DEGREE PROJECT IN THE FIELD OF TECHNOLOGY VEHICLE ENGINEERING AND THE MAIN FIELD OF STUDY ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019 Investigation of jets in the magnetosheath using Cluster measurements ANNAM TANVEER KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
Investigation of jets in the magnetosheath using Cluster measurements A N N A M T A N V E E R A N N A M T @ K T H. S E 0 7 3 5 5 1 8 4 4 4 02-11- 2018
ABSTRACT With the help of the measurements made by Cluster spacecrafts, an investigation of fast plasma flow called jets in the magnetosheath has been made. The investigation covers a large statistical study of jets with two definitions of jets and therefore two different approaches to detect jets. The study has been divided into three parts. The first part is to automatically detect the magnetosheath. The second part of the study is to detect magnetosheath jets with the different approaches. The final part is to analyse the jets to obtain statistical results. All three parts were made possible by analysing the Cluster data using MatLab. Several scripts were written in MatLab, to identify magnetosheath, to detect magnetosheath jets, visualize the magnetosheath and the magnetosheath jets and to analyse the magnetosheath jets statistically. A short introduction of the relevant space physics in form of a short literature study is done to help the reader understand the investigation. Important results obtained in this study are the properties of jets such as an average duration of about 7-12 s, absolute ion velocity of about 200-322 kms -1, scale size of about 0.38-0.44 R E, particle density of about 22-47 cm -3, kinetic energy density of about 1.7-3.3 njm -3 and absolute value of magnetic field of about 14-92 nt along the positive x-coordinate in a geocentric solar ecliptic coordinate system. Jets are detected at both positive and negative x-coordinates in a geocentric solar ecliptic coordinate system although they are more common on the positive side.
SAMMANFATTNING Med hjälp av mätningar gjorda av Cluster-satelliterna har en undersökning av snabba plasmaflöden, jets, i magnetosheath genomförts. Undersökningen innefattar en statistisk studie av jets som definieras på två olika sätt och därmed används två olika metoder för att detektera jets. Studien har delats in i tre delar. Den första delen går ut på att automatiskt detektera magnetosheath. Den andra delen innefattar detektering av magnetosheath jets genom att nyttja de två olika metoderna. Den tredje delen går ut på att analysera jets för att få statistiska resultat. Samtliga delar har genomförts genom att analysera Cluster data med hjälp av MatLab. Ett flertal skript skrevs i MatLab för att identifiera magnetosheath, detektera magnetosheath jets, visualisera magnetosheath samt magnetosheath jets och även för att analysera magnetosheath jets statistiskt. För att hjälpa läsaren få en uppfattning om studiens omfattning inleds studien med en kort introduktion av berörande rymdfysik. De viktiga resultaten som erhölls under studiens gång är egenskaperna för jets som till exempel en ungefärlig varaktighet på 7-12 s, absolut jon-hastighet på ungefär 200-322 kms -1, skalär storlek på cirka 0.38-0.44 R E, partikel densitet på ungefär 22-47 cm -3, kinetisk energi densitet på cirka 1.7-3.3 njm -3 och absolut värdet för magnetfält på cirka 14-92 nt längs positiva x-koordinaten i ett geocentriskt solekliptiskt koordinatsystem. Förekomsten av jets har en utbredning över både positiva och negativa x-koordinater i ett geocentriskt solekliptiskt koordinatsystem men är dock vanligare på den positiva sidan. - 3 -
TABLE OF CONTENTS Abstract...- 2 - Table of contents...- 4-1. Introduction...- 5-1.1. Plasma and the Solar Wind...- 5-1.2. Plasmoids and Magnetosheath Jets...- 7-1.3. Cluster Mission and Instruments...- 8-1.4. Problem Formulation... - 10-1.5. Nomenclature... - 10-2. Methods & Means... - 11-2.1. Part one: Detecting The Magnetosheath... - 11-2.2. Part two: Detecting Magnetosheath Jets... - 14-2.2.1. Method 1... - 14-2.2.2. Method 2... - 16-2.2.3. Visualization of Jets... - 16-2.3. Part three: Statistical Analysis... - 17-3. Results... - 18-3.1. Part one: Detecting Magnetosheath... - 18-3.2. Part two: Detecting Magnetosheath Jets... - 18-3.3. Part three: Statistical Analysis... - 20-3.3.1. The x-coordinate in the GSE coordinate system... - 20-3.3.2. Duration... - 21-3.3.3. Velocity... - 23-3.3.4. Scale Size... - 27-3.3.5. Particle Density... - 29-3.3.6. Kinetic Energy Density... - 33-3.3.7. Magnetic Field... - 37-3.3.8. Summary of part three... - 41-4. Discussion... - 42-4.1. Part one: Detecting Magnetosheath... - 42-4.2. Part two: Detecting Jets... - 42-4.3. Part three: Statistical Analysis... - 43-5. Conclusions... - 44-6. Future Work... - 45-7. Acknowledgements... - 45-8. References... - 46-9. Script References... - 49-10. Appendix... - 50-10.1. MatLab Script Inputs... - 50 -
1. INTRODUCTION 1.1. PLASMA AND THE SOLAR WIND Plasma is the most common state of matter in space, more than 99% of all matter is in the plasma state. The outermost layer of the Sun, the corona, is a plasma, and merges into the solar wind which carries the plasma across space, see figure 2 [17]. Plasma contains electrons and ions in form of an ionized gas and can therefore conduct electric currents and affect magnetic and electric fields [1]. The atmosphere of the Sun consists of multiple layers such as the photosphere, chromosphere and the corona. The lowest layer in the atmosphere, the photosphere, is the layer from which energy is released in form of sunlight. It s considered to be the surface of the Sun. Space weather originates from the photosphere in form of solar flares and coronal mass ejection (CME). The chromosphere and the corona are layers on top of the photosphere and can only be seen during a full solar eclipse since the light released from the photosphere is brighter compared to the chromosphere. The corona is the part of the Sun that is composed of gas flow directed towards outer space, i.e. away from the Sun in all directions. The corona is believed to have temperatures up to 2 10 6 K, 300 times the temperature of the photosphere [2]. Solar events such as a CME are associated with solar flares, collisions of accelerated electrons with the photosphere. The loops of the magnetic field created by this event are called coronal loops. CME is the coronal mass ejection from coronal loops. The particles released by a CME can contain matter with a mass up to 10 13 kg and velocities up to 2000 kms 1 which scatters across space [3]. Matter in the upper part of the corona, the layer furthest away from the Sun, break free of the magnetic field lines bound to the gravity of the Sun. This happens in the dark regions called coronal holes, see figure 1 [2]. Some of this matter head towards Earth in form of the solar wind, see figure 1 and 2. The plasma from the solar wind is dense and highly conductive with a weak magnetic field. An electric field is therefore generated by the solar wind, mapping down to the ionosphere of Earth. The magnetic field is frozen into the plasma which causes the solar wind to drag the ionospheric plasma with it, inducing an electric field [17]. Figure 1. Illustration of coronal loops. When the solar wind encounters the magnetic field of Earth, the geomagnetic field, it creates a shock wave. Since the solar wind usually travels at velocities between 300 1000 kms 1, it is supersonic and creates a bow shock which deflects the solar wind along the flanks of the magnetopause, see figure 2. The magnetopause is the boundary layer between the geomagnetic field and the solar wind [4], located at about 11 R E from Earth in a sunward direction and 15 16 R E at the flanks above and below Earth [5]. - 5 -
The distance from the centre of the Earth to the nose of the bow shock is about 14 R E, in the sunward direction, one R E being one Earth radius, i.e. 6371 km [6][7]. The flanks of the bow shock are located about 22 28 R E from Earth [5]. The particles then travel around Earth along the magnetosheath, the part of the magnetic field between the bow shock and the magnetopause, instead of crashing directly into Earth [8]. The solar wind later regains speed along the magnetopause, at the magnetotail, the extension of the magnetosphere directed away from the Sun, reaching out to about 80 220 R E from Earth [4]. Some of the plasma penetrates the magnetopause and gets trapped in the magnetosphere creating the plasma sheet [7], see figure 2. The magnetosphere is the part of space dominated by the geomagnetic field [17], see figure 2. The distance and therefore the shape of the magnetosphere is determined by the solar wind, such is the case for the magnetopause and the bow shock due to the varying dynamic pressure of the solar wind. If a high-pressure solar wind hits Earth, the bow shock will be pushed closer towards Earth and as will the magnetopause and magnetosphere [9]. Figure 2. Illustration of the interaction between the geomagnetic field and the solar wind. Satellites and space craft traveling through space weather can be affected by the surrounding plasma, leading to disturbance or even destruction of electronic equipment due to the conductive property of plasma [10] [11]. The well-known space weather phenomenon called aurora borealis is a result of solar wind particles travelling along magnetic field lines down towards the polar regions and are therefore also called polar lights. The solar wind particles collide with particles in Earth s atmosphere at an altitude of between 80 300 km which creates the aurora. [12] - 6 -
1.2. PLASMOIDS AND MAGNETOSHEATH JETS The overall structure of plasma in the magnetosheath, the part of the geomagnetic field between the bow shock and the magnetopause, associated with the magnetic field is called a plasmoid, i.e. an isolated clear density-enhanced structure [13]. Intermittent fast flows of plasmoids in the magnetosheath are called magnetosheath jets. The relative uniform magnetosheath, sometimes consists of plasmoids and magnetosheath jets. The plasmoids in the magnetosheath are believed to consist of several populations. Plasmoids can be considered as a sub-population of magnetosheath jets depending on the definition of the jets [24]. In this study a magnetosheath jet will be defined in two ways, the first definition of a jet is plasmoids with a kinetic energy density over 3 njm 3. The other definition will be plasmoids with an 100% kinetic energy density increase compared to the background. Plasmoids can appear in different modes. The terminology used in this report will follow the terminology used by [24]. Fast plasmoids are associated with an increase in the flow velocity compared to the surrounding magnetosheath flow velocity [14]. Embedded plasmoids are not associated with an increase in the flow velocity compared to the surrounding magnetosheath flow velocity, i.e. the background magnetosheath flow velocity and the plasmoid flow velocity are equal [14]. Paramagnetic plasmoids are plasmoids for which the absolute value of the magnetic field increases, i.e. positive structures. Paramagnetic plasmoids located in the magnetosheath are located near the magnetopause for Mercury, see figure 3, [15][16]. Diamagnetic plasmoids are plasmoids for which the absolute value of the magnetic field decreases, i.e. negative structures in the magnetic field. Diamagnetic plasmoids appear to exist in the solar wind and the magnetosheath, see figure 3. It may be that solar wind magnetic holes, i.e. embedded diamagnetic plasmoids, from the solar wind which cross the bow shock and enter the magnetosheath are one and the same occurrence and therefore have the same signature. No diamagnetic fast plasmoids are found in the magnetosheath [15][16]. Figure 3. Illustration of what kind of plasmoids appear in the magnetic field for Mercury. The shape, size and number of plasmoids are for illustrative purposes only and does not reflect reality. - 7 -
In summation, magnetosheath jets are defined as jets for which an isolated and clear enhancement of kinetic energy density is detected due to an increase in either velocity, density or both. A cause for magnetosheath jets could be small-scale structuring of the bow shock or a discontinuity in the solar wind, acceleration due to Flux Transfer Events (FTE) or the less likely reason, magnetic slingshot effects [8][9]. Magnetosheath jets could cause local changes in form of, for an example, reconnection rate or even cause a flow of plasma directly into the magnetosphere [16]. 1.3. CLUSTER MISSION AND INSTRUMENTS The European Space Agency (ESA) designed the Cluster mission to enable studies of the solar wind plasma structures in the space environment near Earth in collaboration with Japan, NASA and the Russian Space Agency (RSA). After a launch failure of the first Cluster spacecrafts year 1996, another set of space craft was successfully launched year 2000. Since Cluster orbits Earth which rotates around the Sun, the path of Cluster enables possibilities to study several plasma regions of interest in the space environment near Earth such as the polar regions, solar wind, bow shock area, magnetopause, and the magnetotail [18]. The Cluster mission has four identical cylindrical spacecrafts in a polar orbit with a relative distance of 200 18000 km from each other in a tetrahedral configuration, see table 1 for orbit details. The multi-point measurements enable 3D analysis of plasma properties. Each spacecraft is equipped with 11 instruments with a mass of 72 kg out of the total mass of 1200 kg for one spacecraft. Each spacecraft deploys four wire booms of 50 m in orbit and four smaller experimental and communication antenna booms [18]. For more detailed information about the Cluster mission and its spacecrafts, see reference [18]. Table 1. Table of Cluster mission orbit details [18]. Orbit Polar Apogee 19.6 R E Perigee 4 R E Orbital period 57h Inclination 90 Mission plan 2 years Status Still operating The Cluster mission enables studies of e.g. solar wind plasma structures and FTEs since the various instruments on board provide measurements of, amongst other things, the magnetic field and the electric field with high accuracy. Combining measurements and calculations helps investigation of different properties of plasma, for an example, differential plasma quantities such as current density can be derived with the help of Ampere s law and the magnetic field measurements [18]. Measurements of the electric field can be of importance while investigating the magnetic reconnection process and measurements of the magnetic field makes it possible to investigate nonlinear wave-particle interactions to determine if they could be the source of plasma transport mechanisms. Table 2 summarizes the different instrument onboard each one of the Cluster spacecrafts [18]. - 8 -
Table 2. Table of Cluster mission instruments [18], for more detailed descriptions, see reference [18]. Instrument Acronym Property and usage Electron Drift Instrument EDI Electric field measurements Electric Field and Wave experiment EFW Electric field measurements Active Spacecraft Potential Control ASPOC Control of potential Instruments Fluxgate Magnetometer FGM Magnetic field measurements Research with Adaptative Particle Imaging Detectors RAPID Ion distribution measurements Spatio-Temporal Analysis of Field Fluctuation experiment STAFF Current structure measurements for source identification of plasma waves and turbulence Waves of High frequency and Sounder for WHISPER Emits short pulses to stimulate plasma resonances Probing of Electron density by Relaxation Wide band data WBD Provides electric field waveforms, spectrograms of plasma waves and radio emissions Digital wave processing DWP Coordinates WEC measurements and performs particle correlations Cluster Ion Spectrometry CIS Ion distribution measurements. Plasma Electron and Current Experiment PEACE Electron count measurements The Wave Experiment Consortium (WEC) consists of EFW, STAFF, WHISPER and DWP. The EFW instrument measures the electric field and can also measure density fluctuations. It provides high time resolution density fluctuations measurements in four points. The measurements can be used to study non-linear waves which are believed to accelerate plasma and determine properties such as motion and shape of plasma structures and plasma acceleration. Sensors at the end of the 50 m booms allow differential measurements. The probe-to-probe distance is about 100 m. The sensors are spherical and can be operated in Langmuir mode, collecting electron current to provide measurements of plasma density and electron temperature [18] [19]. The EFW provides with the particle density in this study which is needed to calculate the kinetic energy density. For more detailed information about the EFW, see reference [19]. The CIS instrument is an ionic plasma spectrometer and it measures the distribution of ions with the help of two sensors which provide the full 3D ion distribution of the major species with high time resolution and mass per charge plasma composition. Both sensors use symmetric optics which results in continuous space coverage and the dynamic range capability makes it suitable for solar wind measurements [18] [20]. The CIS instrument provides with the ion velocity in this study. For more detailed information about CIS, see reference [20]. The FGM instrument consists of two magnetometers and provides high sample rates and high time resolution four-point measurements. The FGM calculates the current without making assumptions of current sheet shape nor its orientation. The FGM provides with the measurements of the magnetic field for this study [18][ 21]. For more detailed information about FGM, see reference [21]. - 9 -
1.4. PROBLEM FORMULATION The purpose of this paper is to make a statistical investigation of magnetosheath jets using data from the Cluster satellites. The relevant data for this study is the particle density, ion velocity, magnetic field and the kinetic energy density. The kinetic energy density is derived with the help of the particle density and the ion velocity. The study will be made in three parts. For the first part, ion spectra of the kinetic energy density will be studied to try to determine when the solar wind particles enter the magnetosheath using MatLab. For the second part, detection and visualization of positions of magnetosheath jets within the magnetosheath will be made and lastly a statistical analysis of the jets will be made. Since Cluster consists of almost 18 years of data collection at the point of this 20 weeks study, the aim will be to study at least one year of data for spacecraft 1 (SC1). If time permits, years will be added in the investigation up until year 2010 since SC1 has poor data coverage after that. 1.5. NOMENCLATURE The most used parameters in this study are listed in table 3 below where m p is the proton mass, 1.67 10 27 kg and only used to define the kinetic energy density since the ions are assumed to contain protons solely. Table 3. Table of the most commonly used parameters in this study. Description Denotation Unit Definition Time, duration t s Measured by various instruments Ion velocity V kms -1 Measured by CIS Scale size s R E s = Vt Particle density n e cm -3 Measured by EFW Kinetic energy density W kin njm -3 m p n e V 2 2 10 12 Magnetic field B nt Measured by FGM The formula used for the kinetic energy density is the classic formula for calculations of kinetic energy with a factor of 10 12 to compensate for the units for the particle density and the ion velocity. - 10 -
2. METHODS & MEANS Using the measurements from the instruments CIS, EFW and FGM used for the Cluster satellites which has been operating since the year 2000, the ion velocity, particle density and the magnetic field measurements can be investigated. The kinetic energy density is derived by using the formula in table 3. The analysis of the measurements is made in MatLab. Two scripts were used for the first part of the study. One of them was used to download 10 years of satellite data [Cload] from the Cluster Science Archive (CSA). The second script reads and plots data from the first spacecraft [CplotW]. The first part of the study is to confidently detect the magnetosheath, the second part is to detect magnetosheath jets and the final part of the study is to perform a statistical analysis of the jets properties. All parts are done with the help of MatLab scripts. The used inputs for the scripts are described in Appendix 10.1. Every time interval of the detected part of the magnetosheath is defined as a magnetosheath passage in this study and one day is defined as 00: 00 23: 59 UTC time which means that the passages will be cut-off at midnight. 2.1. PART ONE: DETECTING THE MAGNETOSHEATH The first part is done in two steps. Firstly, a script is written to detect magnetosheath [Cmsh], each successful detection is defined as a magnetosheath passage. The second step is to visualize the positions of the magnetosheath passages with another script [Cmshmap]. The data from the satellite is stored in cdf files. This type of format is compact and compressed and must be converted to other format types to be readable. Since the data to be analysed cover the years 2000-2010, the amount of data to process from all spacecrafts is about 500 GB. The script [CplotW] first reads the cdf files for the position of the satellite, energy measurements, the ion velocity and the magnetic field measurements. It is then possible to generate seven subplots, or panels, including the kinetic energy density, the ion energy spectrum, the magnetic field in different directions, the absolute values of the magnetic field, ion velocities in different directions, the particle density and the positions of the satellite in geocentric solar ecliptic (GSE) coordinates. The plotting function is used to verify magnetosheath passages during test sampling throughout method 1 and method 2. The GSE coordinate system has its x-axis directed towards the Sun and the z-axis perpendicular to the ecliptic plane, see figure 4. Figure 4. Illustration of the GSE coordinates with the blue sphere representing the Earth in an orbit around the yellow sphere representing the Sun. - 11 -
The different regions of the space environment close to the Earth can be seen in the energy spectrum in panel b in figure 5. The data for the energy spectrum seen in panel b in figure 5 is retrieved from the CIS instrument in form of a vector containing the energy level channels, the sample times in a vector and a flux matrix with 31 differential energy flux column wise and per time unit row wise. By checking differential energy fluxes in the flux matrix, a number of times, and comparing the values to the plot in panel b in figure 5, magnetosheath passages can be found. The colour bar to the right in panel b indicates differential energy flux and red colour is high energy level whilst blue is low energy level. The magnetosheath has high differential energy flux throughout several channels in the middle of the energy spectrum. To detect a magnetosheath passage, the energy must therefore exceed a certain threshold value throughout several channels. The number of channels was decided by evaluating different energy spectrums for confirmed passages with the help of the script [CplotW]. High energy level leading to a shut Plasma sheet Magnetosheath Solar wind a) b) c) d) e) f) g) Figure 5. An example of a figure generated by the script [CplotW] with illustrations of the energy represented by high energy electrons, plasma sheet, magnetosheath and the solar wind. - 12 -
The white areas in the energy spectrum appear when the CIS instrument is shut off due to high energy electrons penetrating the instrument, for instance readings in the Van Allen Belt. The high energy level readings can be recognized by the red colour which spreads over all 31 energy channels. The plasma sheet has high energy flux in the upper part of the spectrum whilst the solar wind has a narrow band of high energy flux. The ion spectrogram can be used to identify the different regions and is therefore useful for identification of the magnetosheath since it has high values of the energy flux throughout several energy channels, see figure 5. A magnetosheath passage was defined by the script [Cmsh] when the flux was 1 10 6 log kevcm 2 s 1 sr 1 kev 1 for at least 3 channels starting in the middle (channel 15) for the minimum time of a magnetosheath passage, 5 min. The part of the script [CplotW] which reads data is re-used for the script [Cmsh]. To separate the magnetosheath regions from the high energy electron regions, a criterion for low energy channels was set for the flux too to filter out the high energy electron regions, which means that the energy cannot be high throughout the whole spectrum if a magnetosheath passage is to be detected. With both criteria fulfilled, a minimum duration to define a magnetosheath passage was set to 5 minutes after a test sampling of the script [Cmsh] and comparison to plots generated by [CplotW]. The five-minute limit and average flux criteria to define a passage was derived by iterative work in the same manner as before. The trial-and-error based test sampling was performed in rounds of about 30 samples per year of data of random dates within the years 2000-2010 to verify results obtained by the script [Cmsh] when the 10 years data was processed and several times before that. When the obtained results were satisfactory, that is, a detection of passage with at least 95% accuracy, the times for which a passage were saved in UTC and Epoch. UTC time is Coordinated Universal Time whilst Epoch time is seconds elapsed since 1 January 1970, 00: 00. Times, dates, positions for the passages were saved in form of Excel workbooks named after year and month of the passages. One yearly Excel workbook consisting magnetosheath passages overview data such as date, number of passages and total duration of the passages was also created, see figure 6. Figure 6. Part of an Excel workbook file saved by the script [Cmsh] for year 2004 shown as an example. Data quality issues, such as corrupt data, data gaps, not enough data were handled by while, for and if loops in the script so that the script could run for a year at a time. The output for [Cmsh] is two Excel files. The first one gives an overview of magnetosheath passages as described above whilst the second Excel file gives an overview of the positions of the magnetosheath passages per year and month and is used to map the detected magnetosheath them by the script [Cmshmap]. A script was written to read and plot the positions of the magnetosheath in GSE coordinates for an overview of magnetosheath positions around Earth [Cmshmap]. - 13 -
2.2. PART TWO: DETECTING MAGNETOSHEATH JETS The second part is approached by two different methods, the first is by setting an absolute limit to the kinetic energy density, as a jet criterion. The second is by calculating a background kinetic energy density and then setting a limit to the ratio between the actual kinetic energy density and the background energy to a certain value. Initially these values were set to 2 njm 3 for the first method and 2 for the second, meaning an increase of 100% of the kinetic energy density for the second approach. These values were set by evaluating plots generated by the script [CplotW]. The limit for the kinetic energy density was finally set to 3 njm 3 instead of the initial 2 njm 3 after a trial-anderror process since a too low limit allows whole passages to be defined as a jet and a too high limit excludes to many jets, both cases makes it difficult to understand the data. The scripts for both approaches were written in parallel and have the same structure throughout except for the difference in the jet criterion. Earlier studies have defined jets differently, for an example, jets are defined as intervals when the anti-sunward component of the dynamic pressure in the subsolar magnetosheath exceeds half of its upstream solar wind value in one study [22]. The limitations are set by rules such as the x- component of the ion velocity must be negative, the area before and after a jet must be a magnetosheath passage for over one minute [22]. Another study defines jets as dynamic pressure pulse where the ratio between the dynamic pressure and the background dynamic pressure must be over 2 for 20 minutes [13][23]. These studies were done using data from another mission called Time History of Events and Macroscale Interactions during Substorms (THEMIS) [13]. The first study mentioned [22], uses the same limit of a jet that this study does in method 2 whereas the second study [23], uses ratios above 1 for method 2 but has another limitation of 20 minutes duration of background pressure. The various definitions of jets in the studies mentioned are similar to the first constraint in this study mathematically although the other constraints differ or are non-existent. 2.2.1. Method 1 In the example plot in figure 5, the kinetic energy density is shown in panel a. Figure 7 is a clarification of a kinetic energy density plot in panel a showing a magnetosheath jet for both methods. A jet for method 1 is defined as described above, by having a kinetic energy density over 3 njm 3. It should be noted that figure 7 shows a limit of 2 njm 3 for method 1 and ratio 2 for method 2 to make the difference between the methods clearer. Figure 7. An example of a plot of kinetic energy density of a magnetosheath passage showing a magnetosheath jet with the different criterions. The black line represents method 1 whilst the blue line represents method 1. - 14 -
The duration of a jet is defined as the interval between the intersections of the red dashed line and a jet, in other words, the intersection of the black and blue lines at both sides of the maximum energy point. The script [Cjet1] identifies jets using method 1 first reads data from the yearly overview magnetosheath passage Excel files generated by [Cmsh]. If a passage is detected a certain date, the script then reads the cdf files containing Cluster data with the help of the re-used script lines from the script [CplotW] for that certain date and time for the passages. The interesting data in this study is particle density, velocity, magnetic field and position. The kinetic energy density is derived with the help of the particle density data and the ion velocity for each passage. A jet is recorded when the above criterion is fulfilled, see figure 7. Since the different instruments used to measure the data have different sample rates, interpolation is used to bring the data to a common time line. The data for maximum points of each jet in a magnetosheath passage, see figure 7, is saved for the particle density, absolute velocity, absolute magnetic field and all components for the position. The times are given in Epoch and converted to UTC time with the help of the script [Cirftime]. The outputs for the script [Cjet1] are two Excel workbook files. The first file is a yearly overview file containing information about the dates of the passages, number of passages, number of passages containing jets and number of jets retrieved by method 1, see figure 8. Figure 8. Part of an overview Excel workbook file saved by the script [Cjet1] shown as an example. The second Excel file is a detailed monthly file containing information about the point of maximum kinetic energy density such as duration of a jet, time of maximum point, the kinetic energy density of maximum point, particle density at the maximum point, absolute velocity at the maximum point, absolute magnetic field at the maximum point and all components of the position at the maximum point, see figure 9. During the coding process, several test samplings were made to ensure at least 95% accuracy of detection of jets by comparing detected jets data with plots of kinetic energy density. At least 150 test samplings were made during the coding and at least 100 more when the script was complete. The Excel files obtained were later processed by other scripts. See Appendix 10.1 for inputs and further information about the script [Cjet1]. Figure 9. Part of a detailed Excel workbook file saved by the script [Cjet1] shown as an example. - 15 -
2.2.2. Method 2 A jet by the second approach is defined by having an increase of 100% in the kinetic energy density compared to the background kinetic energy density. The illustration for such a jet is presented figure 7, except instead of the kinetic energy density, the ratio between the kinetic energy density and the background kinetic energy density will be analysed. The structure of the script [Cjet2] is very similar to the one in the script [Cjet1] in all ways except the criterion of the jet and the saving process, see chapter 2.2.1 for the details. The limit is set by first calculating the background kinetic energy density by using the MatLab built-in function called movmean which calculates a moving mean for a certain vector, in this case, the kinetic energy density. The mean is calculated for a certain time window at a time for the complete duration of a magnetosheath passage. The upper limit of the time window was chosen by comparing other relevant studies such as those mentioned in references [14][15][16] and set to 10 minutes to enable possible future study. The lower limit of the time window was set by the minimum time for a passage, 5 minutes. The ratio is then derived by simple division between the kinetic energy density and the background kinetic energy density. The ratio limit is set to 2, giving an increase of 100% in the kinetic energy density. Using movmean, the background data for the particle density, absolute velocity and the absolute magnetic field is also obtained. Following the same coding process as for [Cjet1], the outputs for script [Cjet2] are also two Excel files, one yearly overview file and one detailed monthly one although the overview file is the same file as for method 1. The file is just filled in with number of passages containing jets and number of jets retrieved by method 2 to enable a comparison between the methods and avoid excessive amount of Excel files, see figure 8 for the structure of the Excel file. Once again, several test samplings were made to ensure at least 95% accuracy of detection of jets, at least 150 test samplings were made during the coding and 100 more when the script was complete. The years 2001-2010 were processed by the scripts [Cjet1][Cjet2] since no passages were found year 2000, see details about the chosen range in chapter 1.4. The Excel files obtained by method 2 were also later processed by other scripts, see chapter 2.2.3 and 2.3. See Appendix 10.1 for inputs and further information about the script [Cjet2]. 2.2.3. Visualization of Jets The data in the detailed Excel files generated by the scripts [Cjet1] [Cjet2] was plotted with the help of the script [Cjetsmap] to gain an overview over the huge amount of jet data. The script [Cjetsmap] plots the data for all 10 years with each position component of the GSE coordinate system as its respective axis. The approximate position of the bow shock and magnetopause is plotted into the same plot as the overview of the positions visualization of jets with the help of the script [CplotBSMP]. Note that the positions of the bow shock and magnetopause is only approximate since they depend on various factors such as the solar wind pressure as described in chapter 1.1. The script [Cjetsmap] is pretty straight forward, it first reads the overview Excel file created by the scripts [Cjet1][Cjet2] to check if a jet exists and then goes into the detailed Excel file to read the position components and then plots the components for each jet. The script [Cjetsmap] works for both methods described above by chapter 2.2.1 and 2.2.2 the output is one plot. See Appendix 10.1 for inputs and further information about the script [Cjetsmap]. - 16 -
2.3. PART THREE: STATISTICAL ANALYSIS The final part is to make a statistical study of the jets data obtained by the scripts [Cjet1] [Cjet2]. The statistical study is made with the help of the script [Chist]. The script [Chist] follows the same procedure as [Cjetsmap], see chapter 2.2.3, to read data except it reads the data for duration, kinetic energy density, particle density, velocity, magnetic field and x-component of the position and the background data for kinetic energy density, particle density, velocity and magnetic field. The data is saved in form of vectors for all 10 years and sorted and categorised. Since the duration of jets and the ion velocity is saved, the scale length, s has also been calculated and included in the statistical analysis. The mean value of the kinetic energy density, particle density, velocity and magnetic field and respective ratios is then plotted against the x-component of the position, see section 3.3. Histograms are also made with a normalized number on the y-axis for the kinetic energy density, particle density, velocity and magnetic field and respective ratios, see section 3.3. The normalized y-axis is created with the help of a sub-function of MatLabs histogram function called Normalization and works in pair with the sub-function PDF. A PDF is a probability density function. This kind of histogram generated by MatLab allows for an estimation of relative probability of a bin by calculating the area of a bin without knowing the exact number of observations, in this case the number of measurements of each bin. The sum of all bars on the PDF plots is less than or equal to 1. It should be noted that method 1 picked up jet durations above 300 s, which is unreasonable compared to other studies. Test sampling showed that high energy magnetosheath passages could be detected as jets for the whole duration of the passage which lead to jet durations above 300 s up to several hours. These jets were therefore filtered out for the statistical analysis but are still defined as jets for method 1. About 1% of the jets, corresponding to 3676 jets for the years 2001-2010, were filtered out in the script [Chist] before plotting results for method 1. No occurrence of a jet duration above 300 s is found for method 2. In the final step of analysis, some statistical information for the data is saved in two Excel files, one for each method. The outputs for the script [Chist] are 48 figures, 23 for method 1 and 25 for method 2 in addition to the two Excel files. The script works for both methods described above by chapter 2.2.1 and 2.2.2. See Appendix 10.1 for inputs and further information about the script [Chist]. - 17 -
3. RESULTS The results below are structured in the same manner as section 2 and therefore divided into three parts. 3.1. PART ONE: DETECTING MAGNETOSHEATH The visualization of positions of magnetosheath passages is created by the script [Cmshmap] using Excel files generated by the script [Cmsh] can be seen in figure 10. About 13780 magnetosheath passages were detected between the years 2001-2010 with a total duration of about 16040 h, corresponding to 18.3% of the orbit time. Figure 10. Detected positions of magnetosheath passages visualized for year 2002 generated by script [Cmshmap] shown as an example with all distances given in RE in a GSE coordinate system. 3.2. PART TWO: DETECTING MAGNETOSHEATH JETS The number of jets found for the years 2001-2010 varies depending on the method used. The number of jets found with method 1 was 139 565 and 70 460 with method 2, almost half of the amount for the first method. A total of 26% of the total number of magnetosheath passages contain jets with method 1 whilst 44% of the total number of magnetosheath passages contain jets with method 2 which can be seen in the pie charts in figure 11. A possible reason for the findings in figure 11 is that method 1 is not able to find jets in magnetosheath passages with low energy whilst method 2 does not have the same constriction as long as an increase compared to the background value exists. Method 1 Method 2 26% 74% 44% 56% Msh without jets Msh with jets Msh without jets Msh with jets Figure 11. Pie charts showing the portions of magnetosheath passages containing jets with method 1 (left) and method 2 (right). - 18 -
The visualization of magnetosheath jets created by the script [Cjetsmap] using Excel files generated by the scripts [Cjet1] [Cjet2] can be seen in figure 12. Figure 12 shows that a most of the jets tend to be concentrated between and between the bow shock and magnetopause, especially for negative z- coordinates for both methods. Method 1 has detected more jets for extreme y-coordinates whilst method 2 has detected more jets between [0,5] R E for x-axis and [5,10] R E for z-axis. Figure 12. Detected positions of magnetosheath jets within the magnetosheath visualized for years 2001-2010 generated by script [Cjetsmap] for method 1 (left) and method 2 (right) for the projections XY, XZ and YZ. All distances are given in RE in a GSE coordinate system. - 19 -
3.3. PART THREE: STATISTICAL ANALYSIS The following figures in this chapter are generated by the script [Chist] using Excel files created by scripts [Cjet1] [Cjet2]. All figures in this chapter cover the years 2001-2010. All figures with x- component as x-axis have been derived by taking the mean value of for the duration, kinetic energy density, particle density, velocity and magnetic field for certain ranges to get an overview of values along the magnetosheath. 3.3.1. The x-coordinate in the GSE coordinate system Figure 13 shows that the jets detected in this study are usually found between about [-5,10] R E in GSE x-coordinates for both methods. Negative x-coordinates indicates that the distance is anti-solar distance, see figure 4 for clarification. Method 2 seems to indicate two different populations but method 1 does not have a strong indication of two or several populations. Figure 13. Overview of the x-coordinate of magnetosheath jets with normalized PDF on the y-axis using method 1 (upper) and method 2 (lower). Compared to other studies, where the findings of jets with a negative x-coordinate is rare or nonexistent, they are rather common here. As described in section 1.2, plasmoids can be described as a sub-population of magnetosheath jets and plasmoids can appear in four modes. The indication of several populations can be an indication of such modes for method 2. - 20 -
3.3.2. Duration Figure 14 shows that the duration of the jets detected in this study is usually under 50 s for both methods, the most common values are under 20 s since one bar represent 10 seconds with a relative probability of 72% for method 1 and 82% for method 2. Figure 14. Duration of jets with normalized PDF on the y-axis using method 1 (upper) and method 2 (lower). Compared to other studies, the duration of jets has a reasonable order of magnitude since the most common values are under 20 s whereas durations over 100 s are extremely rare, yielding similar results as other studies even though other studies have analysed data from other spacecrafts [16][22][23]. - 21 -
Figure 15 shows that the duration of the jets detected in this study usually last longer in the part of the magnetosheath in the negative x-component, accordingly to the mean value between certain ranges, especially for method 2 for which there is a greater spread for the jets. The jet duration decreases for both methods along the x-component towards the bow shock area and the Sun. Figure 15. Duration of jets with x-component of the position on the x-axis using method 1 (upper) and method 2 (lower). Since the relative probability of shorter duration of a jet is higher, jets most commonly are short-lived and exist on the positive x-axis and have a mean value of about 14-24 s for method 1 and 7-12 s for method 2 within x GSE of [0,20] R E according to figure 15. - 22 -
3.3.3. Velocity Figure 16 shows that the velocity of the jets detected in this study have double peaks for both methods. The jet velocity is usually between 100-500 kms -1 for method 1 and 0-500 kms -1 for method 2, according to figure 16. Both methods indicate two different populations in the PDF although the distributions of the PDFs are not the same for the different methods. Figure 16. The absolute value of the velocity of jets with normalized PDF on the y-axis using method 1 (upper) and method 2 (lower). As stated above, the indication of several populations can be an indication of different plasmoid modes, the statement is valid for the velocity as well. - 23 -
Figure 17 shows that the velocity of the jets detected in this study is almost evenly distributed along the x-coordinate in the magnetosheath with method 1. Method 2 shows a distribution with lower values at the negative x-coordinate and higher values towards a Sunward direction. Figure 17. The absolute value of the velocity of jets with x-component of the position on the x-axis using method 1 (upper) and method 2 (lower). Since jets most commonly exist on the positive x-axis, jets are assumed to have a mean velocity of about 299-346 kms -1 for method 1 and 200-322 kms -1 for method 2 within x GSE of [0,20] R E according to figure 17, although since two populations are indicated in figure 17, these mean values of the velocity are not too reliable although compared to other studies, the order of magnitude of the mean velocity is reasonable [22]. - 24 -
Figure 18 shows that the ratio between the velocity and the background velocity of the jets detected in this study has a distribution that resembles a Poisson distribution for both methods. The ratio is usually between 1-1.5 for method 1 which means an increase of 0-50% whereas the ratio for method 2 is usually between 1-2 which means an increase of 0-100%. Figure 18. The absolute value of the velocity ratio of jets with normalized PDF on the y-axis using method 1 (upper) and method 2 (lower). Compared to other studies, the order of magnitude of velocity increase in jets is reasonable [22] although method 1 displays a lower velocity increase compared to method 2 as stated above. - 25 -
Figure 19 shows that the ratio between the velocity and the background velocity of the jets detected in this study is almost evenly distributed along the magnetosheath with method 1 with no clear variation. Method 2 shows a distribution with higher ratios for extreme negative x-coordinates an even distribution for the rest of the magnetosheath. Figure 19. The absolute value of the velocity ratio of jets with x-component of the position on the x-axis using method 1 (upper) and method 2 (lower). Since jets most commonly exist on the positive x-axis, jets are assumed to have a mean velocity increase of about 1.07-1.17 for method 1 and 1.35-1.42 for method 2 within x GSE of [0,20] R E according to figure 19. In other words, the mean velocity increase of jets is 7-17% for method 1 and 35-42% for method 2. - 26 -
3.3.4. Scale Size Figure 20 shows that the scale size of the jets detected in this study is exponentially distributed for both methods. The scale size is usually between 0-1.5 R E for method 1 and 0-1 R E for method 2. Figure 20. The scale size of jets with normalized PDF on the y-axis using method 1 (upper) and method 2 (lower). Compared to other studies, the scale size of jets has a reasonable order of magnitude [13][15][22]. Both methods have the most common values under 1.5 R E. - 27 -
Figure 21 shows that the scale size of the jets detected in this study has high values towards extreme negative x-coordinates and decreases towards the Sunward direction for method 1 whereas method 2 has low values for extreme negative x-coordinates but no clear variation along rest of the x- coordinate. Figure 21. The scale size of jets with x-component of the position on the x-axis using method 1 (upper) and method 2 (lower). Since jets most commonly exist on the positive x-axis, jets are assumed to have a mean scale size of about 0.73-1.13 R E for method 1 and 0.38-0.44 R E for method 2 within x GSE of [0,20] R E according to figure 21 and still in a reasonable order of magnitude compared to other studies [22]. - 28 -
3.3.5. Particle Density Figure 22 shows that the particle density of the jets detected in this study has a distribution that has several peaks and distributions within one plot for both methods. The particle density is usually under 150 cm -3 for method 1 and under 100 cm -3 for method 1 according to figure 22. Figure 22. The particle density of jets with normalized PDF on the y-axis using method 1 (upper) and method 2 (lower). Compared to other studies, the particle density is within reasonable limits, especially method 2 [13][14][22]. Once again, the different modes of plasmoids is indicated for the particle density as well. - 29 -
Figure 23 shows that the particle density of the jets detected in this study has no clear variation along the x-coordinate for either methods although method 2 shows a distribution with lower values along the negative x-coordinate. Figure 23. The particle density of jets with x-component of the position on the x-axis using method 1 (upper) and method 2 (lower). Since jets most commonly exist on the positive x-axis, jets are assumed to have a mean particle density of about 41-69 cm -3 for method 1 and between about 22-47 cm -3 for method 2 within x GSE of [0,20] R E according to figure 23 and are within reasonable limits compared to other studies [22]. - 30 -
Figure 24 shows that the ratio between the particle density and the background particle density of the jets detected in this study has a distribution which resembles a Poisson distribution for both methods. Common values of the ratio are between 1-2 for method 1 and 0.5-2.5 for method 2. Figure 24. The particle density ratio of jets with normalized PDF on the y-axis using method 1 (upper) and method 2 (lower). - 31 -
Figure 25 shows that the ratio between the particle density and the background particle density of the jets detected in this study is almost evenly distributed along the magnetosheath, showing no clear variation for method 1. Method 2 shows a distribution with lower values for extreme negative x-coordinates. There is no clear variation along the x-coordinate for either methods. Figure 25. The particle density ratio of jets with x-component of the position on the x-axis using method 1 (upper) and method 2 (lower). Even though no clear variation is detected, it should be noted that for extreme negative x- coordinates, the particle density ratio is just under 1, with a value of 0.99, giving a slight decrease of the particle density of 1%. Although since jets are most common in the positive x-axis according to this and other studies, the mean value of the particle density will be assumed to be between 1.1-1.6 for method 1 and 1.4-1.6 for method 2 within x GSE of [0,20] R E according to figure 25. - 32 -
3.3.6. Kinetic Energy Density Figure 26 shows that the kinetic energy density of the jets detected in this study is usually between 3-5 njm -3 for method 1 whilst 0-5 njm -3 for method 2. The lower limit of 3 njm -3 for method 1 is set by the criteria for a jet for method 1 and therefore creates the cut-off value on the lower limit. One bar in figure 26 represents 1 njm -3. Figure 26. The kinetic energy density of jets with normalized PDF on the y-axis using method 1 (upper) and method 2 (lower). - 33 -
Figure 27 shows that the kinetic energy density of the jets detected in this study is almost evenly distributed along the x-coordinate for method 1 whilst method 2 shows a distribution with lower values closer to extreme values. There is no clear variation along the x-coordinate for either methods. Figure 27. The kinetic energy density of jets with x-component of the position on the x-axis using method 1 (upper) and method 2 (lower). Since jets most commonly exist on the positive x-axis, jets have a mean kinetic energy density of about 3.6-4 njm -3 for method 1 and 1.7-3.3 njm -3 for method 2 within x GSE of [0,20] R E according to figure 27. - 34 -
Figure 28 shows that the ratio between kinetic energy density and background kinetic energy density of the jets detected in this study is usually between 0.5-2.5 for method 1 and 2-3 for method 2. The lower limit of 2 for method 2 is set by the criteria for a jet for method 2 and therefore creates the cut-off value on the lower limit. One bar in figure 28 represents a half step in the ratio, an increase of 50%. Figure 28. The kinetic energy density ratio of jets with normalized PDF on the y-axis using method 1 (upper) and method 2 (lower). - 35 -
Figure 29 shows that the ratio between the kinetic energy density and the background kinetic energy density has higher values along the x-coordinate in a Sun-ward direction for method 1 but no clear variation along the rest of the magnetosheath. For method 2, the ratio has no clear variation along the x-coordinate. Figure 29. The kinetic energy density ratio of jets with x-component of the position on the x-axis using method 1 (upper) and method 2 (lower). Since jets most commonly exist on the positive x-axis, the mean values of the kinetic energy density ratio are assumed to be between about 1.2-1.8 for method 1 and 2.6-2.9 for method 2 within x GSE of [0,20] R E according to figure 29. - 36 -
3.3.7. Magnetic Field Figure 30 shows that the magnetic field of the jets detected in this study has a distribution that resembles a Poisson distribution for both methods. The magnetic field is usually between 0-50 nt for method 1 and 0-60 nt for method 2, according to figure 30. Figure 30. The absolute value of the magnetic field of jets with normalized PDF on the y-axis using method 1 (upper) and method 2 (lower). Compared to other studies, the values for the absolute magnetic field are reasonable, even the peaks of the distributions have similar values, between 10-20 nt [22]. - 37 -
Figure 31 shows that the magnetic field of the jets detected in this study is higher for extreme negative x-coordinates but shows no clear variation along the magnetosheath for method 1. Method 2 shows a distribution with lower values apart from the interval of 0-5 R E for the x-coordinate. Figure 31. The absolute value of the magnetic field of jets with x-component of the position on the x-axis using method 1 (upper) and method 2 (lower). Since jets most commonly exist on the positive x-axis, jets are assumed to have mean values of the absolute magnetic field between about 12-19 nt for method 1 and 14-92 nt for method 2 within x GSE of [0,20] R E according to figure 31. - 38 -
Figure 32 shows that the ratio between the absolute magnetic field and the absolute background magnetic field of the jets detected in this study has a distribution that resembles a normal distribution for both methods. The ratio is usually between 0.5-1.5 for both methods. Figure 32. The absolute value of the magnetic field ratio of jets with normalized PDF on the y-axis using method 1 (upper) and method 2 (lower). Note that a ratio under 1 gives a decrease of the magnetic field compared to the background magnetic field. - 39 -
Figure 33 shows that the ratio between the absolute magnetic field and the absolute background magnetic field of the jets detected in this study is higher towards along the x-coordinate in a Sunward direction for method 1. Method 2 shows a distribution with a slight increase along the positive x-coordinate. Figure 33. The absolute value of the magnetic field ratio of jets with x-component of the position on the x-axis using method 1 (upper) and method 2 (lower). Since jets most commonly exist on the positive x-axis, jets are assumed to have mean values of the magnetic field ratio between about 1-1.15 for method 1 and 0.98-1.13 for method 2 within x GSE of [0,20] R E according to figure 33. - 40 -