TGFs with respect to the number of simulated TGFs, depending on the number of satellites in the fleet, and their relative distance. On panel (b), the mean number of satellites hit by TGF photons, per fleet, per TGF, is represented the same way. On panel (c), we present the mean number of TGF photon hits on all the satellites of the fleet, per TGF. Panel (d) shows the mean number of photons received by the main satellite. Finally, panel (e) presents the mean distribution of photon hits per satellite, per TGF, depending on their relative distance, using a 20 satellites fleet.

## 3.1. Reference Case

The reference case is defined by the following parameters: vertical TGFs (not tilted), with $10^{18}$ photons produced at the source, at 15 km. We consider satellites flying at 400 km and distributed on two different orbits ("Config. 2" in Figure 3), an effective detection surface of 100 cm$^2$ per satellite, and an orbit inclination of 25°.

One can see the results in Figure 4a. On panel (a), one can see that the ratio of detected TGFs over simulated TGFs reaches a maximum of 3% for the highest number of satellites (20) and the largest distance between them used here (10°). In fact, this configuration maximizes the field of view of the fleet. On panel (b), one can see that the mean number of satellites hit is higher for constellations with a high number of satellites, but a small distance between them. If the objective of the future mission is to detect TGF photons simultaneously by at least 4 satellites, the constellation should be at least ~5 satellites and should be distant by less than 5° from each other. Calculations have shown also that for distances smaller than ~3°, >95% of the detections are multi-detections (>4 satellites). These results are in agreement with the calculated radial distribution of TGFs.

On panel (c), the number of photons received by the fleet in average is shown, and one can see that the maximum TGF photons is received for a higher number of satellites and a smaller distance between detectors. This number goes from ~50, to ~350 for the best configuration. One can note that to get in average more than 100 photons, the constellation should also be composed of at least ~5 satellites which should be distant by less than 5° from each other.

On panel (d), one can see the average number of photons in the main satellite of the fleet, for each TGF that has got at least one photon hit in a satellite of the fleet. This number is maximum for distances of ~4° between satellites. Finally, on panel (e), the distribution of photons over the different satellites of the fleet is represented, depending on the distance between satellites. One can confirm the results of panel (d) for the number of TGF photon hits on the main satellite (satellite number = 1), the maximum is reached for distances of ~4°. However, it also confirms panel (c) on the total number of TGF photons hit on the whole fleet. Then, according to the scientific objectives of the future mission, one can choose the configuration to get for instance numerous photons in several satellites.

## 3.2. Sensitivity to Different TGF Intensities and Altitudes

The reference case uses a TGF produced at 15 km of altitude, with a number of $10^{18}$ photons at the source. However, it has been shown that a high number of TGFs can have intensities lower, for instance TGFs detected by aircraft has been shown to reach about $10^{14}$ photons at the source only (Bjørge-Engeland et al., 2024). Similarly, the source altitude can also reach lower altitudes such as 10 km. For that reason, we also performed simulations using a source altitude of 12 km, in order to quantify the differences in the satellite detection. Concerning the number of photons produced at the source, the results can easily be scaled by multiplying or dividing the number of photons shown in panels (c), (d) and (e) by the wanted factor.

One can see the results using a TGF source altitude of 12 km in Figure 4b. The general trends are the same, however, as expected, the TGF photons reaching the satellites altitude is lower, and limits the number of detected TGF to a maximum of ~1.3% (panel (a)). The mean number of photons in the fleet can reach only ~50 photons for 20 very close satellites. TGFs produced deeper in the atmosphere are less detectable due to absorption of the Earth atmosphere. Of course, satellites favor the detection of intense TGF and are produced higher in altitude. However, weaker TGFs can still be detected from space (see Figure 6 and Section 3.5).
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Results of the simulations of Terrestrial Gamma ray Flash observation with satellite constellations are represented. One configuration is represented on one line (from A to H). Each panel (from (a) to (e)) corresponds to one monitored variable calculated. Further details are described in Section 3.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Number of Terrestrial Gamma ray Flash (TGF) photons hit depending on satellite altitudes, per satellite. Simulated TGF are produced at 15 km. The effective detection surface per satellite is 100 cm². Only one satellite is simulated for the result of this figure.</figcaption></figure>

### 3.3. Satellite Altitude Dependency

In this section, we investigate how the variables vary for a different satellite altitude. Figure 4c shows the results for satellites orbiting at 600 km, instead of 400 km in the reference case. One can see that the proportion of detected TGFs is greater, reaching 3.3% of TGF triggered for the best case (20 satellites separated by 10° each). A higher altitude involves a greater field of view, and thus a higher ratio of triggered TGFs. The low density atmosphere between 400 and 600 km does not absorb many photons during their propagation, but the fluence is lowered by the widening of the beam. This effect is visible in panel (c), with the lowest number of photons received on average on the fleet.

We performed a further study about the satellite altitude and TGF detections, by quantifying the TGF photons hit by only one satellite. The methodology is the same, a Monte Carlo code is used to quantify the number of photons between TGF altitude (15 km) and the satellite altitudes (between 400 and 1,900 km). In order to increase the statistics, we used 3 satellites, spatially separated such that their field of view does not overlap each other. Then we reported the results corresponding to one satellite alone. We obtained the results presented in Figure 5. The number of photons decreases with satellite altitude increasing due to the beam widening. When using the TGF triggering method, a limit around 900–1,000 km of altitude makes the number of detections fall, due to the number of photons passing below the threshold of 22 cts/ms.

<figure><img src="image_8.png" /><figcaption>**Figure 6.** Results of simulations, with same parameters as the reference case, with 10 satellites and 5° between satellites, except for the effective detection surface which vary from 5 to 400 cm² per detector, and the number of photons at the source.</figcaption></figure>
### 3.4. Orbital Configuration Dependency

We investigate the impact of the orbital configuration on TGF observations. We used 3 different configurations, the first one that is used in the reference case, where satellites are distributed onto two orbits. Then, we simulate Config. 1 of Figure 3, the results are shown in Figure 4d. Config. 3's results are shown in Figure 4e.

For all satellites on the same orbit, Figure 4d shows that even if the number of detected TGFs is a little increased (panel (a)), the mean number of satellite hits is smaller, limiting their distance to <3° to get a majority of multi-detections. On the contrary, in Configuration 2 (Figure 4a) and 3 (Figure 4e), TGFs can be detected by more than 4 satellites in average for distances between satellites up to 5°.

### 3.5. Effective Detection Surface Dependency

We use a single case to show the influence of the effective detection surface on TGF detections. We have chosen the reference case with a constellation of 10 satellites and a distance inter-satellite of 5°. We simulated surfaces between 5 and 400 cm². We have used different number of photons at the source, between 10¹⁶ and 10¹⁹ photons, to see the impact on the number of detections. The threshold is calculated depending on the detection surface for each simulation run, as explained in Section 2.5. Results are shown in Figure 6.

One can note that for detection areas greater than ~50 cm² for 10¹⁸ sources, the increase with the detection area of the TGF detection rate is weak, going from 1% for 50 cm² to almost 2% for 400 cm². It seems that using a larger detection area than 50 cm² does not improve the detection efficiency of TGFs for a source intensity of 10¹⁸. This result is limited by the fact that we use only a fixed number of photons at the source. We have performed the simulations for different source intensities, down to 5 × 10¹⁶ photons at the source. One can clearly see that the plateau is reached for larger detection surfaces for weaker TGFs. The lower limits for TGF detections here is 5 × 10¹⁶, even for great detection surfaces. Sources of 10¹⁶ photons and below are too weak, no detections are performed. 10¹⁷ sources can be detected but with detection surfaces greater than 200 cm². It's worth mentioning that even if the number of detection is not increasing much when the effective area is increased, it will allow a greater number of TGF photon hits, allowing to make more precise analysis and better science.

### 3.6. Orbit Inclination Dependency

We vary the orbit inclination of the satellites, simulating orbits with 5°, 25° and 80° inclinations. The 25° inclination corresponds to the reference case (Figure 4a). Results concerning 5° and 80° inclinations are respectively presented in Figures 4g and 4h.

The orbit inclination plays a big role in TGF detections, seeing the TGF density distribution (Figure 1). In fact, the high TGF density at low latitudes involves a high TGF detection rate for low orbit inclination such as 5° shown here. This was for instance the advantage of AGILE, which was on a 2.5° inclination orbit (Marisaldi et al., 2010). The low number of TGFs which can be seen on Figure 4h is caused by the reduced time of the satellites over the tropics, where the TGF density is high, but the effect is artificially enhanced by the use of Fermi data which omit TGF for latitudes above 25°. Even if the TGF density is expected to be lower at high latitudes, as was for instance explored by RHESSI (Smith et al., 2010, 2020) and ASIM (Maiorana et al., 2021), the results are therefore underestimated. It will be very interesting to explore these high latitudes with a satellite constellation to complete these results and TGF density map.

## 4. Discussion

### 4.1. Optimal Configuration to Study TGFs

In this study, we have explored the impact of six parameters in a satellite constellation dedicated to TGF measurements. Conclusions can be drawn on some parameters, but others should be adapted to the scientific objectives of the future mission discussed.

For instance, no matter how many satellites compose the fleet and their relative distances, the detection area should be greater than ~50 cm², and satellite altitudes lower than ~900 km in order to maximize the number of TGF that could be detected. Then, it seems natural that the number of TGFs detected can be maximized when the
satellite data can be post-analyzed on-ground. However, more complex triggering algorithms than the one exposed in this work could be developed to increase onboard TGF detections.

In the case of a future mission dedicated to TGFs multi-detection, this work helps to draw limits on the studied parameters to optimize multi-detections. First, the best orbital configuration to maximize the number of multi-detected TGFs is to distribute the fleet onto two orbit planes. The distance between the satellites has to be chosen through a compromise between maximizing the number of TGF detected and the number of TGF multi-detected: this leads to a distance around 5° between satellites.

The orbit inclination should be adapted to the mission scientific aims, either to detect a high number of TGFs, at equator, or to explore a variety of TGFs at different latitudes.

Finally, even if a large number of satellites will induce a higher cost, which could become prohibitive, the number of detections increases with the number of satellites, so the higher, the better.

## 4.2. New TGF Science With Satellite Constellation

Since the first TGF detection by satellite 30 years ago, tens of thousands TGFs have been detected so far by satellites. Simple TGF detections are not anymore the main objective of scientific missions dedicated to TGF study. The scientific objectives are now linked to the big scientific questions in atmospheric electricity: shed light on the physical processes involved in the initiation of TGFs, and their impact on the Earth atmosphere. Multi-detections of TGF can be performed using small satellite constellation in formation flight, and bring essential informations, inaccessible up to now about the TGF photon beam geometry, their diversity in terms of type, fluence, altitude, beam tilt, and beam opening angle, for instance.

One particular example can be the determination of TGF altitude source, and of the multiple or extensive origin of TGFs. Using simultaneous measurements would allow triangulation to determine the source location, without being forced to assume the associated leader detected by a lightning detection network to be the origin. For that, at least 4 satellites would be required, but, once again, the more the better. A minimum number of photons received by each satellite is also necessary (to be estimated in a further study), to get each satellite light curve statistically resolved to use it in the solving algorithm that will be used. In the present work, we did not perform the study to determine the minimum satellite configuration needed to calculate the origin of TGFs with a good spatial resolution, but this will be part of a next work on this subject.

The beaming direction, its distribution and the evaluation of its tilt are also essential informations to know about TGFs, as they directly impact the calculation of the source fluence, and thus their impact on the atmosphere, on risks associated with TGFs (Pallu et al., 2021, 2023), and the understanding of the involved physical processes. Finally, with large enough effective detection surface, we could hope to detect weaker TGFs that are rarely detected by satellites, which could not be associated with leaders, or even detect the gamma ray phenomena discovered recently, namely Flickering Gamma ray Flashes (Marisaldi et al., 2024; Østgaard et al., 2024).

## 4.3. Technical Challenges of Such a Mission

Although this work assumes a very ideal basis for a future small satellite constellation, it is clear that some technical challenges will have to be resolved to perform such observations. One of the main challenges will be to perform a formation flight on small satellites. In fact, this would require an active control system to keep satellites close to each other, even if at deployment they lie on the same orbit. Active control systems are not always possible on small satellites, in particular on nanosatellites, for which the mass budget and the power budget are really constrained. Another technical challenge is the real time communication between all the satellites of the fleet, in order to allow the definition of onboard TGF triggers using data of several satellites, instead of using only a trigger per satellite, as presented in this work. A TGF trigger using close-by satellites instead of only one or the whole fleet, would lower the threshold and allow it to detect weaker TGFs. Another solution is to send all the measurements on the ground, without being on-board analyzed. This would cost in terms of satellite communication, but it has been already performed for Fermi-GBM data, since November 2012, increasing the number of TGF detections (Roberts et al., 2018).
## 5. Conclusion

In this work, we have studied the impact of six parameters of a small satellite constellation in formation flight on their TGF detection rate, multi-detection rate, and number of photons observed. Some parameters impact the general detection of TGFs, not depending on the number of satellites nor their configuration (effective surface detection and satellite altitude). On the contrary, other parameters have to be chosen carefully depending on the scientific objectives of the future mission, such as their relative distance, and the orbit inclination and configuration.

## Data Availability Statement

The Fermi-GBM catalog used for the TGF density map presented is available online (Fermi-GBM TGF catalog, 2025). Simulation results of Figure 4 may be downloaded from Pallu (2025).

## Acknowledgments

This work is supported by the French Space Agency (CNES) in the framework of the R&D program for the development of the Fast Gamma ray Spectrometer (FGS).

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