Novel method and tool to identify solitary waves in the Martian plasma environment

Abstract

This paper introduces a method and an innovative graphical user interface (GUI) tool to identify bipolar solitary wave structures in the Mars Atmosphere and Volatile EvolutioN (MAVEN) mission dataset. As input to this tool, we utilized medium-frequency burst mode calibrated electric field data obtained from the Langmuir Probe and Waves (LPW) instrument aboard MAVEN. To detect solitary waves, we first discuss the typical theoretical solitary wave structure and its key features. Based on these features, we developed a series of mathematical conditions that are applied to the LPW electric field dataset. After rigorous testing, a MATLAB executable GUI application named SWIT (Solitary Wave Identifying Tool) was developed. The output of SWIT provides the amplitude, width, and time of occurrence of the solitary waves. Furthermore, we evaluate the accuracy and limitations of SWIT. It is found that SWIT demonstrates high efficiency. It is a dedicated identifier for analyzing medium-frequency electric field measurements from the MAVEN spacecraft to search for solitary wave structures in the Martian plasma environment. It is suggested that this novel method can be applied to datasets from different spacecraft in other planetary plasma environments with minor modifications.

1 Introduction

Electrostatic solitary waves (ESWs) are nonlinear, isolated electric field pulses observed in space plasmas. These waves typically propagate along the direction of the magnetic field and exhibit negligible fluctuations in the perpendicular component of the magnetic field. They were first detected in auroral plasma by the S3-3 polar-orbiting satellite (Temerin et al., 1982). Later, high-resolution electric field measurements from the Geotail spacecraft revealed that broadband electrostatic noise (BEN) consists of isolated bipolar solitary structures (Matsumoto et al., 1994). Since then, ESWs have been observed in various regions of the Earth’s magnetosphere, such as the auroral zone (Ergun et al., 1998; Pickett et al., 2004), magnetopause (Cattell et al., 2002; Graham et al., 2015; Graham et al., 2016), magnetosheath (Pickett et al., 2003; Holmes et al., 2018; Shaikh et al., 2024), bow shock (Hobara et al., 2008; Wang et al., 2014; Vasko et al., 2018; Vasko et al., 2020; Sun et al., 2022; Kamaletdinov et al., 2022), plasma sheet (Ergun et al., 2009; Tong et al., 2018; Mozer et al., 2018; Wang et al., 2022), magnetotail (Norgren et al., 2015), inner magnetosphere (Vasko et al., 2017a), dusk flank region (Arya and Kakad, 2025), and so on. As new observations continue to emerge, theoretical (Singh and Lakhina, 2001; Pickett et al., 2005; Kakad et al., 2007; Lakhina et al., 2008a; Lakhina et al., 2008b, 2009; Kakad et al., 2009; Lakhina et al., 2011a; Lakhina et al., 2011b; Olivier et al., 2015; Maharaj et al., 2015; Kakad et al., 2016; Singh et al., 2024) and simulation (Omura et al., 1996; Umeda et al., 2002; Kakad et al., 2013; Kakad et al., 2014; Lotekar et al., 2016; Kakad A. et al., 2017; Lotekar et al., 2017; Vasko et al., 2017b; Dillard et al., 2018; Lotekar et al., 2019; Kakad and Kakad, 2019) studies have been conducted to investigate their generation mechanisms. In general, monopolar (double layer), bipolar, and occasionally observed tripolar structures fall under the ESW category. In this paper, the term solitary waves refers specifically to bipolar solitary structures.

In fluid models, ESWs can be classified as ion or electron acoustic solitary waves (IASWs/EASWs), depending on the dominant driving species. EASWs exhibit phase velocities of a few thousand kilometers per second, whereas IASWs typically have phase velocities of a few hundred kilometers per second. A review article on ESWs as acoustic soliton models is provided by Lakhina et al. (2021). In kinetic models, ESWs are interpreted as ion or electron holes in phase space, depending on the polarity of the associated potential structures (Eliasson and Shukla, 2006; Aravindakshan et al., 2018a; Aravindakshan et al., 2018b, Aravindakshan et al., 2020; Aravindakshan et al., 2021; Aravindakshan et al., 2023). In space plasmas, they play a role in the acceleration, heating, energy dissipation, and trapping of charged particles (Ergun et al., 2004; Andersson and Ergun, 2012; Mozer et al., 2013; Kakad et al., 2017a; Kakad et al., 2017b; Wang et al., 2023).

ESWs are not confined to Earth’s plasma environment; they have also been observed in the Martian magnetosheath (Kakad et al., 2022; Thaller et al., 2022; Pandey et al., 2025a; Pandey et al., 2025c), the Venusian plasma environment (Malaspina et al., 2020), and Saturn’s magnetosphere (Williams et al., 2006). By studying the ambient plasma parameters, various generation mechanisms have been proposed for the ESWs (Singh et al., 2022; Rubia et al., 2023; Varghese et al., 2024a; Varghese et al., 2024b). In case of Mars, in recent studies the ESWs have been reported using the electric field data from Langmuir Probe and Waves (LPW) instrument aboard the Mars Atmosphere and Volatile Evolution (MAVEN) mission. However, ESWs on Mars have not been studied as extensively as those on Earth. The LPW instrument measures the y-component of the electric field in the spacecraft’s coordinate system (Andersson et al., 2015). Therefore, limited information is available about the propagation of ESWs. A statistical study of ESWs would provide valuable insights into their occurrence in the plasma environment of an unmagnetized planet like Mars, helping to understand their role in particle dynamics. However, manual detection of solitary waves from such a large dataset is a real challenge.

In this paper, we present a tool for identifying bipolar solitary waves from the MAVEN dataset. Previously, Kojima et al. (2000) developed a method to identify ESWs from the Geotail spacecraft dataset. They employed a bit-pattern comparison technique using two sample waveforms of ESWs with opposite polarity. They defined an ESW index that quantifies the deviation from or similarity to the sample waveforms. This process is carried out by shifting the sample waveforms in time to match the observed signals. However, since the width of ESWs in the time domain can vary, different sample waveforms with varying pulse widths are required. Hansel et al. (2021) used the Solitary Wave Detector (SWD) on NASA’s Magnetospheric Multiscale (MMS) mission to map solitary waves in the Earth’s magnetosphere, identifying 60% of all bipolar solitary waves. It is based on a pseudo-standard deviation technique. In the present paper, we use a cumulative-integration-based approach to identify solitary waves. The developed tool is rigorously tested using LPW medium-frequency electric field data from the MAVEN spacecraft, and its efficiency in detecting solitary waves is examined. The paper is organized as follows: the methodology and module sequence in the program are detailed in Sections 2, 3, respectively. The usage and requirements of the Solitary Wave Identifying Tool (SWIT) are elaborated in Section 4. The results are discussed in Section 5. Finally, the study is summarized and concluded in Section 6.

2 Methodology

First, we present the mathematical formulation of a solitary wave and outline its key properties using cumulative integration and first-order differentiation. We examined discrepancies between the ideal and observed solitary wave structures and used this information to ensure accurate identification of solitary waves in the real data. Below, in different subsections, we describe the specific criteria employed in the program to identify solitary waves. We assume the following form for the electric potential linked to the solitary wave structure, as outlined by Kojima et al. (2000) and Krasovsky et al. (1997),where is the peak of potential at position and is the distance where potential falls by times of . Spacecraft measurements provide electric field data in the time domain rather than the space domain. Therefore, on substituting in Equation 1 and using , we getwhere is the magnitude of the phase velocity of the solitary wave and is assumed to be constant.

To reduce parametric dependency and focus on the behavior of the electric field as a function of time, we take , , and ; then Equation 2 becomes,Equation 3 represents the typical electric field profile of solitary waves associated with positive or negative potential and traveling in either negative or positive direction. Based on this, we label the electric field profiles, where the negative half-cycle occurs first, followed by the positive half-cycle, as type-1 solitary waves. Conversely, those electric field profiles where the positive half-cycle occurs first, followed by the negative half-cycle, are labeled as type-2 solitary waves. Here, the positive and negative peaks in the solitary wave profile are termed as and , with their corresponding time instances as and , respectively.

An electric field profile of the type-1 solitary waves in the time domain is shown in Figure 1A. Its cumulative integration (CI), defined as , is displayed in Figure 1B. It may be noted that the negative sign in CI is used to maintain analogy with the electric potential. The first-order derivative of the electric field profile, , is shown in Figure 1C. The vertical blue dashed lines indicate the instance of and , with their midpoint marked by the black dashed line. The vertical red dashed lines indicate the initial and final instances, where the peak of CI decreases by 99.7%. The width of the solitary wave structure is defined as the time interval between and . Here, we list properties of the ideal form of solitary wave based on Figure 1; (i) Equal absolute values of and , (ii) Equal durations of negative and positive half cycle, (here and ), (iii) Continuous increase in the from to , (iv) In CI profile, no change in sign from time to , (v) Single turning point between to in . Here, the type-1 or type-2 categories are used only for convenience, and they do not signify the polarity of the potential structure associated with the electric field. The polarity of the potential can not be identified unless the direction of propagation of solitary waves is known. We consider all the above-listed properties of the solitary wave while setting different criteria in a MATLAB executable GUI tool named SWIT to identify solitary waves. In reality, the observed solitary wave structure does not follow its exact ideal form. Therefore, while dealing with the data, the properties mentioned above are treated as references and conditionally modified to meet the requirements. The modified conditions and their implementation in the SWIT are discussed in the next Section 3.

FIGURE 1

As an example, the type-1 solitary wave structure seen in LPW electric field data is displayed in Figure 1D with its CI in panel (E) and first-order derivative in panel (F). We mark the instances and by following the turning points in the electric field before and after the and , respectively. The turning points are the locations where the slope of the curve changes its sign. As far as the first property of the solitary wave structure is concerned, it is unlikely that in real data, we encounter . Therefore, we define a symmetry parameter for amplitude as . Here, can vary between 0 and 1, and = 1 represents 100% symmetry in amplitudes. We set a minimum acceptable limit on as 0.6. If falls below 0.6, then the bipolar electric field pulse is not treated as solitary wave. In Figure 1D, the absolute positive and negative peaks differ by 0.17 and = 0.95. Hence, it satisfies the acceptance criteria for being selected as solitary wave. Similarly, achieving equal durations for the positive and negative half-cycles is an ideal scenario (i.e., property-2). We defined a symmetry parameter for solitary wave half-cycle duration as . If exceeds 0.6, then the bipolar pulse is selected. A threshold value of 0.6 was set after visually inspecting many burst datasets. For values greater than 0.6 (such as 0.65 or 0.70), a significant number of solitary wave structures go undetected, even though they could have been identified through visual inspection.

Next, let us discuss the solitary wave properties (iii)-(v). The solitary waves are typically observed in high-resolution electric field data. Between and , a few outliers may disrupt the continuous increase of the electric field, introducing the local irregular slope variations. These variations may not be visually apparent, but they can result in multiple turning points in within and . To address this issue, the moving average smoothing method is employed. Ideally, one anticipates a single peak in CI associated with the solitary wave. Therefore, we also examined the turning points before and after the peak of the CI. These conditions are elaborated in the next Section 3.

3 Module sequence in SWIT

This subsection describes the logical workflow of different modules in the computer program, emphasizing the significance of each step in the process. For clarity, the explanation focuses solely on type-1 solitary wave, as the logic used to detect the type-2 solitary wave is identical, differing only in sign at specific points. A flowchart illustrating the main structure of the SWIT program is presented in Figure 2. It may be noted that SWIT is developed using MATLAB software.

FIGURE 2

3.1 Data loading and filtering

In this study, we use the medium-frequency (100 Hz–32 kHz) burst-mode calibrated electric field data obtained from the LPW instrument onboard MAVEN (Andersson, 2024). The sampling frequency is 65,536 Hz, and the duration of a single burst is typically 62.5 ms (4,096 data points) or an integral multiple of this. Initially, using “process_burst_events.m” program file, the user can convert electric field raw data into individual “.mat” files that contain the electric field and time information for each burst event that occurred on a given day. These individual burst files (time and electric field) serve as input to the SWIT module. At this stage, the electric field signal and corresponding time series data for a single burst event get loaded. Additionally, the user must provide the sampling rate of the data in Hz.

A Butterworth bandpass filter is applied to the electric field signal based on the input sampling frequency, with appropriate lower cut-off and upper cut-off frequencies. The lower cut-off frequency is used to eliminate long-term variations in the signal. Essentially, this process detrends the cumulative integration of a signal. Also, the higher cut-off frequency helps in removing the high-frequency noise. As an example, a series of electric field pulses observed in LPW electric field data on 9 February 2015 are depicted in Figure 3A. We can see that the solitary wave marked with the dashed rectangle exhibits small kinks. The frequency associated with these kinks is significantly higher than the frequencies of the solitary waves. The process of filtering removes these kinks. Figure 3B depicts the filtered signal, where the kinks have been eliminated. The and are chosen to ensure that the overall solitary wave structure of the signal remains largely unaffected. We have selected 100 Hz and 15 kHz for medium-frequency LPW electric field measurements. Figure 3C depicts the CI for the filtered electric field signal shown in Figure 4B. The use of CI in solitary wave identification is elaborated in the next subsection.

FIGURE 3

FIGURE 4

3.2 Cumulative integration and peak identification

Theoretically, each bipolar electric field pulse of type-1 will give rise to one positive peak in CI. We used this approach to identify the location of likely solitary waves in the observed electric field signal. The CI of the filtered signal is calculated, and the location of several peaks apparent in CI is identified. Each peak in CI corresponds to the center of the respective solitary wave structure (see Figure 3C). A peak in CI is identified if the amplitudes of the five preceding and five following points are smaller and decrease continuously on both sides of the peak. Next, the occurrence of turning points in CI preceding and following such peaks are identified and marked as and . As an example, the time variation of CI associated with one solitary wave structure is shown in Figure 3D. The turning points in CI before and after a peak shown with a blue asterisk are marked by vertical dashed black lines. It is noted that the solitary wave structure is located within and only. We estimated and , and if their magnitude exceeds 0.5 mV/m, then that solitary wave structure is considered for further analysis. The resolution of electric field data is 0.3 mV/m; therefore, we chose a limit of 0.5 mV/m as the acceptance criteria for solitary wave structures. In this way, each peak in the CI undergoes similar scrutiny. We ensure that each identified solitary wave structure is well-separated and is not a part of wave oscillations. This is carried out by checking the number of turning points in between two successive solitary waves identified by the program. If there are two or more turning points between of the first solitary wave and of the next solitary wave in the case of two successive type-1 solitary waves, such structures will be selected.

It may be noted that a major part of the solitary wave identification is covered by different steps elaborated so far. However, electric field data often possess small amplitude oscillations close to the solitary wave structure. Therefore, solitary waves identified within the turning points obtained in the previous step undergo further refinement to minimize error in the identification of solitary wave. A previously discussed issue involves the presence of multiple turning points in within the interval from to . To address this, the filtered signal from to is further smoothed using points, where is determined as one-fourth of the signal length between and . This criterion is developed by examining numerous examples of solitary waves. If multiple turning points persist after smoothing, then such solitary waves are rejected. We also examined the values of the electric field signal at its various turning points in and around the solitary wave, as illustrated in the schematic of the solitary wave profile in Figure 4. We check the values of signals at , . Here, the superscripts and refer to the first and second turning points, respectively. The subscripts represent the positive and negative half-cycle of solitary wave. The ranges for and , within which the values must fall, are represented by the blue and green shaded regions in Figure 4. For , in positive and negative half cycles, the limits are set as 0.25 and 0.25, respectively, which is indicated by blue shaded rectangles. Similarly, for also, in positive and negative half cycles, the limits are set as 0.25 and 0.25, respectively, as marked by green shaded rectangles. The limits for and are provided as input parameters in the GUI, expressed as percentage values of and . In the ideal case, we do not expect oscillations attached to solitary wave. However, in real data, because of such oscillations, we encounter turning points in . Therefore, it is essential to apply conditions on the amplitudes of their turning points. It minimizes the selection of the false positive solitary waves. If we reduce the limit to less than 0.25, we are making conditions stringent, and the selection criteria tend towards the ideal solitary wave. These ranges are selected based on the visual inspection of several electric field signals to minimize the false positives. Finally, we check the duration of the positive and negative half-cycle. Here, the time of the first turning point associated with positive and negative cycles are and , respectively. As mentioned in the preceding section, we consider the identified structure as solitary wave only if they have minimum 60% symmetry in their amplitude and width (i.e., and ). Finally, in the output, we write and of solitary waves, with their time of occurrence and , width of solitary waves in milliseconds, and type of solitary wave, i.e., type-1 or type-2.

4 Solitary wave identifying tool

By integrating all the conditions mentioned above, we developed a stand-alone desktop GUI application, SWIT, using MATLAB software. The requirements and instructions for the use of SWIT are given below.

4.1 Hardware and software requirements

This stand-alone desktop application SWIT is developed using MATLAB 2024b. It is freely available at https://zenodo.org/doi/10.5281/zenodo.15174978 for download (Pandey et al., 2025b). The package includes an installer (.exe) that contains the MATLAB Runtime R2024b, which provides the necessary shared libraries for the execution of the program. To install the application, users must download the ZIP file, extract its contents, and run the installer on a Windows 10 or later version (64-bit). The installation requires a system with at least an Intel or AMD x86-64 processor (2 GHz or faster), a minimum of 4 GB RAM (8 GB or more is recommended), and at least 8–10 GB of free disk space for the MATLAB Runtime and application files. Detailed installation and usage instructions can be found in the included ReadMe file.

4.2 Instructions for SWIT

Upon executing the file, a window appears at the center of the screen, as shown in Figure 5. There are three load buttons for input parameters: electric field, time series data, and number density data. Users are required to load these data files in format only. Among these, the electric field data is mandatory, while time series data and number density data are optional. The time series data is used solely for plotting purposes. If time series data is not loaded, an array will be considered in its place, ranging from 1 to , where is the length of the electric field signal (i.e., the number of data points). To the right of these buttons, there is a field displaying the filenames of the loaded files. To the right of this button, units for labels are shown. The background number density data is used here to obtain the electron and ion plasma frequencies. There are two options: users can either load density data, which must have the same length as the electric field data, or provide a single value of number density in the given field. In the latter case, the same number density value will be applied across all time instances. It may be noted that electric field burst mode data have durations in milliseconds, whereas the ambient plasma density data is available at either 4 or 8 s. Therefore, in the case of MAVEN medium frequency electric field data, the second option is more suitable. Users can choose the appropriate unit of density, either in or . By default, this value is set to 5 , and the user can change it based on the event under consideration. If both an array and a single value are provided, then the priority is set to the array. Users must also provide the sampling frequency in Hz, which is set to 65,536 Hz here for the medium-frequency electric field data from the LPW instrument.

FIGURE 5

Other parameters like and that show amplitude and width symmetry are set to 0.6 (recommended limit). Users can vary it between 0.6-1, where 1 represents 100% symmetry and width match, which is an ideal scenario. The threshold values for and are set to 25% which are recommended limits. Users can reduce these numbers to zero, which means there are no oscillations attached to solitary wave, which depicts an ideal case.

Once the electric field data is loaded, the user can click on the “View” button to plot the electric field in the upper panel and its spectrogram in the lower panel. There will be two horizontal black dashed lines in the lower panel corresponding to the electron plasma frequency and ion plasma frequency . This will provide a hint to the user as to whether the solitary waves are driven by electrons or ions. Solitary waves are often associated with an enhancement in the power spectral density (PSD) across a broad frequency range. If the enhanced frequencies lie below the ion plasma frequency, the waves are likely to be ion-driven. Conversely, if the frequencies fall between the ion and electron plasma frequencies, the waves are likely to be driven by electrons. Next, by clicking the “Run” button, the user can execute the internal program to identify solitary waves. It marks and with red and blue circles, respectively, in the upper panel. The plotted Figure can be exported in various formats, such as , , , , , and . A “Download” button allows users to save the output in , , , , and file formats. The output file consists of a matrix with six columns, where the number of rows equals the number of solitary waves identified. These columns, respectively, indicate the , , , , solitary wave width, and type (either 1 or 2) for identified solitary waves. To reuse the program, the user can click the “Reset” button. The error message or running status of the program is displayed in the remark field provided at the bottom side of the GUI window.

To evaluate SWIT’s baseline performance, we used a Dell G15 5,330 system with Windows 11, powered by 13th-generation Intel Core i5-13450HX CPU (2.4 GHz), and 16 GB RAM. The start-up time of SWIT is approximately 6–9 s after launch. Its RAM usage, measured as the active private working set, ranges from 100 to 300 MB. The total memory footprint (working set) is approximately 900 MB, including around 200 MB of shared memory. We evaluated the CPU time required for data loading and visualization. For example, loading a 62.5 ms signal sampled at 65,536 Hz takes approximately 0.6 ms. On average, loading a 1-s burst signal takes around 8 ms. Similarly, the time required to plot the signal and its spectrogram also varies with signal length. For a 1-s signal, rendering both panels takes about 3 s of CPU time.

5 Results

In this section, we discuss the efficiency of SWIT and some results based on the analysis of medium-frequency calibrated burst mode electric field data from MAVEN for February 2015. In the development of SWIT, we ensure high efficiency, which is needed for the automatic identifier. However, in spite of all these measures, the automatic program may detect some solitary waves, which may be either false positive or false negative. Therefore, the number of solitary waves identified by visual inspection and through automatic programs can differ. In such a scenario, one needs to check the efficiency of SWIT by comparing the number of solitary waves identified visually and through SWIT. For this purpose, we took the electric field data from 1 January 2021 as an example. It contains 2,966 individual burst datasets having durations between 62.5 and 375 ms. Each individual burst is loaded in SWIT GUI with recommended input criteria (i.e., = 0.6, = 0.6, = 25%, and = 25%), and solitary wave characteristics are documented. Next, for all these individual 2,966 bursts, through visual inspection, we identified the presence or absence of solitary waves and noted the total number of solitary waves for each bursts. This analysis is summarized in the Appendix Table A1. Figure 6 represents the four different burst signals from panel (A)-(D) observed on 1 January 2021. Panels (A) and (B) represent good examples of burst illustrating a series of solitary waves. Whereas panels (C) and (D) of Figure 6 represent burst examples with no solitary waves. It may be noted that in panel (A), there is one solitary wave, which is marked with a dashed rectangle. This solitary wave was selected in visual inspection, but SWIT discarded it. This is the case of a false negative. This solitary wave was discarded by SWIT due to the presence of more than one turning point in between and as described in Section 3.2. However, SWIT has identified major solitary wave structures. In Figure 7A, we have plotted the number of solitary waves identified by SWIT (red circle) and through visual inspection (blue asterisk) for bursts grouped in 10 bins. Here, each bin contains 296 burst datasets, except for the last one, which contains 302. The corresponding efficiency is shown in Figure 7B. One can see that for most of the bins, efficiency is above 90%. Overall, a total of 738 solitary waves have been identified by visual inspection, whereas SWIT identifies 698 solitary waves. This clearly indicates that SWIT operates with high efficiency. We defined efficiency as, . The efficiency, can vary between 0–1, where 1 indicates 100% efficiency. For 1 January 2021, the average efficiency is 0.94.

FIGURE 6

FIGURE 7

To justify the choice of parameters , , and the turning points threshold, we considered and values of 0.55, 0.60, and 0.65, and turning points thresholds of 22.5%, 25.0%, and 27.5%. (see Table 1). Efficiency was estimated by comparing solitary waves identified through (i) visual inspection and (ii) SWIT. This analysis was performed for burst events on 1 January 2021. The efficiency was found to be highest when and were set to 0.60, and the turning points threshold to 25%. A confusion matrix corresponding to these optimal values is provided in the Appendix (see Table A2).

Further, to test SWIT, we analyzed the electric field burst datasets for 19 days in February 2015. A total of 50,835 bursts were recorded during February 2015. SWIT identified a total of 3,682 solitary waves. The mean amplitude and width of these waves are approximately 3.2 mV/m and 0.328 ms, respectively (see Table A3). The amplitude as a function of width is shown in Figure 7C for these identified solitary waves. It may be noted that, in general, the amplitude varies between mV/m, and the durations vary between ms for the considered datasets. The number of solitary waves identified in a given signal through visual inspection can vary with individual users. This variability arises because many solitary waves observed may deviate from their ideal form (refer to Figure 1). While building a SWIT, we have defined a series of criteria for identifying solitary waves. If any criterion is nearly satisfied but not fully met, the program rejects the waveform to identify it as a solitary wave. For instance, we impose a condition requiring up to 40% deviation between and . If the symmetry is 59.9%, the program will reject the solitary wave waveform. However, a user may not visually recognize the difference between 60% and 59.9% deviation. This scenario can slightly affect the detection of solitary waves. Nonetheless, these criteria are essential to minimize the identification of false positives. Sometimes, a solitary wave is embedded within random oscillations. While such a solitary wave may not be considered significant during visual inspection, SWIT can identify it if all the defined conditions are met.

6 Summary and conclusion

The paper presents a new automatic tool to identify bipolar solitary waves from high-resolution electric field measurements by a spacecraft. It is named as SWIT and is well tested for the medium-frequency (100 Hz–32 kHz) calibrated burst mode electric field data recorded by MAVEN spacecraft. We began by discussing features of the ideal form of the solitary waves and then compared them with the observed electric field bipolar pulse. Accordingly, the criteria to identify solitary waves in the electric field data were built. The series of implemented criteria and their significance in the logical development of the computer program are elaborated. Fundamentally, SWIT is based on the cumulative integration of filtered electric field signals to identify the locations of the bipolar structures present in the data. In the output, SWIT provide and of solitary waves, with their time of occurrence and , type (i.e., type-1 or type-2) and width (in milliseconds). Additionally, the Figure visible in GUI can be exported in , , , , , and formats. SWIT is optimized for scalability with medium-frequency burst mode electric field data. The burst durations are in multiples of 62.5 ms and could go up to 437.5 ms. The efficiency of SWIT is tested with the medium frequency electric field data recorded by MAVEN, which is found to be above 90%. While SWIT effectively identifies bipolar solitary waves, their interpretation as phase space holes or acoustic solitons is beyond the scope of the present work. Additionally, it should be noted that MAVEN measures only a single component of the electric field, which can limit the detection of solitary waves depending on the angle between the wave propagation direction and the orientation of the probes, i.e., the y-axis of the spacecraft coordinate system.

The SWIT GUI is developed using MATLAB 2024b as a stand-alone desktop application for Windows. In order to run this application, users need the MATLAB Runtime, which is included in the installer. The instructions for the installation and usage of SWIT can be found in the accompanying ReadMe file. Initially, using “process_burst_events.m” program file for MATLAB, the user can convert electric field raw data into individual “.mat” files that contain the electric field and time information separately for each burst files that occurred on a given day. These individual burst files (time and electric field) serve as input to the SWIT module. The recommended parameters for , , and are 0.6, 0.6, 25% and 25%, respectively. However, the user can change these parameters. When and are increased and/or and are decreased, then the conditions tend towards the ideal solitary wave.

SWIT serves as an important resource for conducting detailed statistical analyses, enabling users to explore the characteristics of solitary waves and their relationships with altitude, local time, and space weather conditions, particularly for the Martian plasma environment. The insights gained from this analysis help in understanding the generation of solitary waves in the plasma environment of unmagnetized planets like Mars. This automatic tool will reduce analysis time and aid in processing large-scale, high-resolution data acquired by spacecraft. SWIT is a versatile package that allows modifications in its code to make it applicable for high-resolution electric field datasets from other spacecraft, enabling comparative studies of solitary waves across different planetary plasma environments. In a nutshell, SWIT will be useful to explore the dynamics of bipolar solitary wave structures with good accuracy and efficiency in planetary plasma environments.

References

• 1

  AnderssonL. (2024). MAVEN LPW medium frequency burst mode calibrated electric-field data collection. 10.17189/8DBB-Y985

  • CrossRef
  • Google Scholar
  • View reference in article

• 2

  AnderssonL.ErgunR. E. (2012). “The search for double layers in space plasmas,”, 197. Washington, DC: American Geophysical Union, 241–250. 10.1029/2011GM001170

  • CrossRef
  • Google Scholar
  • View reference in article

• 3

  AnderssonL.ErgunR.DeloryG.ErikssonA.WestfallJ.ReedH.et al (2015). The langmuir probe and waves (LPW) instrument for MAVEN. Space Sci. Rev.195, 173–198. 10.1007/s11214-015-0194-3

  • CrossRef
  • Google Scholar
  • View reference in article

• 4

  AravindakshanH.KakadA.KakadB. (2018a). Bernstein-greene-kruskal theory of electron holes in superthermal space plasma. Phys. Plasmas25, 052901. 10.1063/1.5025234

  • CrossRef
  • Google Scholar
  • View reference in article

• 5

  AravindakshanH.KakadA.KakadB. (2018b). Effects of wave potential on electron holes in thermal and superthermal space plasmas. Phys. Plasmas25, 122901. 10.1063/1.5046721

  • CrossRef
  • Google Scholar
  • View reference in article

• 6

  AravindakshanH.YoonP. H.KakadA.KakadB. (2020). Theory of ion holes in space and astrophysical plasmas. Mon. Notices R. Astronomical Soc. Lett.497, L69–L75. 10.1093/mnrasl/slaa114

  • CrossRef
  • Google Scholar
  • View reference in article

• 7

  AravindakshanH.KakadA.KakadB.YoonP. H. (2021). Structural characteristics of ion holes in plasma. Plasma4, 435–449. 10.3390/plasma4030032

  • CrossRef
  • Google Scholar
  • View reference in article

• 8

  AravindakshanH.VaskoI. Y.KakadA.KakadB.WangR. (2023). Theory of ion holes in plasmas with flat-topped electron distributions. Phys. Plasmas30, 022903. 10.1063/5.0086613

  • CrossRef
  • Google Scholar
  • View reference in article

• 9

  AryaN.KakadA. (2025). Lower hybrid and solitary waves in dusk flank region of the earth’s magnetosphere. Adv. Space Res.75, 876–885. 10.1016/j.asr.2024.08.065

  • CrossRef
  • Google Scholar
  • View reference in article

• 10

  CattellC.CrumleyJ.DombeckJ.WygantJ.MozerF. (2002). Polar observations of solitary waves at the Earth’s magnetopause. Geophys. Res. Lett.29, 1065. 10.1029/2001GL014046

  • CrossRef
  • Google Scholar
  • View reference in article

• 11

  DillardC.VaskoI.MozerF.AgapitovO.BonnellJ. (2018). Electron-acoustic solitary waves in the Earth’s inner magnetosphere. Phys. Plasmas25, 022905. 10.1063/1.5007907

  • CrossRef
  • Google Scholar
  • View reference in article

• 12

  EliassonB.ShuklaP. K. (2006). Formation and dynamics of coherent structures involving phase-space vortices in plasmas. Phys. Rep.422, 225–290. 10.1016/j.physrep.2005.10.003

  • CrossRef
  • Google Scholar
  • View reference in article

• 13

  ErgunR.CarlsonC.McFaddenJ.MozerF.MuschiettiL.RothI.et al (1998). Debye-scale plasma structures associated with magnetic-field-aligned electric fields. Phys. Rev. Lett.81, 826–829. 10.1103/PhysRevLett.81.826

  • CrossRef
  • Google Scholar
  • View reference in article

• 14

  ErgunR.AnderssonL.MainD.SuY.-J.NewmanD.GoldmanM.et al (2004). Auroral particle acceleration by strong double layers: the upward current region. J. Geophys. Res. Space Phys.109, A12220. 10.1029/2004JA010545

  • CrossRef
  • Google Scholar
  • View reference in article

• 15

  ErgunR.AnderssonL.TaoJ.AngelopoulosV.BonnellJ.McFaddenJ.et al (2009). Observations of double layers in Earth’s plasma sheet. Phys. Rev. Lett.102, 155002. 10.1103/PhysRevLett.102.155002

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 16

  GrahamD. B.KhotyaintsevY. V.VaivadsA.AndréM. (2015). Electrostatic solitary waves with distinct speeds associated with asymmetric reconnection. Geophys. Res. Lett.42, 215–224. 10.1002/2014GL062538

  • CrossRef
  • Google Scholar
  • View reference in article

• 17

  GrahamD. B.KhotyaintsevY. V.VaivadsA.AndreM. (2016). Electrostatic solitary waves and electrostatic waves at the magnetopause. J. Geophys. Res. Space Phys.121, 3069–3092. 10.1002/2015JA021527

  • CrossRef
  • Google Scholar
  • View reference in article

• 18

  HanselP. J.WilderF.MalaspinaD. M.ErgunR. E.AhmadiN.HolmesJ. C.et al (2021). Mapping MMS observations of solitary waves in Earth’s magnetic field. J. Geophys. Res. Space Phys.126, e2021JA029389. 10.1029/2021JA029389

  • CrossRef
  • Google Scholar
  • View reference in article

• 19

  HobaraY.WalkerS.BalikhinM.PokhotelovO.GedalinM.KrasnoselskikhV.et al (2008). Cluster observations of electrostatic solitary waves near the earth’s bow shock. J. Geophys. Res. Space Phys.113, A05211. 10.1029/2007JA012789

  • CrossRef
  • Google Scholar
  • View reference in article

• 20

  HolmesJ.ErgunR.NewmanD.WilderF.SturnerA.GoodrichK.et al (2018). Negative potential solitary structures in the magnetosheath with large parallel width. J. Geophys. Res. Space Phys.123, 132–145. 10.1002/2017JA024890

  • CrossRef
  • Google Scholar
  • View reference in article

• 21

  KakadA.KakadB. (2019). Generation of series of electron Acoustic solitary wave pulses in plasma. Phys. Plasmas26, 102105. 10.1063/1.5113743

  • CrossRef
  • Google Scholar
  • View reference in article

• 22

  KakadA.SinghS.ReddyR.LakhinaG.TagareS.VerheestF. (2007). Generation mechanism for electron acoustic solitary waves. Phys. plasmas14, 052305. 10.1063/1.2732176

  • CrossRef
  • Google Scholar
  • View reference in article

• 23

  KakadA.SinghS.ReddyR.LakhinaG.TagareS. (2009). Electron acoustic solitary waves in the Earth’s magnetotail region. Adv. Space Res.43, 1945–1949. 10.1016/j.asr.2009.03.005

  • CrossRef
  • Google Scholar
  • View reference in article

• 24

  KakadA.OmuraY.KakadB. (2013). Experimental evidence of ion acoustic soliton chain formation and validation of nonlinear fluid theory. Phys. Plasmas20, 062103. 10.1063/1.4810794

  • CrossRef
  • Google Scholar
  • View reference in article

• 25

  KakadB.KakadA.OmuraY. (2014). Nonlinear evolution of ion acoustic solitary waves in space plasmas: fluid and particle-in-cell simulations. J. Geophys. Res. Space Phys.119, 5589–5599. 10.1002/2014JA019798

  • CrossRef
  • Google Scholar
  • View reference in article

• 26

  KakadA.KakadB.AnekalluC.LakhinaG.OmuraY.FazakerleyA. (2016). Slow electrostatic solitary waves in Earth’s plasma sheet boundary layer. J. Geophys. Res. Space Phys.121, 4452–4465. 10.1002/2016JA022365

  • CrossRef
  • Google Scholar
  • View reference in article

• 27

  KakadA.KakadB.OmuraY. (2017a). Formation and interaction of multiple coherent phase space structures in plasma. Phys. Plasmas24, 060704. 10.1063/1.4986109

  • CrossRef
  • Google Scholar
  • View reference in article

• 28

  KakadB.KakadA.OmuraY. (2017b). Particle trapping and ponderomotive processes during breaking of ion acoustic waves in plasmas. Phys. Plasmas24, 102122. 10.1063/1.4986030

  • CrossRef
  • Google Scholar
  • View reference in article

• 29

  KakadB.KakadA.AravindakshanH.KourakisI. (2022). Debye-scale solitary structures in the Martian magnetosheath. Astrophysical J.934, 126. 10.3847/1538-4357/ac7b8b

  • CrossRef
  • Google Scholar
  • View reference in article

• 30

  KamaletdinovS.VaskoI.WangR.ArtemyevA.YushkovE.MozerF. (2022). Slow electron holes in the Earth’s bow shock. Phys. Plasmas29, 092303. 10.1063/5.0102289

  • CrossRef
  • Google Scholar
  • View reference in article

• 31

  KojimaH.OmuraY.MatsumotoH.MiyagutiK.MukaiT. (2000). Automatic waveform selection method for electrostatic solitary waves. Earth, planets space52, 495–502. 10.1186/BF03351653

  • CrossRef
  • Google Scholar
  • View reference in article

• 32

  KrasovskyV.MatsumotoH.OmuraY. (1997). Bernstein-greene-kruskal analysis of electrostatic solitary waves observed with geotail. J. Geophys. Res. Space Phys.102, 22131–22139. 10.1029/97JA02033

  • CrossRef
  • Google Scholar
  • View reference in article

• 33

  LakhinaG.KakadA.SinghS.VerheestF. (2008a). Ion-and electron-acoustic solitons in two-electron temperature space plasmas. Phys. Plasmas15, 062903. 10.1063/1.2930469

  • CrossRef
  • Google Scholar
  • View reference in article

• 34

  LakhinaG.SinghS.KakadA.VerheestF.BharuthramR. (2008b). Study of nonlinear ion-and electron-acoustic waves in multi-component space plasmas. Nonlinear Process. Geophys.15, 903–913. 10.5194/npg-15-903-2008

  • CrossRef
  • Google Scholar
  • View reference in article

• 35

  LakhinaG.SinghS.KakadA.GoldsteinM.VinasA.PickettJ. (2009). A mechanism for electrostatic solitary structures in the Earth’s magnetosheath. J. Geophys. Res. Space Phys.114, A09212. 10.1029/2009JA014306

  • CrossRef
  • Google Scholar
  • View reference in article

• 36

  LakhinaG.SinghS.KakadA.PickettJ. (2011a). Generation of electrostatic solitary waves in the plasma sheet boundary layer. J. Geophys. Res. Space Phys.116. 10.1029/2011JA016700

  • CrossRef
  • Google Scholar
  • View reference in article

• 37

  LakhinaG. S.SinghS.KakadA. (2011b). Ion-and electron-acoustic solitons and double layers in multi-component space plasmas. Adv. Space Res.47, 1558–1567. 10.1016/j.asr.2010.12.013

  • CrossRef
  • Google Scholar
  • View reference in article

• 38

  LakhinaG. S.SinghS.RubiaR.DevanandhanS. (2021). Electrostatic solitary structures in space plasmas: Soliton perspective. Plasma4, 681–731. 10.3390/plasma4040035

  • CrossRef
  • Google Scholar
  • View reference in article

• 39

  LotekarA.KakadA.KakadB. (2016). Fluid simulation of dispersive and nondispersive ion acoustic waves in the presence of superthermal electrons. Phys. Plasmas23, 102108. 10.1063/1.4964478

  • CrossRef
  • Google Scholar
  • View reference in article

• 40

  LotekarA.KakadA.KakadB. (2017). Generation of ion acoustic solitary waves through wave breaking in superthermal plasmas. Phys. Plasmas24, 102127. 10.1063/1.4991467

  • CrossRef
  • Google Scholar
  • View reference in article

• 41

  LotekarA.KakadA.KakadB. (2019). Formation of asymmetric electron acoustic double layers in the Earth’s inner magnetosphere. J. Geophys. Res. Space Phys.124, 6896–6905. 10.1029/2018JA026303

  • CrossRef
  • Google Scholar
  • View reference in article

• 42

  MaharajS.BharuthramR.SinghS.LakhinaG. (2015). Existence domains of slow and fast ion-acoustic solitons in two-ion space plasmas. Phys. Plasmas22, 032313. 10.1063/1.4916319

  • CrossRef
  • Google Scholar
  • View reference in article

• 43

  MalaspinaD. M.GoodrichK.LiviR.HalekasJ.McManusM.CurryS.et al (2020). Plasma double layers at the boundary between Venus and the solar wind. Geophys. Res. Lett.47, e2020GL090115. 10.1029/2020GL090115

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 44

  MatsumotoH.KojimaH.MiyatakeT.OmuraY.OkadaM.NaganoI.et al (1994). Electrostatic solitary waves (ESW) in the magnetotail: BEN wave forms observed by GEOTAIL. Geophys. Res. Lett.21, 2915–2918. 10.1029/94gl01284

  • CrossRef
  • Google Scholar
  • View reference in article

• 45

  MozerF.BaleS.BonnellJ.ChastonC.RothI.WygantJ. (2013). Megavolt parallel potentials arising from double-layer streams in the earth’s outer radiation belt. Phys. Rev. Lett.111, 235002. 10.1103/PhysRevLett.111.235002

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 46

  MozerF.AgapitovO.GilesB.VaskoI. (2018). Direct observation of electron distributions inside millisecond duration electron holes. Phys. Rev. Lett.121, 135102. 10.1103/PhysRevLett.121.135102

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 47

  NorgrenC.AndréM.VaivadsA.KhotyaintsevY. V. (2015). Slow electron phase space holes: Magnetotail observations. Geophys. Res. Lett.42, 1654–1661. 10.1002/2015GL063218

  • CrossRef
  • Google Scholar
  • View reference in article

• 48

  OlivierC.MaharajS.BharuthramR. (2015). Ion-acoustic solitons, double layers and supersolitons in a plasma with two ion-and two electron species. Phys. Plasmas22, 082312. 10.1063/1.4928884

  • CrossRef
  • Google Scholar
  • View reference in article

• 49

  OmuraY.MatsumotoH.MiyakeT.KojimaH. (1996). Electron beam instabilities as generation mechanism of electrostatic solitary waves in the magnetotail. J. Geophys. Res. Space Phys.101, 2685–2697. 10.1029/95JA03145

  • CrossRef
  • Google Scholar
  • View reference in article

• 50

  PandeyS.KakadA.KakadB. (2025a). First observational evidence of plasma waves in the Martian magnetosheath jet. Mon. Notices R. Astronomical Soc. Lett.537, L7–L13. 10.1093/mnrasl/slae105

  • CrossRef
  • Google Scholar
  • View reference in article

• 51

  PandeyS.KakadA.KakadB. (2025b). Solitary wave identifying tool (SWIT) for electric field dataset from MAVEN spacecraft. 10.5281/zenodo.15174978

  • CrossRef
  • Google Scholar
  • View reference in article

• 52

  PandeyS.KakadA.KakadB.SinghK.KourakisI. (2025c). Double layers in the Martian magnetosheath. Astrophysical J.981, 44. 10.3847/1538-4357/adad6f

  • CrossRef
  • Google Scholar
  • View reference in article

• 53

  PickettJ.MeniettiJ.GurnettD.TsurutaniB.KintnerP.KlattE.et al (2003). Solitary potential structures observed in the magnetosheath by the cluster spacecraft. Nonlinear Process. Geophys.10, 3–11. 10.5194/npg-10-3-2003

  • CrossRef
  • Google Scholar
  • View reference in article

• 54

  PickettJ.KahlerS.ChenL.-J.HuffR.SantolikO.KhotyaintsevY.et al (2004). Solitary waves observed in the auroral zone: the cluster multi-spacecraft perspective. Nonlinear Process. Geophys.11, 183–196. 10.5194/npg-11-183-2004

  • CrossRef
  • Google Scholar
  • View reference in article

• 55

  PickettJ.ChenL.-J.KahlerS.SantolikO.GoldsteinM.LavraudB.et al (2005). On the generation of solitary waves observed by cluster in the near-Earth magnetosheath. Nonlinear Process. Geophys.12, 181–193. 10.5194/npg-12-181-2005

  • CrossRef
  • Google Scholar
  • View reference in article

• 56

  RubiaR.SinghS.LakhinaG.DevanandhanS.DhanyaM.KamalamT. (2023). Electrostatic solitary waves in the venusian ionosphere pervaded by the solar wind: a theoretical perspective. Astrophysical J.950, 111. 10.3847/1538-4357/acd2d7

  • CrossRef
  • Google Scholar
  • View reference in article

• 57

  ShaikhZ.VaskoI.HutchinsonI.KamaletdinovS.HolmesJ.NewmanD.et al (2024). Slow electron holes in the Earth’s magnetosheath. J. Geophys. Res. Space Phys.129, e2023JA032059. 10.1029/2023JA032059

  • CrossRef
  • Google Scholar
  • View reference in article

• 58

  SinghS.LakhinaG. (2001). Generation of electron-acoustic waves in the magnetosphere. Planet. Space Sci.49, 107–114. 10.1016/S0032-0633(00)00126-4

  • CrossRef
  • Google Scholar
  • View reference in article

• 59

  SinghK.KakadA.KakadB.KourakisI. (2022). Fluid simulation of dust-acoustic solitary waves in the presence of suprathermal particles: application to the magnetosphere of Saturn. Astronomy and Astrophysics666, A37. 10.1051/0004-6361/202244136

  • CrossRef
  • Google Scholar
  • View reference in article

• 60

  SinghK.VargheseS. S.SainiN. S.KourakisI. (2024). Oblique electrostatic solitary and supersolitary waves in earth’s magnetosheath. Astrophysical J.971, 25. 10.3847/1538-4357/ad5c6b

  • CrossRef
  • Google Scholar
  • View reference in article

• 61

  SunJ.VaskoI. Y.BaleS. D.WangR.MozerF. S. (2022). Double layers in the Earth’s bow shock. Geophys. Res. Lett.49, e2022GL101348. 10.1029/2022GL101348

  • CrossRef
  • Google Scholar
  • View reference in article

• 62

  TemerinM.CernyK.LotkoW.MozerF. (1982). Observations of double layers and solitary waves in the auroral plasma. Phys. Rev. Lett.48, 1175–1179. 10.1103/PhysRevLett.48.1175

  • CrossRef
  • Google Scholar
  • View reference in article

• 63

  ThallerS. A.AnderssonL.SchwartzS. J.MazelleC.FowlerC.GoodrichK.et al (2022). Bipolar electric field pulses in the Martian magnetosheath and solar wind; their implication and impact accessed by system scale size. J. Geophys. Res. Space Phys.127, e2022JA030374. 10.1029/2022JA030374

  • Pubmed Abstract
  • CrossRef
  • Google Scholar
  • View reference in article

• 64

  TongY.VaskoI.MozerF.BaleS. D.RothI.ArtemyevA.et al (2018). Simultaneous multispacecraft probing of electron phase space holes. Geophys. Res. Lett.45, 11–513. 10.1029/2018GL079044

  • CrossRef
  • Google Scholar
  • View reference in article

• 65

  UmedaT.OmuraY.MatsumotoH.UsuiH. (2002). Formation of electrostatic solitary waves in space plasmas: particle simulations with open boundary conditions. J. Geophys. Res. Space Phys.107, 1449. 10.1029/2001JA000286

  • CrossRef
  • Google Scholar
  • View reference in article

• 66

  VargheseS. S.SinghK.KourakisI. (2024a). Electrostatic solitary waves in a bi-ion plasma with two suprathermal electron populations–application to Saturn’s magnetosphere. Mon. Notices R. Astronomical Soc.527, 8337–8354. 10.1093/mnras/stad3763

  • CrossRef
  • Google Scholar
  • View reference in article

• 67

  VargheseS. S.SinghK.VerheestF.KourakisI. (2024b). Electrostatic solitary waves in electronegative Martian plasma. Astrophysical J.977, 100. 10.3847/1538-4357/ad8b49

  • CrossRef
  • Google Scholar
  • View reference in article

• 68

  VaskoI.AgapitovO.MozerF.BonnellJ.ArtemyevA.KrasnoselskikhV.et al (2017a). Electron-acoustic solitons and double layers in the inner magnetosphere. Geophys. Res. Lett.44, 4575–4583. 10.1002/2017gl074026

  • CrossRef
  • Google Scholar
  • View reference in article

• 69

  VaskoI.KuzichevI.AgapitovO.MozerF.ArtemyevA.RothI. (2017b). Evolution of electron phase space holes in inhomogeneous plasmas. Phys. Plasmas24, 062311. 10.1063/1.4989717

  • CrossRef
  • Google Scholar
  • View reference in article

• 70

  VaskoI.MozerF.KrasnoselskikhV.ArtemyevA.AgapitovO.BaleS.et al (2018). Solitary waves across supercritical quasi-perpendicular shocks. Geophys. Res. Lett.45, 5809–5817. 10.1029/2018GL077835

  • CrossRef
  • Google Scholar
  • View reference in article

• 71

  VaskoI. Y.WangR.MozerF. S.BaleS. D.ArtemyevA. V. (2020). On the nature and origin of bipolar electrostatic structures in the Earth’s bow shock. Front. Phys.8, 156. 10.3389/fphy.2020.00156

  • CrossRef
  • Google Scholar
  • View reference in article

• 72

  WangR.LuQ.KhotyaintsevY. V.VolwerkM.DuA.NakamuraR.et al (2014). Observation of double layer in the separatrix region during magnetic reconnection. Geophys. Res. Lett.41, 4851–4858. 10.1002/2014GL061157

  • CrossRef
  • Google Scholar
  • View reference in article

• 73

  WangR.VaskoI.ArtemyevA.HolleyL.KamaletdinovS.LotekarA.et al (2022). Multisatellite observations of ion holes in the Earth’s plasma sheet. Geophys. Res. Lett.49, e2022GL097919. 10.1029/2022GL097919

  • CrossRef
  • Google Scholar
  • View reference in article

• 74

  WangC.HuangS.YuanZ.JiangK.ZhangJ.DongY.et al (2023). In situ observation of electron acceleration by a double layer in the bow shock. Astrophysical J.952, 78. 10.3847/1538-4357/acdacb

  • CrossRef
  • Google Scholar
  • View reference in article

• 75

  WilliamsJ.ChenL.-J.KurthW.GurnettD.DoughertyM. (2006). Electrostatic solitary structures observed at Saturn. Geophys. Res. Lett.33, L06103. 10.1029/2005GL024532

  • CrossRef
  • Google Scholar
  • View reference in article