Investigation of jets in the magnetosheath using Cluster measurements

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

A

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

S

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 RE, 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}

T

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 -

1. I

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 ∙ 106 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 1013 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.

The distance from the centre of the Earth to the “nose” of the bow shock is about 14 RE, in the sunward direction, one RE being one Earth radius, i.e. 6371 km [6][7]. The flanks of the bow shock are located about 22 − 28 RE 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 RE 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].

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

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 RE

Perigee 4 RE

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

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

Instruments

ASPOC Control of potential

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

Probing of Electron density by Relaxation

WHISPER Emits short pulses to stimulate plasma resonances 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].

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 mp 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 RE 𝑠 = 𝑉𝑡

Particle density ne cm-3 Measured by EFW

Kinetic energy density Wkin nJm-3 𝑚𝑝𝑛𝑒𝑉

2

2 ∙ 10 12

Magnetic field B nT Measured by FGM

2.

M

&

M

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

Magnetosheath

Solar wind

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].

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.

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 ∙ 106 _{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-usedfor 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].

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-and-errorprocess 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

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].

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 magnetopauseis 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].

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, 23for method 1 and 25 for method 2in 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].

74% 26%

Method 1

Msh without jets Msh with jets

56% 44%

Method 2

Msh without jets Msh with jets

3.

R

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.

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-z-coordinates whilst method 2 has detected more jets between [0,5] RE for x-axis and [5,10] RE for z-axis.

Figure 12. Detected positions of magnetosheath jets within the magnetosheath visualized for years 2001-2010

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 13shows that the jets detected in this study are usually found between about [-5,10] RE 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).

3.3.2. Duration

Figure 14shows 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).

Figure 15shows 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).

3.3.3. Velocity

Figure 16shows 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).

Figure 17shows 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] RE according

Figure 18shows 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).

Figure 19shows 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 xGSE of [0,20] RE

3.3.4. Scale Size

Figure 20shows 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 RE for method 1 and 0-1 RE 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).

Figure 21shows 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 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 RE for method 1 and 0.38-0.44 RE for method 2 within xGSE of [0,20] RE according to

3.3.5. Particle Density

Figure 22shows 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).

Figure 23shows 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

Figure 24shows 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

Figure 25shows 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

3.3.6. Kinetic Energy Density

Figure 26shows 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

‘

Figure 27shows 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] RE according to

Figure 28shows 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

Figure 29shows 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 xGSE of

3.3.7. Magnetic Field

Figure 30shows 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).

Figure 31shows 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 RE 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 xGSE

Figure 32shows 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).

Figure 33shows 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 Sun-ward 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 xGSE of

3.3.8. Summary of part three

The statistical analysis consist of many figures and the results from the figures are summarized and presented in tables 4 and 5 below.

Table 4. Summary of statistical analysis results for the x-coordinate, duration of jets, ion velocity and scale size of jets.

xGSE tdur V s Method 1 [-5,10] RE 72% under 20 s [14-24] s*1 [299,346] kms-1_*1 7-17% increase*12 [0.73,1.13] RE*1 Method 2 [-5,10] RE 82% under 20 s [7-12] s*1 [200-322] kms-1_*1 35-42% increase*12 [0.38, 0.44] RE*1 Comment • Jets found for

negative xGSE for both methods • 2 or more populations detected for method 2 • Similar results as other studies • Short lived closer to the Sun, decrease along xGSE for

both methods

• No clear variation along xGSE for either

methods although higher ratios for extreme negative xGSE

for method 2 • 2 or more

populations detected for both methods

• Similar results as other studies • Decrease along

xGSE for method

1 but no clear variation for method 2

*1 _{Since the majority occurrence of jets exist is on the positive x-axis.}

*2 _{Compared to the background value.}

Table 5. Summary of statistical analysis results for the particle density, kinetic energy density and magnetic field.

ne Wkin B Method 1 [41,69] cm-3_*1 10-60% increase*12 [3.6,4] nJm-3_*1 20-80% increase*12 [12,19] nT*1 under 15% increase*12 Method 2 [22,47] cm-3_*1 40-60% increase*12 [1.7, 3.3] nJm-3_*1 60-90% increase*12 [14,92] nT *1 -2-13%* increase*12 Comment • Similar results as other

studies for method 2 • No clear variation along

xGSE for either methods

• Lower values for extreme negative xGSE,

even slight decrease*2

of ne (1%) for method 2

• 2 or more populations detected

• No clear variation along the xGSE for

either methods • Increase*12 _along

xGSE for method 1

• About 12% of the jets have a ratio under 1 for method 1 (decrease*2₎

• Similar results as other studies • No clear variation along xGSE*1 for

either methods although higher values for [0,5] RE for the xGSE for

method 2

• Up to about 50% decrease*2_,

mostly for negative xGSE for both

methods. • Increase*2 _{along x}

GSE for method

1 and a slight increase*2 _along

positive xGSE for method 2 *1 _{Since the majority occurrence of jets exist is on the positive x-axis.}

4.

D

The section below is structured in the same manner as section 2 and 3 and therefore divided into three parts.

4.1.PART ONE:DETECTING MAGNETOSHEATH

The detection of magnetosheath passages cover about 18% of the orbit time of Cluster spacecraft 1 between the years 2001-2010. The detection of magnetosheath passages is highly dependent on the position of the spacecraft, the function of the instruments and the script written to detect the passages [Cmsh]. The position dependence is obvious, only magnetosheath within the reach of the spacecraft and its instrument can be detected. Since the instruments are tested for accuracy and reliable, there is no doubt about the quality of the data obtained from Cluster satellites.

The script [Cmsh] is dependent on the definitions made for a magnetosheath passage for the duration and energy level, 5 min and a flux of 1 ∙ 106 log keVcm−2_s−1_sr−1_ke𝑉−1 _{for at least 3} channels. Test sampling shows that at least 97% of the passages were confirmed by checking plots created by the script [CplotW]. The remaining 3% in all the sampled cases is a detection for a longer period of time than an actual magnetosheath passage. This is due to the satellite passing a strong solar wind directly after a magnetosheath passage and since the strong solar wind passes the magnetosheath passage criteria, it is also included in the detected passages. This also explains why some of the passages, and therefore jets, found are positioned beyond the bow shock area. Another limitation of the script [Cmsh] is the one-day cut-off at midnight which reduces the number of passages. Redefining the definitions of a magnetosheath passage did not yield sufficient accuracy of at least 95% so this flaw was accepted due to time limitation of the study.

4.2.PART TWO:DETECTING JETS

The detection of magnetosheath jets depends on part 1 and the scripts written to detect jets. As the robustness of the results from part one is discussed above, only the performance of the scripts to detect jets will be discussed here.

The scripts to detect jets depends on the definitions of jets for both methods. The biggest difference is the jet limitations set by method 1 and 2 for the kinetic energy density, being a limit of 3 nJm-3 _for

method 1 and an increase of at least 100% compared to the background kinetic energy density for method 2. Method 1 detects twice the amount of jets compared to method 2 although only 26% of the magnetosheath passages have jets with method 1 whereas method 2 has 76% as shown by figure 11. This means that method 1 has a larger number of jets for the statistical analysis compared to method 2.

Method 1 picked up jet durations above 300 s which turned out to be a false positive detection of a jet since the total duration of a magnetosheath passage was detected as a jet due to it being a high energy passage. High energy magnetosheath passages can be caused by strong solar winds. About 1% of the jets were filtered out due to this, showing that method 2 is more secure since no

occurrence of a jet duration above 300 s is found for method 2.

4.3.PART THREE:STATISTICAL ANALYSIS

The results of the statistical analysis depend on the results obtained in part two, the detection of jets. Method 2 yields more reliable jets data, see section 4.2, and this section will be analysed accordingly.

Similar results have been obtained for this study for the duration of jets, scale size, particle density and magnetic field as other studies [13][22], especially for method 2. For the magnetic field, the peaks of the distributions show very similar results as some of the other studies made within the area of magnetosheath jets [22].

Jets are found at negative xGSE for both methods although most of the jets are found for positive xGSE

and therefore mean values of results below are given for positive xGSE. The jets detected at negative

xGSE are rare or non-existent in other studies, making them incomparable with other studies. Some of

the other studies [16] have found a concentrated amount of jets between the magnetopause and bow shock although this study shows a greater spread of jets. This could be due to the variations in the definitions of a magnetosheath jet and the amount of data processed in this study and because this study is done for the space environment close to the Earth and not Mercury.

Both methods conclude an average duration of a jet being under 20 s with high relative probabilities, 72% for method 1 and 82% for method 2. Jets are short lived, and the duration decreases along xGSE.

For positive xGSE, the average duration is between 14-24 s for method 1 and 7-12 s for method 2.

Since method 2 is more reliable, the average duration of a jet is assumed to be 7-12 s for positive xGSE.

There is no clear variation of the ion velocity for jets along xGSE for either method although higher

ratios for extreme negative xGSE for method 2 is obtained leading to a higher increase of velocity in

jets for extreme negative xGSE. Since method 2 is more reliable, the average ion velocity of a jet is

assumed to be 200-322 kms-1 _{for positive x}

GSE and common values of the increase of ion velocity

compared to the background ion velocity are between 35-45%.

A decrease along xGSE for the scale size for method 1 is noted but there is no clear variation of the

scale size in xGSE for method 2. Since method 2 is more reliable, the average scale size of a jet is

assumed to be between 0.38-0.44 RE.

There is no clear variation of the particle density for jets along xGSE for either methods although lower

ratios for extreme negative xGSE for method 2 is obtained leading to a lower increase of particle

density compared to the background particle density. There is even a slight decrease of about 1% on an average for method 2 for these extreme negative xGSE. Since method 2 is more reliable, the

average particle density of a jet is assumed to be 22-47 cm-3 _{for positive x}

GSE and common values of

the increase of particle density compared to the background particle density are between 40-60%. There is no clear variation of the kinetic energy density for jets along xGSE for either methods. An

increase of the kinetic energy density compared to the background energy along xGSE is obtained for

method 1 although method 2 shows no variation along xGSE. About 12% of the jets studied have a

kinetic energy density ratio under 1 for method 1 although this is impossible to analyse for method 2 since method 2 evaluates ratios over 2 which excludes decreases of the kinetic energy density. These jets could be surrounded by a high energy magnetosheath and or high energy jets which gives high background values of the kinetic energy density and therefore a ratio under 1. Since method 2 is more reliable, the average kinetic energy density of a jet is assumed to be between 1.7-3.3 nJm-3 _for

positive xGSE and common values of the increase of kinetic energy density compared to the

There is no clear variation of the magnetic field for jets along xGSE for either method although higher

values are obtained for [0,5] RE for xGSE for method 2. An explanation for the high magnetic field

readings could be a magnetosheath passage through high energy areas. A decrease of the absolute magnetic field value compared to the background absolute magnetic field up to about 50% on average is noted for both methods, mostly on the negative xGSE. An increase of the absolute magnetic

field value compared to the background absolute magnetic field along xGSE is noted for both methods.

Since method 2 is more reliable, the average value of the magnetic field of a jet is assumed to be between 14-92 nT for positive xGSE and common values of the increase of the magnetic field

compared to the background magnetic field are between -2-13% on an average. Jets associated with magnetic field increases are described as paramagnetic plasmoids whereas diamagnetic plasmoids are associated with magnetic field decreases, as described in section 1.2.

A population of 2 or more is indicated for xGSE, the ion velocity and the particle density and therefore

the mean values are assumed to be a generalization. These exact mean values may differ a lot for the different populations. The different populations are believed to indicate the different modes of plasmoids described in section 1.2 since fast plasmoids are believed to be associated to an increase in the flow velocity compared to the surrounding magnetosheath flow velocity whereas embedded plasmoids are not.

5.

C

A summary of the results and the discussion for the investigation of magnetosheath jets has been made in bullet points for an easy overview and values are valid for method 2 unless stated otherwise.

• Method 2 yields more reliable jets data and is comparable with other studies.

• Method 2 has similar results as other results regarding order of magnitude for the duration of jets, scale size, particle density and especially the magnetic field.

• Jets are detected on negative xGSE as well as positive xGSE although most of the jets are

detected for positive xGSE.

• The average duration of a jet is under 20 s and the duration decreases along xGSE. The

average duration of a jet is assumed to be 7-12 s for positive xGSE.

• The average ion velocity of a jet is assumed to be 200-322 kms-1 _{for positive x}

GSE. The

increase of ion velocity compared to the background ion velocity is between 35-45%. • The average scale size of a jet is assumed to be between 0.38-0.44 RE.

• The average particle density of a jet is assumed to be 22-47 cm-3 _{for positive x}

GSE. The

increase of particle density compared to the background particle density is between 40-60%. • The average kinetic energy density of a jet is assumed to be between 1.7-3.3 nJm-3 _for

positive xGSE. The increase of kinetic energy density compared to the background kinetic

energy density is between 60-90% on an average.

• The average value of the magnetic field of a jet is assumed to be between 14-92 nT for positive xGSE. An increase of the absolute magnetic field value compared to the background

absolute magnetic field along xGSE is noted and is between -2-13% on an average for positive

xGSE.

• A population of 2 or more is indicated for xGSE, the ion velocity and the particle density and

For negative xGSE, following statements can be made:

• The ion velocity for jets has higher ratios for extreme negative xGSE leading to a higher

increase of velocity in jets for extreme negative xGSE.

• The particle density has lower ratios for extreme negative xGSE leading to a lower increase of

particle density compared to the background particle density and even the occurrence of a decrease of about 1% on an average.

• A decrease of the absolute magnetic field value compared to the background absolute magnetic field up to about 50% on average.

6.

F

W

The script written to detect the magnetosheath passages [Cmsh] has it flaws and even though it is a bit slow, it does the job with the compromises made. To get faster and more reliable results, this script should be improved by for an example filtering out the passages beyond the bow shock area. If the passages containing a strong solar wind could be verified by another spacecraft, the results would also be more reliable.

Method 2 is best suited for future investigations due to reasons mentioned in section 4 although alterations to the definition of a magnetosheath jet could be made. By making similar assumptions as other studies on for an example, the direction of the velocity, the study would be better suited for additional comparisons.

The statistical analysis could be extended by investigating the different populations detected for xGSE,

the ion velocity and the particle density. The PDFs could be further investigated to determine a possible correlation between the different PDFs and modes of plasmoids.

The results of the jets detected for negative x-coordinates should be verified by other studies to increase the reliability of these results and therefore this area is suitable for future study.

The compromises mentioned above such as the ones made for the definition of a magnetosheath jet, the limited statistical analysis and analyse of only one out of four spacecrafts had to be made due to the time limitation of the investigation. The most interesting part for future study in the author’s opinion is the one of another spacecraft which was beyond the scope of this study due to time limitation but would be profitable and advised.

7.

A

This study has been made possibly by the help of Fredik Löfblom in form of proofreading and support throughout the study.

Three scripts [Cmsh][Cjet1] [Cjet2] written by the author use the “IRFU folder” which was created by IRF Uppsala.

8.

R

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[3]. Hundhausen A. 1999. Coronal Mass Ejections. In: Strong KT, Saba JLR, Haisch BM, Schmelz JT editors. The Many Faces of the Sun. Springer, New York, NY.

[Accessed 16 May 2018]. DOI: https://doi.org/10.1007/978-1-4612-1442-7_5

[4]. Margaret G Kivelson, Christopher T Russel. 1995. Introduction to space physics. Cambridge

University Press. Chapter 9, The magnetopause, magnetotail and magnetic reconnection; p.227-287.

[5]. Donald H Fairfield. 1971. Average and unusual locations of the Earth’s magnetopause and bow shock. American Geophysical Union.

[Accessed 16 May 2018]. DOI: https://doi.org/10.1029/JA076i028p06700

[6]. Margaret G Kivelson, Christopher T Russel. 1995. Introduction to space physics. Cambridge University Press. Chapter 5, Collisionless shocks; p.129-163.

[7]. Margaret G Kivelson, Christopher T Russel. 1995. Introduction to space physics. Cambridge University Press. Chapter 10, Magnetospheric configuration; p.288-329.

[8]. Margaret G Kivelson, Christopher T Russel. 1995. Introduction to space physics. Cambridge University Press. Chapter 8, Plasma interactions with unmagnetized bodies; p.203-226.

[9]. Margaret G Kivelson, Christopher T Russel. 1995. Introduction to space physics. Cambridge University Press. Chapter 6, Solar wind interactions with magnetized planets; p.164-182.

[10]. RB Horne, SA Glauert, NP Meredith, D Boscher, V Maget, D Heynderickx, D Pitchford. 2013. Space weather impacts on satellites and forecasting the Earth’s electron radiation belts with SPACECAST. American Geophysical Union.