Instrument Characterization of the THEMIS EFI
Sara Lindgren
December 2011 Supervisors
Christopher M. Cully Swedish Institute of Space Physics (IRF)
Uppsala University, Sweden
John W. Bonnell Space Sciences Laboratory (SSL)
University of California at Berkeley, USA
1 Abstract
In March 2007 five satellites were launched as part of the NASA mission THEMIS. The aim of the mission is to answer the unknown questions regarding the onset of substorms. THEMIS data has also been used within other research fields. Today many scientists aim to investigate wave phenomena, such as whistler waves, wave interactions in the radiation belts and general turbulence in the magnetosphere and the solar wind. These processes occur at intermediate frequencies (a few hundreds of Hertz). Correct and reliable results require good knowledge of the frequency re- sponse, the so called transfer function, for the electric field instrument (EFI).
Post-launch calibrations have given good knowledge of the instrument’s response at high and low frequencies. However, at intermediate frequencies (50-3000 Hz) the transfer function has only been determined via calculations/simulations and not yet obtained from data collected in space. Moreover, the transfer function changes sub- stantially in this range, as the instrument transitions from a resistive low-frequency coupling to a capacitive high-frequency coupling. The transition is known as the RC roll-off. In this thesis, data from different regions and with different electrical set- tings have been analyzed to estimate the EFI sensors’ sheath impedance and transfer function. Data have been collected during July 2009 and March 2011. From the first period, I-V curves where extracted for four different regions (i.e. with different plasma conditions) and their associated sheath impedance calculated. I-V curves are graphical representations of how the voltage differs with the changed bias cur- rent. From the sheath impedance and the measured free-space capacitance the RC roll-off can been directly calculated. An experiment was also conducted in March 2011 where the instrument was run in a special mode designed to measure the rela- tive transfer function with the probes run at different bias setting, yielding different sheath impedances.
The analysis of the I-V curves and relative transfer function show similar results, which clearly differ from the earlier believed values. Values for the sheath impedance are lower (4-6 MΩ) than the expected (30 MΩ) and depend on the usher setting. The usher is an electronic device which should shield the sensor from the photoelectron produced by illumination of the preamplifier. This lower sheath resistance implies higher than expected RC roll-off frequency, a result which is confirmed by the results from the relative transfer function. The roll-off is between 2-3 kHz, compared to the 400-500 Hz assumed prior to this study based on the assumption of a sheath impedance of around 30 MΩ. Popul¨arvetenskaplig sammanfattning
I mars 2007 sk¨otsfem NASA satelliter upp, tillh¨orandeTHEMIS (Time History of Events and Macroscale Interactions during Substorms). De fem satelliter ¨arplacerats i n˚agot olika omloppsbanor kring jorden, vilket g¨oratt de kan ge b˚aderumslig och tidsm¨assig uppl¨osning. THEMIS skall unders¨oka olika fenomen i jordens magnetosf¨ar,d˚aframf¨orallt n˚agotsom kallas geomagnetiska substormar. Resultaten fr˚andenna avhandling kommer dock inte p˚averka substormsforskningen, utan forskning d¨arTHEMIS EFI data anv¨andsf¨or att unders¨oker olika v˚agfenomen, t.ex. s˚akallade Chorus eller Whistlers v˚agor.THEMIS- satelliterna ¨arutrustande med ett flertal vetenskapliga instrument, varav ett skall anv¨andas f¨oratt m¨ataelektiska f¨alt.Instrumentet kallas Electric Field Instrument (EFI) och best˚ar av tv˚aradiella och ett axiellt bompar. I ¨andenav varje bom finns en liten sensor. EFI fungerar likt en voltmeter, och m¨aterpotentialskillnaden parvis mellan tv˚asensorer. De tre bommarna ger forskarna en 3-dimentionel representation av det elektriska f¨altet.
Eftersom satelliterna befinner sig i rymden kommer m¨atningarna ske i plasma, det fj¨arde tillst˚andf¨ormateria (de f¨ormajoriteten mer bekanta ¨arfast, flytande och gas). Plasma best˚arav laddade partiklar - elektroner och joner. Sensorerna kommer att p˚averkas av dessa laddade partiklar, samt av str˚alningenfr˚ansolen (en str¨omav fotoner). Sensorerna blir negativt laddade av de elektroner som tr¨affardem fr˚anplasman, och positivt laddad fr˚anden fotoelektriska effekten. Den fotoelektriska effekten inneb¨aratt fotoelektroner emit- terar fr˚anytan d˚aden belyses med elektromagnetisk str˚alning av tillr¨ackligt h¨ogfrekvens, t.ex. UV str˚alning fr˚ansolen. Detta ger upphov till tre sorters ”str¨ommar”mellan sensor- erna och den omgivande plasman: en elektron-, jon-och fotostr¨om.Kombinationen av dessa str¨ommar,som en funktion av sp¨anning,¨arsensorns s.k. IV-kurva. IV-kurvan beskriver hur sp¨anningoch str¨omberor av varandra, se figur 1. F¨oratt kunna g¨oravetenskapliga m¨atningar¨ardet viktigt att instrumentet anv¨andsinom det linj¨araomr˚adetav IV-kurvan, annars kommer sm˚astr¨omfluktuationergenerera alltf¨orstora f¨or¨andringarav sp¨anningen. Detta ˚astadkoms genom att man drar en str¨omfr˚ansensorn, den s.k. bias-str¨ommen.
Figure 1: IV-kurva fr˚anEFI visas i svart. Samt elektrontr¨ommen(r¨od), jontr¨ommen(gr¨on)och fotostr¨ommen(lila).
1 Som tidigare n¨amnt vill forskare anv¨andaTHEMIS data f¨oratt unders¨oka olika v˚agfenomen i jordens magnetosf¨ar.De olika plasmav˚agornahar dock olika frekvenser, och EFI har inte ett linj¨artsamband mellan in- och utdata ¨over hela frekvensomr˚adet,se figur 2. F¨oratt f¨orst˚avarf¨orbeh¨over vi mer kunskap om den elektroniska kopplingen mellan sensorerna och det omgivande plasmat. Kopplingen kan ses som ett motst˚andoch kondensator parallel- lkopplade. Varf¨or?Vad vi egentligen m¨ater¨arm¨angdenladdade partiklar, d.v.s. en str¨om, fr˚anplasman till sensorn. Men d˚astr¨ommenskall g˚agenom plasman uppst˚arett motst˚and. Vi kan allts˚ase det som att det finns en resistor mellan plasman och sensorn. Vidare vet vi ocks˚aatt tv˚aladdade objekt, med ett visst avst˚andemellan, kommer fungera likt en kondensator. Detta kommer ¨aven ske mellan plasman och sensorn, d¨ar”avst˚andet” avg¨ors av en plasmakarakt¨ar,den s.k. Debye-l¨angd.
Men varf¨orser vi ett frekvensberoende? Klassisk ell¨aras¨ageross att vid l˚agafrekvenser kan kondensatorn antas vara en ¨oppen krets, d.v.s. kopplingen kommer bli helt beroende av motst˚andet.Medan vid h¨ogafrekvenser kommer ist¨alletkondensatorn dominera kretsen. Detta ger EFI en l˚agfrekvent koppling som best¨amsav motst˚andetoch en h¨ogfrekvent kop- pling som best¨amsav kondensatorn. Hur EFI kopplar till plasman som funktion av frekvens beskrivs som instruments frekvensg˚ang.Som tidigare n¨amns¨arfrekvensg˚angenicke-linj¨ar, se figur 2.
Figure 2: Frekvensg˚ang
Experiment och ber¨akningarsom genomf¨ortsinom ramen f¨ordenna avhandling har best¨amt frekvensg˚angenf¨orEFI genom tv˚atillv¨agag˚angss¨att.Under 2009, tv˚a˚arefter uppskjutnin- gen, samlades sp¨anningsdatain d¨arman stegvis f¨or¨andrade hur mycket str¨omman drog fr˚an sensorn, d.v.s. bias-str¨ommen.Str¨ommenf¨or¨andrades,i 16 steg, fr˚an-260 till +10 nA. F¨or varje nytt v¨ardegjordes en m¨atningav potentialskillnaden mellan samtliga sensorer (d.v.s. tv˚aradiella bompar och ett axiellt). V¨ardenaf¨orde erh˚allnastr¨omoch sp¨anningsv¨ardena plottades mot varandra. Detta gav IV-kurvor i likhet med den som visas i figur 1.
F¨oratt ber¨aknavar ¨overg˚angen(f1 p˚akurvan, figur 2) mellan den resistiva och kapaci- tiva kopplingen beh¨ovsv¨ardetf¨ormotst˚andetoch kondensatorn (kom ih˚agden elektriska kopplingen mellan sensorn och plasmat). Denna ¨overg˚angspunktkallas f¨orRC roll-off. Fr˚an IV-kurvor kan motst˚andetber¨aknassom inversen av lutningen av den linj¨aradelen. V¨ardet f¨orkondensatorn kan ber¨aknas med relativt god s¨akerhet teoretiskt, d.v.s. utan behov ex- perimentellt data.
2 I den andra metoden m¨atervi frekvensg˚angenmer direkt genom att anv¨andadata insamlat 2011 d¨arolika stor bias-str¨omdras fr˚ande tv˚aradiella bomparen. V¨ardetf¨orbias-str¨ommen p˚averkar hur stort/liten motst˚andetblir, vilket i sin tur p˚averkar vid vilken frekvens RC roll- off intr¨affar.Tanken var d¨arf¨oratt de tv˚aolika inst¨allningarnaskulle ge olika frekvensg˚angar f¨orde olika bomparen, d¨arroll-off:en sker vid olika frekvenser. Det insamlade datat fr˚an bompar 1/2 plottades ¨over bompar 3/4. Denna funktion kommer att vara linj¨arf¨orutom vid de tv˚afrekvenser d¨arde respektive sensorernas RC roll-off intr¨affar,se figur 3.
Figure 3: Relativ frekvensg˚ang
Resultaten fr˚ande tv˚ametoderna visar b˚adaatt RC roll-off intr¨affarmellan 2-3 kHz f¨or den nominella inst¨allningenf¨orEFI. Detta ¨aren stor skillnad fr˚antidigare antagande d¨ar RC roll-off antogs ligga omkring 400-500 Hz. Resultaten fr˚andenna avhandling kommer d¨arf¨oratt ha en stor inverkan p˚aforskning av v˚agfenomeninom ett intermedi¨artfrekven- somr˚ade,inom vilket m˚angaforskare anv¨ander data insamlat med EFI THEMIS.
3 Contents
1 Introduction 12
1.1 Plasma physics and the solar wind ...... 12
1.2 Earth’s magnetic regions ...... 13
1.3 Aurora and auroral substorms ...... 15
1.4 Wave phenomena ...... 16
2 THEMIS 20
2.1 Objectives ...... 20
2.2 Construction and Instrumentation ...... 22
3 Probe physics 26
3.1 Objects in sunlit plasma ...... 26
3.2 I-V curves ...... 28
4 The experiment 33
4.1 Sheath capacitance and impedance ...... 33
4.2 Transfer function ...... 35
4.3 Sensor Diagnostic tests ...... 37
4.4 Bias experiment ...... 39
4.5 Relative transfer function ...... 40
5 Analysis and coding 41
5.1 I-V curves and sheath impedance ...... 41
5.1.1 Corrections of the current data ...... 41
5.1.2 Corrections of the voltage data ...... 42
4 5.1.3 Obtaining the sheath impedance ...... 43
5.2 Relative transfer function ...... 44
6 Results 46
6.1 I-V curves ...... 46
6.1.1 Effect of the corrections ...... 46
6.1.2 Different regions ...... 48
6.1.3 Summary of I-V curves ...... 53
6.1.4 Sheath impedance, (the linear part) ...... 54
6.1.5 Sheath impedance, (the entire sweep) ...... 64
6.2 Relative transfer functions ...... 66
6.2.1 THEMIS Alpha ...... 67
6.2.2 THEMIS Delta ...... 68
6.2.3 THEMIS Echo ...... 69
7 Discussion 70
7.1 I-V curves ...... 70
7.1.1 Voltage corrections ...... 70
7.1.2 Voltage separation between I-V curves ...... 70
7.1.3 Differences in the maximum photocurrent ...... 71
7.2 Sheath impedance ...... 72
7.2.1 Variations depending on region ...... 72
7.2.2 Variations depending on guard- and usher settings ...... 74
7.2.3 Lower resistance than expected ...... 75
7.3 Transfer functions ...... 76
8 Conclusions 80
9 Appendix 82
9.1 Appendix A - Spikes in the voltage data ...... 82
9.1.1 THEMIS Alpha - Magnetosphere ...... 82
9.1.2 THEMIS Bravo - Solar wind ...... 85
5 9.1.3 THEMIS Charlie - Magnetosheath ...... 87
9.1.4 Conclusions regarding the voltage spikes ...... 87
9.2 Appendix B - Summery plots ...... 89
6 List of Figures
1.1 Earth’s magnetic field ...... 13
1.2 Earth’s magnetic regions ...... 14
2.1 The THEMIS satellite ...... 23
2.2 The booms onboard the THEMIS satellite ...... 24
3.1 Sunlit sphere in vacuum ...... 26
3.2 Conducting sphere with no external sun light ...... 27
3.3 Conducting sphere in sunlit plasma ...... 28
3.4 Current balance for the sphere; theoretical I-V curve ...... 32
4.1 Sketch of the connection between the spacecraft, probe and plasma . 33
4.2 Sketch of the transfer function ...... 37
4.3 Relative transfer function, obtained from data in-orbit ...... 40
6.1 Correction for the spacecraft potential ...... 47
6.2 Correction for the bleed through factor ...... 47
6.3 Correction for the bleed through factor ...... 48
6.4 I-V curve in the Magnetosphere, THEMIS Alpha ...... 49
6.5 I-V curve in the Magnetosphere, THEMIS Alpha ...... 50
6.6 I-V curve in the Magnetosphere, THEMIS Delta ...... 50
6.7 I-V curve in the Magnetosphere, THEMIS Echo ...... 51
6.8 I-V curve in the Solar wind, THEMIS Bravo ...... 51
6.9 I-V curve in the Magnetosheath, THEMIS Charlie ...... 52
6.10 I-V curve in the Plasmasphere, THEMIS Delta ...... 52
7 6.11 I-V curve in the Plasmasphere, THEMIS Echo ...... 53
6.12 Key figure over the bar plots showing the sheath impedance . . . . . 55
6.13 Sheath impedance in the Magnetosphere, THEMIS Alpha ...... 56
6.14 Sheath impedance in the Magnetosphere, THEMIS Alpha ...... 57
6.15 Sheath impedance in the Magnetosphere, THEMIS Delta ...... 58
6.16 Sheath impedance in the Magnetosphere, THEMIS Echo ...... 59
6.17 Sheath impedance in the Solar wind, THEMIS Bravo ...... 60
6.18 Sheath impedance in the Magnetosheath, THEMIS Charlie . . . . . 61
6.19 Sheath impedance in the Plasmasphere, THEMIS Delta ...... 62
6.20 Sheath impedance in the Plasmasphere, THEMIS Echo ...... 63
6.21 Sheath impedance through the entire sweep, Magnetosphere . . . . . 64
6.22 Sheath impedance through the entire sweep, Solar wind ...... 65
6.23 Sheath impedance through the entire sweep, Magnetosheath . . . . . 65
6.24 Sheath impedance through the entire sweep, Plasmasphere ...... 66
6.25 Relative transfer function, THEMIS Alpha ...... 67
6.26 Relative transfer function, THEMIS Delta ...... 68
6.27 Relative transfer function, THEMIS Echo ...... 69
7.1 Relative transfer function, obtained from data in-orbit ...... 77
9.1 Voltage spikes in the Magnetosphere, THEMIS Alpha - boom 1/2 . . 83
9.2 Voltage spikes in the Magnetosphere, THEMIS Alpha - boom 3/4 . . 84
9.3 Voltage spikes in the Magnetosphere, THEMIS Alpha - boom 1/2 . . 84
9.4 Voltage spikes in the Magnetosphere, THEMIS Alpha - boom 3/4 . . 85
9.5 Voltage spikes in the Solar wind, THEMIS Bravo - boom 1/2 . . . . 86
9.6 Voltage spikes in the Solar wind, THEMIS Bravo - boom 3/4 . . . . 86
9.7 Voltage spikes in the Magnetosheath, THEMIS Charlie - boom 3/4 . 87
9.8 Summary plot THEMIS Alpha; 06-12a.m. - Magnetosphere . . . . . 89
9.9 Summary plot THEMIS Alpha; 6-12p.m. - Magnetosphere ...... 90
9.10 Summary plot THEMIS Bravo; 00-06a.m. - Solar wind ...... 91
9.11 Summary plot THEMIS Bravo; 12-06a.m. - Magnetosphere . . . . . 92
8 9.12 Summary plot THEMIS Charlie; 06-12a.m. - Solar wind ...... 93
9.13 Summary plot THEMIS Charlie; 06-12p.m. - Magnetosheath . . . . 94
9.14 Summary plot THEMIS Delta; 00-06a.m. - Magnetosphere . . . . . 95
9.15 Summary plot THEMIS Delta; 06-12a.m. - Plasmasphere ...... 96
9.16 Summary plot THEMIS Delta; 12-06p.m. - Plasmasphere ...... 97
9.17 Summary plot THEMIS Delta; 06-12a.m. - Plasmasphere ...... 98
9.18 Summary plot THEMIS Delta; 12-06p.m. - Plasmasphere ...... 99
9.19 Summary plot THEMIS Delta; 06-12a.m. - Plasmasphere ...... 100
9.20 Summary plot THEMIS Echo; 00-06a.m. - Magnetosphere (part 1) . 101
9.21 Summary plot THEMIS Echo; 06-12a.m. - Magnetosphere (part 2) . 102
9.22 Summary plot THEMIS Echo; 06-12a.m. - Plasmasphere ...... 103
9.23 Summary plot THEMIS Echo; 12-06p.m. - Plasmasphere ...... 104
9.24 Summary plot THEMIS Echo; 06-12p.m. - Plasmasphere ...... 105
9.25 Summary plot THEMIS Echo; 12-06p.m. - Plasmasphere ...... 106
9 List of Tables
1.1 Solar wind properties at Eart’s orbit ...... 13
1.2 Pulsation classes ...... 17
2.1 Typical setting for the sensors, guard and usher on the EFI ...... 25
4.1 SDT-runs THEMIS Alpha ...... 38
4.2 SDT-runs THEMIS Bravo ...... 38
4.3 SDT-runs THEMIS Charlie ...... 38
4.4 SDT-runs THEMIS Delta ...... 38
4.5 SDT-runs THEMIS Echo ...... 39
4.6 Collecting baseline data ...... 39
4.7 Collecting data with changed bias setting ...... 40
6.1 Densities in each region during the SDT sweeps ...... 49
6.2 Differences in knee-points ...... 53
6.3 Voltage separation within, and between boom pair ...... 54
6.4 Sequence of the I-V curves (displacement in voltage) ...... 54
10 Acknowledgements
I want to thank all the researchers, staff and students at the Swedish Institute of Space Physics (Uppsala University, Sweden) and at Space Science Laboratory (University of California at Berkeley, USA) for their support and help in the process of completing this thesis. The biggest thanks to my two supervisors; Chris Cully and John Bonnell for all their help, ideas and encouragement. I especially want to thank Chris for his invaluable support with ideas, programming advices and suggested papers, as well as someone whom I always felt welcome to talk to whenever I have encountered problems or needed someone to discuss possible ideas or solutions that I have encountered during this year. To complete this thesis have been a very interesting and inspiring time and I feel a great honor to have worked at both IRF and SSL. Everything I have learned throughout this experience will be I take with me the rest of my career.
11 Chapter 1
Introduction
1.1 Plasma physics and the solar wind
Matter can be categorized into four groups; solid, liquid, gas and plasma. The fourth state is rather unfamiliar to many people, despite that most of the visible material in the universe is plasma. Plasma is defined as an ionized gas, consisting of charged particles governed by collective behavior through the generated electro- magnetic fields. From fundamental physics we know that charged particles feel a force from the surrounding electric- and magnetic field known as the Lorentz force.
F = q(E + v × B) (1.1)
The object effecting our near-Earth environment the most is our closest star, the sun. The outermost layer of the solar atmosphere is the corona consisting of tenuous plasma, which constantly blows out from the sun into the interplanetary space. This
flow is known as the solar wind. Today the mass flow is approximately 1.6 · 109 kg/s, consisting of mainly hydrogen ions.
The sun has an interplanetary magnetic field (IMF), with field lines moving out from the sun’s surface in a Archimedean spiral due to its rotation. The plasma in
12 the solar wind follows this spiral motion because of the so called frozen-in condition.
This condition comes from that plasma is highly conductive, resulting in that it follows particular magnetic field lines. There are rather big variations in the so- lar wind properties, depending on the ever changing environment of the sun. Some solar wind properties (density, speed and magnetic field) can be seen in the table 1.1.
Table 1.1: Solar wind properties at Eart’s orbit
Mimimum Average Maximum n [cm−3] 0.4 6.5 100 v [km/s] 200 400 900 B [nT] 0.2 6 80
1.2 Earth’s magnetic regions
As mentioned plasma is transported from the sun towards Earth via the solar wind.
Unprotected from this radiation, Earth would be uninhabitable for all living beings.
Fortunately Earth has a powerful intrinsic magnetic field which shields us from of the most harmful radiation. A complete mathematical description of Earth’s magnetic
field is complex, but for most a first approximation is to consider the field as a dipole
field, see figure 1.1.
Figure 1.1: Schematic picture of the dipole field around Earth.
13 The approximation that Earth’s magnetic field is a dipole field does not hold true for all space. At approximately 10RE this approximation breaks down due to the interaction between the solar wind and the magnetic field from the sun. This in- teraction will cause distortion of Earth’s magnetic field lines. Due to the frozen-in condition, mixing between different magnetic regions does not take place under nor- mal conditions giving rise to different plasma regions in Earth’s surrounding. Some of them are shown in figure 1.2.
Figure 1.2: Picture over some of the different region within the near-Earth space environment.
The solar wind travels towards Earth at a supersonic speed, and since Earth and its magnetic field creates an obstacle to this flow, a bow shock is created in the sunward direction. Here the flow is slowed and heated. The region located behind the bow shock is known as the magnetosheath. Here we have much more turbulent plasma conditions and since the speed is reduced the density is higher compared to the solar wind. The force balance between the plasma pressure in the solar wind
14 against the magnetic pressure from Earth’s magnetic field forms a magnetic cavity around Earth, the magnetosphere. The boundary between the magnetosheath and the daytime magnetosphere is known as the magnetopause. Under most conditions the magnetopause is located at a distance of approximately 10RE. However, the position and shape of the magnetopause is strongly dependent on the solar wind properties. On the night side the magnetosphere is elongated into a long tail, the magnetotail. The magnetotail consists of two tail lobes with tenuous plasma and in between the plasma sheet, consisting of relatively hot plasma. It is the magnetic
field lines in the plasma sheet which connect to the auroral zones in the north and south.
The inner part of the magnetosphere is occupied by the plasmasphere, ring cur- rent and radiation belts. The plasmasphere forms a torus of cold and dense plasma, with a temperature of approximately 1eV and densities of >102 cm−3. The plasma originates from the Ionosphere and co-rotates with Earth. The outer border of the plasmasphere is known as the plasmapause. Outside the plasmapause we find the ring current. This is a region with very hot plasma and a westward directed cur- rent. Another important region is the radiation belts. These are also called van
Allen radiation belt (named after their discoverer, James van Allen) and is a torus of energetically charged particles, divided into two distinct belts. The outer belt contains mainly highly energetic electrons and the inner a combination of protons and electrons. [9].
1.3 Aurora and auroral substorms
Auroras are natural light display in the sky, especially common at high latitudes.
In the north they are known as aurora borealis, and in the south aurora australis.
Auroras are caused by the collision between charged particles, originating from the magnetosphere and the solar wind, and atoms in the high altitude atmosphere. The charged particles are directed into the atmosphere by Earth’s magnetic field and
15 accelerated by electric fields generated by the magnetic plasma. The auroral zone forms a oval, typically 10-25◦ from the magnetic poles. However, during geomag- netic storms the zone expands to lower latitudes.
The term auroral substorm was first introduced by Akasofu in 1964 [7] to explain a recurring cycle of auroral activity and magnetic disturbance. As mentioned ear- lier, Earth is shielded from the solar wind by its magnetic field and the frozen-in condition which prevents mixing between the particles in the solar wind and mag- netosphere. However, when the IMF is oriented southward the frozen-in condition breaks down locally, and field lines can marge and reconnect at the magnetopause, known as the growth phase. This gives rise to open magnetic field lines being swept from the dayside into the night side, resulting in a build-up of magnetic energy in the tail lobes. This build-up cause the aurora to move towards the equator. The build-up of energy changes the pressure balance leading to a chain of changes in the near-Earth magnetic- and plasma environment which eventually results in the explosive release of the stored magnetic energy. During the expansion phase the stored energy is released by the reduction of the cross-tail current and reconnection of the field lines in the lobes. There are several signs of the onset of a substorm, but as mentioned before the exact onset mechanism remains unknown. The final part of substorms is the recovery phase, where the activity slows down and the system returns to its initial lower-energy state [2], [7].
1.4 Wave phenomena
There exist a large variety of plasma wave phenomena in the Earth’s magnetosphere.
Like most physical systems, waves may occur if the plasma in space experiences per- turbations. In a general picture, waves can be divided into two categories: ultra-low frequency (ULF) waves which can be described by magnetohydrodynamic (MHD) theory, [6] and higher-frequency which cannot.
16 Plasma can be considered as a conducting fluid. By using simplified forms of the transport equations (conservations of mass, momentum, and energy) and electrody- namic equations (Maxwell’s equations, conservations of electric charge, and gener- alized form of Ohm’s law), the theory of MHD is created [12]. There are several important equations building up the general MHD theory.
∂ρ • The continuity equation:( ∂t + ∇ · ρu = 0) ∂u • Momentum conservation: ρ[ ∂t + u · ∇u] = −∇p + j × B ∂B • Faraday’s law: ∂t = −∇ × E
• Ampere’s law: ∇ × B = µ0j • Ohm’s law: E + u × B = 0
As well as ∇ · B = 0, and that the specific entropy is conserved in a convecting magnetized plasma. MHD waves can be categorized into cold- and warm plasmas.
In cold plasma we assume that the thermal kinetic energy of plasma particles can be ignored, implying that we can neglect the pressure terms in the equations describ- ing MHD theory. In warm plasma, we need to take into consideration the pressure gradient of the momentum equation.
ULF waves, or geomagnetic pulsations, span a frequency range from roughly 1 mHz
- 1 Hz, i.e. frequencies under the ion gyrofrequency, and can be described by MHD theory. Normally there are different pulsations categorized depending on their pe- riod of pulsation, five continuous and two irregular [6].
Table 1.2: Pulsation classes
Pc 1 Pc 2 Pc 3 Pc 4 Pc 5 Pi 1 Pi 2 t [s] 0.2-5 5-10 10-45 45-150 150-600 1-40 40-150 ν [Hz] 0.2-5 0.1-0.2 22-100 7-22 2-7 0.025-1 2-25
17 Waves of interest from THEMIS with slightly higher frequency range, i.e. above ion gyrofrequency and can therefore no be described by MHD theory, known as very-low-frequency (VLF) waves. The VLF waves can further be divided into many subcategories, but regarding in the means of how to give a physical description, we can divide them into waves below electron gyrofrequency and waves with frequencies above. In the region below the electron frequency, roughly 1 Hz - 100 kHz, contains several waves which can be investigated with THEMIS data, such as Whistlers,
Saucers, Chorus emissions, Auroral Hiss and Auroral Kilometric radiation (AKR)
[6], [11].
Chorus emissions are among the most intense plasma waves in the outer magne- tosphere, and are not only of interest in Earth’s magnetosphere. They are also observable in many other planets’ magnetospheres. Chorus emissions are electro- magnetic emissions which propagate as a right-hand polarized whistler mode. They can be distinguished from other types of low frequency whistler-mode emissions by their frequency-time spectral structure with multitudes of discrete elements, rising and falling tones. It is this spectral characteristic which gives the Chorus their name, the rising tones which sound like a chorus of chirping birds. The duration of each rising tone is short, typically between 0.1-1 seconds and Chorus emissions give signals in the frequency range from a couple hundreds of hertz to 5 kHz [11], [8].
Over the years since THEMIS has been in operation, a lot of publications have been made regarding wave phenomena and associated areas, both within the fre- quency region of ULF and VLF waves. Below are some of the publications listed:
• Analysis of Radiation Belt Energetic Electron Phase Space Density Using THEMIS SST Measurements: Cross-satellite Calibration and a Case Study - by Binbin Ni et al., J. Geophys. Res. vol. 116, A03208, 13 pp (2011)
• Observations and Modeling of Forward and Reflected Chorus Waves Captured by THEMIS - by Oleksiy Agapitov et al. Ann. Geophys., 29, 541-550 (2011)
18 • Modulation of Whistler-mode Chorus waves: 1. Role of Compressional Pc4-5 Pulsations, and 2. Role of Density Variations - by Wen Li et al., J. Geophys. Res. (2011) [both in press]
• Observational evidence of the generation mechanism for rising-tone chorus - by C. M. Cully et al., Geophys. Res. Lett. vol. 28, L01106 (2010)
• Identifying the Driver of Pulsating Aurora - by Y. Nishimura et al., Science vol. 330, pp. 81-84 (2010)
• Plasmaspheric trapping of compressional MHD waves - by Kazue Takahashi et al., J. Geophys. Res. vol 115, A12247, 20 pp. (2010)
• Evaluation of Whistler-mode Chorus Intensification on the Nightside During an Injection Event Observed on the THEMIS Spacecraft - by Wen Li et al., (2009)
19 Chapter 2
THEMIS
One of the oldest mysteries in space physics is to fully explore and explain the phenomenon behind auroral substorms. For this purpose a NASA mission, Time
History of Events and Macroscale Interactions during Substorms (THEMIS), was launched on the 17th of March 2007. The THEMIS mission is a set of five NASA satellites, with each satellite carring an identical setup of electric field, magnetic
field and particle instruments [15]. This gives the possibility to place one of them at any given orbit and therefore a more flexible mission. The satellites, one through
five, were named Alpha, Bravo, Charlie, Delta and Echo.
2.1 Objectives
The aim with the THEMIS mission can be divided into several objectives. The main one is to answer some of the fundamental questions regarding substorms: [15].
• Establish when and where substorms start
• Determine how the individual components of the substorms interact
• Determine how the substorms power the aurora
20 • Identify how local current disruption mechanisms couple to the more global
substorm phenomena
The secondary objectives are mainly studies of the radiation belts, including wave phenomena which are important in this region. The investigations of the radia- tion belts are of importance both for scientific purposes, as well as protection of equipment and humans in space. In Earth’s outer radiation belts there is a risk that astronauts and spacecrafts encounter highly energetic electrons, and it is there- fore important to understand and be able to predict variations in the flux of these electrons. During substorms vast amount of energized particles are dumped into the radiation belts. Proposed mechanisms include in-situ energization by VLF and ULF wave activity, steady diffusion and energization of the cold plasma sheet population, and acceleration by the passage of interplanetary shocks. The hope is that with data collected by THEMIS we can distinguish between these mechanisms.
As mentioned the THEMIS mission contains of five identical spacecraft, placed in different orbits. All the orbits are highly elliptical and are chosen such that they will have their apogee line located over the ground-based observation center in
Canada and North America every fourth day. Directly after launching all probes were aligned in the same orbit at 15.4 RE apogee, the so called injection or coast phase. After this the probes have been operated in four scientific phases; dawn phase, tail science phase, radiation belt science phase, dayside science phase [13],
[15]. However, the configuration somewhat changed when probe 2 and 3 (THEMIS
Bravo and Charlie) became part of the ARTEMIS mission. In this mission two of the original THEMIS probes will perform magnetic observations around the Earth-
Moon Lagrangian points L1 and L2 [14].
21 2.2 Construction and Instrumentation
Since the processes aimed to investigate are complex the THEMIS satellites have been equipped with several different types of instruments. The fluxgate magne- tometer (FGM) measures the background magnetic field with the aim to identify and time abrupt reconfigurations in the magnetosphere during substorm onset. The search coil magnetometer’s (SCM) purpose is to measure the magnetic field waves and fluctuations in Earth’s dynamic magnetosphere to find the instability which triggers substorms.
The electrostatic analyzer (ESA) measures the amount of electrons and ions with a certain energy and direction at a given time. The aim is to measure the thermal elec- trons and ions to identify and track the high-speed flows through the magnetotail.
The solid state telescope (SST) measures the super-thermal particle distribution functions with the aim to remotely sense the expansion of the heated plasma sheet during substorm onset [13], [15]. The last instrument is the electric field instrument
(EFI) which is built of six booms, each with an electric field sensor in the end. The aim is to measure the electric field fluctuations and waves in Earth’s magnetosphere associated with substorm onset.
Simply described the EFI is a set of broadband digital voltmeters. The electric
field is measured as the potential differences between the paired sensors at the end of each boom. The signal will therefore be proportional to distance between the sensors.
Vn − Vm = −E · (Xn − Xm) (2.1)
22 where Vn and Vm is the sensor potential at position Xn and Xm and E is the ex- ternal vector electric field. The four radial wire booms are mounted on each side of the spacecraft body, 90 degrees separated. At the end of each boom a radial sensor is placed. The radial sensor consists of a graphite-coated sphere, 8 cm in diameter.
Each sphere is connected to the boom via a 3 meter-long, 0.2-mm thin, stainless steel fine wire. This thin wire is also part of the sensor area measuring the electric
field. Each spacecraft also has two axial booms, one on the top and one on bottom of the spacecraft body. The axial sensor consists of a 0.75 meter-long graphite-coated stacer, with a diameter of 1.6 cm. The radial booms gives x,y components of the electric field and the axial booms provides the third component.
Figure 2.1: A sketch of one of the THEMIS satellite with some of the equipment onboard. Notice that the scale, especially the length of radial boom, is not correct. Figure taken from [5].
23 The radial booms are long for several reasons. As earlier mentioned the charged objects experience a Debye shielding when placed in plasma. To ensure that the spacecraft does not affect the measurements, we want to place the spheres outside the Debye sheath of the spacecraft. Other reasons are that a bigger separation leads to a higher potential difference, which is easier to measure. It also minimizes the influence of the photoelectron cloud around the spacecraft, created by the sunlight removing photoelectron via the photoelectric effect [1]. This potential field should falls off as 1/r, but it tends to extend along the booms out towards the sensors.
Figure 2.2: A sketch of the booms onboard THEMIS. Show a schematic the deployed state of the booms and the placement of guard and usher. Figure taken from [5].
The radial booms onboard the THEMIS satellites are 24.8 m spacebody-to-tip (boom
1/2) and 20.2 m spacebody-to-tip (boom 3/4), while the axial booms (boom 5/6) are 6.93 m tip-to-tip. An important part of the EFI is the so called guard and usher,
figure 2.2. The sunlight removes electrons from the spacecraft and its booms due to
24 the photoelectric effect. Some of these photoelectrons will spiral out along the booms towards the sensors and interfere with the measurements. To try to give protection against this we use these guards. If the guard voltage is set negative compared to the spacecraft potential, most of the photoelectrons will hopefully be reflected back towards the spacecraft or scattered enough to not reach the sensor. Photoelectrons are also emitted from the preamplifier by the photoelectric force, which also could spiral out towards the sphere. For protection towards these we used a so called usher, another set of biased surfaces which instead is held at a positive potential with respect to the sphere. The idea is to attract back the photoelectrons towards the preamplifier. Typical settings for the sensor, guard and usher are shown in table
4.1, values taken from [5].
Table 2.1: Typical setting for the sensors, guard and usher on the EFI
Sensor 180 nA Guard 4 V Usher 4 V
25 Chapter 3
Probe physics
3.1 Objects in sunlit plasma
To measure different properties in space, such as electric fields, plasma temperature or density we use Langmuir probes/sensors mounted onboard a spacecraft. One of the challenges of measurements with probes is to measure the actual plasma po- tential, due to how objects react when placed in sunlit plasma. To describe this phenomena three different cases will be discussed. First, if a conductive sphere is placed in vacuum and exposed to sunlight, i.e. a flow of photons, photoelectrons will be removed from its surface due to the photoelectric effect. This leads to the sphere becoming more and more positively charged. At some point some of the photoelec- trons will be attracted back, see figure 3.1, starting with the least energetic ones.
These two effects within a rather short timeframe reach an equilibrium.
Figure 3.1: Showing a sunlit sphere in vacuum.
26 If we next consider a conducting sphere placed in a plasma, not exposed to an ex- ternal sunlight, the sphere will be hit by both electrons and ions. Since electrons have a lighter mass, and under the assumption that the ion and electron temper- ature are approximately the same, the electrons have higher speed than the ions.
The higher speed leads to that they hit the sphere with a higher frequency and the sphere becomes negatively charged, see figure 3.2. The negative charge will repel some of the electrons, again starting from the ones with the lowest energy/speed.
As in the previous case an equilibrium is reached.
Figure 3.2: Showing a conducting sphere with no external sun light.
In reality, a Langmuir probe in space can be seen as a sunlit conductor in plasma, i.e. a combination between the two above cases. The sunlight will remove pho- toelectrons from the sphere, making the sphere positive which attracts back some electrons, while the electrons in the plasma drives the sphere negative, repelling the electrons. The probe will experience the constant battle between these two effects
[10].
27 Figure 3.3: Showing a conducting sphere in a sunlit plasma.
3.2 I-V curves
In order to make measurements with a probe, we must investigate the current flow between the plasma and the probe. The derivation will be made in steps, but through all steps we assume collisionless and isotropic plasma, with no external magnetic fields. A further assumption is that the surface properties of the sphere is homogenous.
The probes is affected by Debye shielding, an effect which occur to all charged objects placed in plasma. The shielding is effective at a distance on the same scale as the Debye length. The Debye shielding effects give rise to a rather complex the- ory, so we will use two extreme cases. When rp << λD, Orbital Motion Limited (OML) theory can be used. Here the effect from Debye shielding is limited, and the single charges are mainly governed by the probe potential. The other case is rp >> λD, called Sheath Limited (SL). Here the effects of Debye shielding will be important. Since the EFI probes are much smaller than the typically encountered
Debye lengths, from now on we will use the OML-theory [4], [10]. We first look at the electron- and ion current.
28 For V < 0
r kBTe qeVB Ie = −Aneqe · exp(− ) (3.1) 2πme kBTe
r kBTi qiVB Ii = −Aniqi (1 − ) (3.2) 2πmi kBTi
and V > 0
r kBTe qeVB Ie = −Aneqe (1 − ) (3.3) 2πme kBTe
r kBTi qiVB Ii = −Aniqi · exp(− ) (3.4) 2πmi kBTi
... Ie,Ii are the electron and ion current ... A is the probe area
... n is the density
... q is the electron charge
... kB is the Boltzmann constant
... VB is the bias voltage
... Te,Ti are the electron and ion temperatures
... me, mi are the electron and ion masses
29 These formulae are given under the assumption that the plasma does not move with respect to the probe, but for the aim of this thesis the above formulae give a good enough feeling for what the the electron- and ion currents are affected by. However, we cannot exclude the contribution of photoelectrons. Photoelectrons are produced when the sphere is sunlit, giving the photocurrent given as:
For V < 0
Iphoto = I0 (3.5)
and V > 0
Vp −Vp Iphoto = I0 · (1 + ) · exp( ) (3.6) Vph Vph
... Iphoto is the photocurrent [nA]
... I0 is the maximum photocurrent [nA]
... Vp,Vph are the probe and photo potential [V]
The I-V curve are built of contribution of all these three currents; the electron- and ion and photoelectron current. Since they originate from different particles, with different charges, they will react differently depending on the charge of the sphere.
30 Itotal = Ie + Ii + Iphoto (3.7)
If the sphere is negative with respect to the surrounding plasma all created photo- electrons will flow into space. We have saturated the photocurrent. If the probe instead is positive, a small part of the electrons are attracted back. With increas- ing positive voltage, photocurrent is slowly decreasing, see figure 3.4. If the probes potential becomes positive the net photocurrent falls off quickly, since each photo- electron emitted has a low energy. When the probe is negative with respect to the plasma (down to a lower limits) the I-V curve is built up mainly by the electrons.
However, if the probe becomes too negative the plasma electrons cannot reach the spheres’ surface and the electron current is non-existing. As the sphere becomes less and less negative, the most energetic electron can reach its surface and the cur- rent will therefore slowly increase. At positive potentials the total current quickly become dependent only on the plasma electron current. The final current is the ion current, which will have the opposite behavior to the electron current since the only difference is the sign of the charge, see equations 3.1 - 3.6. But since ions have a much slower velocity compared with the electrons (assuming that the ion- and electron temperature are approximately the same), the ion current is significantly smaller and can therefore for the most part be neglected. The only region in which the ion current is important is at very negative probe potentials. The total current, i.e. the IV-curve, will look something similar as in figure 3.4.
Important concepts of the I-V curve are the floating potential and bias setting.
This floating potential is the probe’s potential when no current is drawn from it.
Normally the value is slightly above zero volts. The problem is that for low den- sity regions, like the magnetosphere, solar wind, etc., the I-V curve becomes totally dominated by the photocurrent. Since we now have the floating point place in the
31 part where the I-V curve rounds off in the top, the floating potential varies enor- mously with small fluctuations in the current. This makes it almost impossible to use the instrument for scientific measurement of electric fields. This is resolved by drawing a current from the probe, the so called bias current. With the right set- ting, the floating potential is forced down to the linear part of the I-V curve. There are several benefits with having the operating point at the steep, linear part of the curve. Small current fluctuations will not greatly influence the probe potential, the probe is stably grounded and stray currents and plasma density fluctuations are less probable to affect the measurements. It is therefore important to know the lower
(and upper) limit of the linear part of the I-V curve, since we want to operate the spacecraft at a bias current well within the linear part. The lower point is called the knee-point, and occur when we have saturated the photocurrent [10].
Figure 3.4: Show the typical behavior for the photoelectron current (purple) and the electron (red) and ion current (green) for a biased probe. The black line show the resulting total current.
32 Chapter 4
The experiment
4.1 Sheath capacitance and impedance
Measurements of wave phenomena in the intermediate frequency region requires a well known transfer function. To give a mathematical description of the sphere’s connection to the plasma we can electrically approximate the sphere as being con- nected to the surrounding plasma through a capacitor and resistor, see figure 4.1.
Figure 4.1: Sketch of the connection between the spacecraft, sphere and plasma. Ci is the capacitor after the preamplifier, Cs and Rs are the sheath capacitor and sheath resistor which are placed on the probe side of the preamplifier.
33 The approximation involving the resistor is based on that the electrons with are emitted and attracted back to the sphere form a current. Since the current will travel through the surrounding plasma, a form of resistance occurs. The resistance will in general be non-linear, but we can assumed it to be constant over a reasonable voltage range. The reasoning behind the capacitor is that the sphere is charged, lead- ing to a capacitance between its surface and the surrounding plasma. The strength of the capacitor depends on ”how far away” the plasma is. An estimate for this
”distance” is given by the Debye length. If the ion mobility is negligible, the Debye length can be described as:
s 0kBTe λD = 2 (4.1) neq
... λD is the Debye length
... 0 is the vacuum permittivity
... kB is the Boltzmann constant ... q is the electron charge
... Te is the electron temperatures
... ne is the density of electrons
The value for the capacitor/resistor-connection can be obtained by calculation/ mod- eling. The values are known with rather good precision for the devices after the preamplifier. This thesis aims to give a better understanding of the connection be- tween the sphere and plasma (Cs and Rs). The sheath capacitance can be calculated to a good approximation by calculating the value between the sphere and infinity.
This is a good approximation as long as the Debye length is large enough. Since the Debye length in lower density mediums (magnetosphere, magnetosheath and the
34 solar wind) is of the order 10-100 meter, the Debye length is much larger than the probe size and can be seen as infinity. The sheath impedance can also be estimated through calculations, but these calculations involve bigger uncertainties since they are more untested approximations.
4.2 Transfer function
The transfer function of an electric instrument gives the voltage output relative the input over a certain frequency range (for THEMIS up to 4kHz). To give a mathematical description of the transfer function we use the concept of a voltage divider. As just discussed the connection between the plasma and probe can be seen as a capacitor and resistor in parallel. Known from elementary physics, the gain of a voltage divider is given as:
V Z G = out = | i | (4.2) Vin Zs + Zi
Using the impedance
1 Z = (4.3) C jωC
ZR = R (4.4)
35 equation 4.2 becomes
1 + jωR C G = | s s | (4.5) 1 + jωRs(Cs + Ci)
This can be solved for the two extrema
ω → 0 =⇒ G = 1 (4.6)
C ω → ∞ =⇒ G = s (4.7) Cs + Ci
If the gain is plotted against the frequency, equation 4.5 yields a transfer function with a shape as figure 4.2. Where the transfer function rolls off is given by the sheath impedance and the two capacitance values, shown in equation 4.8, while the difference between f1 and f2 indicates the region in which we have a changing transfer function. But the most important part of the transfer function is the value for the roll-off, f1.
1 f1 = (4.8) 2πRs(Cs + Ci)
1 f2 = (4.9) 2πRs · Cs
36 Figure 4.2: Sketch of the a possible transfer function.
As earlier mentioned the values for the capacitors can calculated with rather good precision, giving a good estimate for Cs/(Cs + Ci). For EFI the previous calculated values are Cs = 14 pF and Ci = 7 pF for the radial booms and Cs = 7 pF and Ci = 6-7 pF for the axial booms [5].
4.3 Sensor Diagnostic tests
During July 2009 a series of sensor diagnostic tests (SDT) were performed onboard the five THEMIS satellites. The test were planned such that data was collected from the magneto- and plasmasphere, magnetosheath, and in the solar wind. Dur- ing most runs the bias current was swept for all boom pairs, but on some occasions only for boom 1/2 (SDT-X). During each sweep the guard- and usher settings were changed, with the aim to see how the sheath resistance depends on those settings.
Five different guard- and usher settings were tested, from -8 to 8 volts with steps of two volts. For each guard setting all five usher settings were used. [5].
37 Table 4.1: SDT-runs THEMIS Alpha
Date Start time Probe pair Region 2009-07-11 09:45:00 SDT-X Magnetosphere 2009-07-11 10:30:00 SDT-Y Magnetosphere 2009-07-11 11:15:00 SDT-Z Magnetosphere 2009-07-11 22:00:00 SDT-X Magnetosphere 2009-07-11 22:45:00 SDT-Y Magnetosphere 2009-07-11 23:30:00 SDT-Z Magnetosphere
Table 4.2: SDT-runs THEMIS Bravo
Date Start time Probe pair Region 2009-07-14 00:00:00 SDT-X Solar wind 2009-07-14 00:45:00 SDT-Y Solar wind 2009-07-14 01:30:00 SDT-Z Solar wind 2009-7-17 04:00:00 SDT-X Magnetosphere
Table 4.3: SDT-runs THEMIS Charlie
Date Start time Probe pair Region 2009-07-14 06:00:00 SDT-X Solar wind 2009-07-14 19:00:00 SDT-X Magnetosheath 2009-07-14 19:45:00 SDT-Y Magnetosheath 2009-07-14 20:30:00 SDT-Z Magnetosheath
Table 4.4: SDT-runs THEMIS Delta
Date Start time Probe pair Region 2009-07-12 04:00:00 SDT-X Magnetosphere 2009-07-12 04:45:00 SDT-Y Magnetosphere 2009-07-12 05:30:00 SDT-Z Magnetosphere 2009-07-13 11:00:00 SDT-X Plasmasphere 2009-07-13 13:00:00 SDT-X Plasmasphere 2009-07-13 13:45:00 SDT-Y Plasmasphere 2009-07-13 14:30:00 SDT-Z Plasmasphere 2009-07-14 11:00:00 SDT-X Plasmasphere 2009-07-14 14:00:00 SDT-X Plasmasphere 2009-07-14 14:45:00 SDT-Y Plasmasphere 2009-07-14 15:30:00 SDT-Z Plasmasphere
38 Table 4.5: SDT-runs THEMIS Echo
Date Start time Probe pair Region 2009-07-12 05:00:00 SDT-X Magnetosphere 2009-07-12 05:45:00 SDT-Y Magnetosphere 2009-07-12 06:30:00 SDT-Z Magnetosphere 2009-07-13 12:00:00 SDT-X Plasmasphere 2009-07-13 14:00:00 SDT-X Plasmasphere 2009-07-13 14:45:00 SDT-Y Plasmasphere 2009-07-13 15:30:00 SDT-Z Plasmasphere 2009-07-14 12:00:00 SDT-X Plasmasphere 2009-07-14 15:00:00 SDT-X Plasmasphere 2009-07-14 15:45:00 SDT-Y Plasmasphere 2009-07-14 16:30:00 SDT-Z Plasmasphere
4.4 Bias experiment
Data were also collected in March 2011. Since THEMIS Bravo and Charlie at that time belongsed to the mission ARTEMIS only data from three satellites could be used for the second part of the thesis project. Data was collected in two steps. In the first all radial booms were set to the same bias settings. These data are used to obtain a baseline. In the second part the bias setting is changed on one of boom pair. The boom pair 3/4 is keep on the original setting (-185 nA), and the boom pair 1/2 changed to -50 nA. The size of the change was determined from the analysis of the previous SDT runs, i.e. a found value which seems to give a change of the sheath impedance of about one order of magnitude.
Table 4.6: Collecting baseline data
Start date End date Probe pair Satellite 2011-03-17 2011-03-28 SDT-X,Y THEMIS Alpha 2011-03-22 2011-03-30 SDT-X,Y THEMIS Delta 2011-03-22 2011-03-30 SDT-X,Y THEMIS Echo
39 Table 4.7: Collecting data with changed bias setting
Start date End date Probe pair Satellite 2011-03-29 2011-04-08 SDT-X,Y THEMIS Alpha 2011-03-30 2011-04-08 SDT-X,Y THEMIS Delta 2011-03-30 2011-04-08 SDT-X,Y THEMIS Echo
4.5 Relative transfer function
Unfortunately we cannot measure the transfer function directly in-orbit since we do not control the input data. Instead we can obtain a relative transfer function by collecting data with different bias setting on the radial boom pairs. This changes the input impedance on one of the probe pairs which give rise to two different transfer functions with their roll-off at different frequencies. If the ratio of the gain of these two signals is plotted, the data with equal bias setting should give a linear response with a value of 1. With the changed bias setting (plotting the result from the changed pair over the unchanged) the function will roll down at the point corresponding to f = 1 and roll back up at f = 1 . This experiment aims to give a result 2πR1Cs 2πR2Cs similar to figure 4.3.
Figure 4.3: Sketch of the relative transfer function if we draw less bias current from boom pair 1/2, and plotted this data over the one obtain for the unchanged boom pair.
40 Chapter 5
Analysis and coding
5.1 I-V curves and sheath impedance
The data has been analyzed by several programs written in IDL (Interactive Data
Language). Below follows a short description of the main points of these codes.
With the code thm IV guard usher.pro we analyzed the SDT data collected in July
2009, obtaining I-V curves and the sheath impedance connected to each curve. First all needed data is downloaded from the THEMIS’s server, and the phase data in- terpolated to the same timeline as the voltage data (i.e. so they both contain equal numbers of data points at the same time points). This is needed since we will use the information in the phase data to pick parts of the voltage- and current data later in the analysis. To correct for some dubious findings in the current data, the subroutine fix current.pro is used.
5.1.1 Corrections of the current data
There are two big analyzing difficulties in the current data. First, it is saved much less frequent than the voltage data. Since the final goal is to plot these data arrays against each other, the current data needs to be interpolated to the same timeline as the voltage data. The other, more complicated, problem was that we have data points between the sweeps. i.e. when the bias setting was changed. Those points are non-physical, and rather an effect of the low data collection speed. In the in-
41 strument paper written by John Bonnell et al. [5], the sweeps were done in 16 steps, from -260 to 10nA. The subroutine fix current.pro is based on this information and will find the start and stop of each sweep from the voltage data and then create a current ramp with 32 steps between the time points found in the voltage data. This adjusted current data is reloaded into the thm IV guard usher.pro.
5.1.2 Corrections of the voltage data
The next step in the analysis regards corrections of the voltage data. For correct measurements we want to measure the voltage difference between the probe and the surrounding plasma. Without any corrections we instead measure the voltage difference between the probe and the spacecraft. The radial booms are considered long enough so that they are not affected by the photoelectric cloud, but the space- craft potential will vary as an effect of the bias sweeps. The other boom pair (not used for bias sweeps) is operated at the standard bias current, and can therefore be as a reference point for the spacecraft’s potential. To obtain the voltage difference between the probe and the surrounding plasma, we therefore subtract the voltage from the other boom pair.
1 V = V − (V + V ) (5.1) 1,2 1,2 2 3 4
1 V = V − (V + V ) (5.2) 3,4 3,4 2 1 2
For the axial booms we need an additional correction. Since the axial booms are much shorter, the spacecraft will have an effected their local potential. This addi- tional potential have been calculated using the code, given the paper by Cully et al.
[1], to be about 0.5 for the length and construction of THEMIS’s axial booms. So to obtain the voltage difference between the probe and the surrounding plasma, we
42 therefore subtract the voltage from the four radial booms multiplied by this extra factor of 0.5 to eliminate the influence of the spacecraft potential.
1 V = V − 0.5 · (V + V + V + V ) (5.3) 5,6 5,6 4 1 2 3 4
5.1.3 Obtaining the sheath impedance
One of the aims with this analysis is to see if the heath impedance is dependent on the guard- or usher settings. After the voltage corrections the next step in the code was to find the indexes corresponding to the different spin phases, as well as the indexes corresponding to when we change guard- or usher setting. We use the phase data to take a mean value of each spin (180 to 180 degrees) for the voltage- and current data. We chose 180 degrees since the sweeps starts at this phase. By doing this averaging we hoped to eliminate effects which vary with the sun phase.
Sets of data belonging to different guard- and usher settings were found with the indexes for phase data. Before dividing the current and voltage data with respect to the guard- and usher setting the data was ”cleaned” from points outside each sweep, i.e. exclude points found at time points when the bias current is changed.
Those data points are a result of taking the mean value of each sweep, i.e. an effect from the analysis method, and can be excluded.
The sheath impedance is found via two methods. First we applied IDL’s linear
fitting function (ladfit) used on the linear part of the I-V curve. This function gave
1 us the admittance, and the impedance follows as Rsheath = admittance . The lin- ear part gives the corresponding admittance/impedance at normal biasing setting
(185 nA). The aim with this analysis is to find possible patterns between the sheath impedance and different guard- and usher settings, as well as finding correlations be- tween sheath impedance and the different regions (i.e. different plasma conditions).
43 The second method is to find the derivative for the entire I-V curve (negative values are excluded since they are also non-physical). This method is aimed to give an indication of how much the bias setting needs to be change when collecting data for the relative transfer function in March 2011.
5.2 Relative transfer function
During March 2011 data were collected in 32 frequency bins, giving the highest sen- sitivity. We will analyze the fff -data, which have been Fourier transformed onboard the THEMIS satellites. Using this data had both pros and cons. Since the data already is Fourier transformed, and binned, we had no control over the resolution of the frequency bias. However, because it is already processed we saved a lot of time in this part of the analysis which was needed due to the time constrains of the thesis. Unfortunately the data was collected during shadow season which makes the data contain spikes which need to be removed before any further analysis. This was done by the code clean data.pro.
Simply calculating an average signal for each probe pair (as a function of frequency) and taking the ratio of the signal proved unsuitably noisy. The problems with this data is mainly there because the distribution is non-Gaussian and the data is au- tocorrelated. In the code baseline.pro, we try to decrease the fluctuations. First problem we encounter is there are a lot of data points with a value of zero. Those points are from when the EFI tries to measure waves with an amplitude below the measurement threshold. This effect is more pronounced at higher frequencies, due to the higher threshold. The mean value is affected by the zeros, we therefore removed all data points which was NaN or had a zero value. Somewhat problematic is that in the highest bins, the majority of the data points were then removed giving poor statistics.
44 Rather than calculating average signals over all data points and then calculating the ratio, we tried averaging over 30-point intervals, calculating a ratio for each interval, and then taking the median value. The result was plotted together with theoretical relative transfer functions for comparison. This theoretical lines were given by the derived equations for gain, see equation 4.5 (section 4.2), for sheath impedance values 3, 4, 5, 6, 10, 15 and 20 MΩ over 25 MΩ. We used these values because they occur in the analysis of the I-V curves (2-3 MΩ for the plasmasphere and 4-6 MΩ for the magnetosphere, magnetosheath and solar wind). The 25 MΩ used for boom 3,4 is the value we see for a bias setting of -50 nA.
45 Chapter 6
Results
6.1 I-V curves
The analysis gives a vast amount of plots, many of them showing very similar pat- terns. We have therefore chosen to include only some typical I-V curves as an example of them all. Different curves are shown for all different regions and satel- lites. This selection is possible since the individual IV-curves do not differ too much as long as the plasma conditions remain the same.
6.1.1 Effect of the corrections
As mentioned in the previous chapter there are two major corrections applied to the data before obtaining the I-V curves. The spacecraft’s potential has been subtracted for all spheres and in addition booms 5/6 have been corrected for the bleed through factor. Below are some examples of I-V curves before and after these corrections.
46 (a) (b)
Figure 6.1: (a) A typical I-V curve before the corrections of the spacecraft poten- tial. (b) Show the same I-V curve after the correction for the spacecraft potential has been applied. The two curves show similar shape, but the corrected have a much steeper slope, i.e. lower sheath impedance.
(a) (b)
Figure 6.2: (a) One example of a I-V curve for the axial booms when the bleed- through factor has not been corrected for. (b) The same I-V curve after the cor- rections have been applied.
47 (a) (b)
Figure 6.3: (a) Another example of a I-V curve for the axial booms without bleed through factor correction with (b) as the reference curve where corrections have been applied. From this and figure 6.2 it is clear that we have a bleed-though effect and corrections are needed.
6.1.2 Different regions
During the SDT runs in July 2009, data was collected in four different regions; magnetosphere, plasmasphere, magnetosheath and the solar wind. Since the plasma conditions are rather different in those regions we expect this to influence the I-V curves and therefore the sheath impedance. From the summary plots (see Appendix
B) we have looked at the data to provide us with values for the densities during each sweep, shown in table 6.1. We should remember these are not exact measurements, especially since we have them as plotted lines with a linear y-axis. We see that there are big differences within data taken in the same region. Most of the values still lie within what can be assumed as natural fluctuations.
48 Table 6.1: Densities in each region during the SDT sweeps
Region Density [cm−3] THA (M’sphere; SDT-1 [x,y,z]) 0.01 THA (M’sphere; SDT-2 [x,y,z]) 1 THB (Solar wind [x,y,z]) 10 THB (M’sphere [x]) 10-100 THC (M’sheath [x,y,z]) 5 THC (Solar wind [x]) 5 THD (M’sphere [x,y,z]) 1-10 THD (P’sphere [x]) 104-106 THD (P’sphere [x,y,z]) 103-104 THE (M’sphere [x,y,z]) 1-10 THE (P’sphere[x]) 105-106 THE (P’sphere [x,y,z]) 102-104
Magnetosphere
Figure 6.4: I-V curves for booms 1 through 4 for THEMIS Alpha in the magneto- sphere. We see saturation for all booms, but also a big difference in the knee-points.
49 Figure 6.5: I-V curves for booms 1 through 4 for THEMIS Alpha in the magneto- sphere. The general trend is the same, but a somewhat different behavior for the green curve (boom 3) compared to figure 6.4.
Figure 6.6: I-V curves for booms 1 through 4 for THEMIS Delta in the magne- tosphere. In difference to from THEMIS Alpha, figure 6.5 and 6.4 the I-V curves from THEMIS Delta show no saturation of the photocurrent be seen within the swept voltage range.
50 Figure 6.7: The data from THEMIS Echo show consistent results as seen from the data collected on THEMIS Delta.
Solar wind
Figure 6.8: I-V curves in the solar wind from booms 1 through 4 from THEMIS Bravo. In these I-V curves we see the saturation and the knee-points for all booms. Regarding the extent of the saturated curve it fallows the same pattern as the data seen from THEMIS Alpha, i.e., that booms 1 and 2 have the least points followed by boom 3 and boom 4 show the greatest extent.
51 Magnetosheath
Figure 6.9: I-V curves for boom 1-4 for THEMIS Charlie in the magnetosheath. Some of the sweeps in the magnetosheath show fluctuations (wiggles in the I-V curve). The fluctuations can also seen in the raw voltage data. This fluctuation are probably due to the turbulent plasma conditions in the magnetosheath. We therefore choose an I-V curve taken from a period where we see no evident turbu- lence.
Plasmasphere
Figure 6.10: I-V curves for boom 1-4 for THEMIS Delta in the plasmasphere. Compared to the curves in the other regions we can see that the slope is much steeper and with no sign of saturation either on the top or bottom of the I-V curve. We can also see that the displacement between the curve for boom 1/2 and boom 3/4 is not constant as for all previous regions.
52 Figure 6.11: I-V curves for boom 1 to 4 for THEMIS Echo in the plasmasphere. Similar pattern regarding the lack of visible saturation as the curves obtain with THEMIS Delta. However, here is the pattern of variation in displacement even bigger. And we can also see it within the boom pair. At around zero volts the I-V curves for boom 1 and 2 cross.
6.1.3 Summary of I-V curves
As can be seen in the figures over the I-V curves, fig. 6.4-6.11, most have a displace- ment both between the boom pair itself, (i.e. boom 1/2 versus boom 3/4) and within the boom pair (i.e. boom 1 versus 2 and boom 3 versus 4). The following three tables show a summary of the observed differences. These summaries are based on all different plots obtained from the analysis.
Table 6.2: Differences in knee-points
Boom 1 Boom 2 Boom 3 Boom 4 [nA] [nA] [nA] [nA] THA (M’sphere; SDT-1 [x,y,z]) -250 -230 -210 -192 THA (M’sphere; SDT-2 [x,y,z]) -250 -230 -210 -192 THB (Solar wind [x,y,z]) -250 -245 -255 -235 THC (M’sheath [x,y,z]) -250 -250 -260 -260 THC (Solar wind [x,y,z]) -260 -260 - -
53 Table 6.3: Voltage separation within, and between boom pair
Displacement Displacement within the between the boom pair [V] boom pairs [V] THA (M’sphere; SDT-1 [x,y,z]) 0.05 0.4 THA (M’sphere; SDT-2 [x,y,z]) 0.05 0.4 THB (Solar wind [x,y,z]) 0.05 0.3 THB (M’sphere [x]) 0.05 - THC (M’sheath [x,y,z]) 0.02 0.25 THC (Solar wind [x,y,z]) 0.02-0.1 0.3-0.4 THD (M’sphere [x,y,z]) 0.03 - THD (P’sphere [x]) 0.03 - THD (P’sphere [x,y,z]) 0.02-0.03 0-0.15 THE (M’sphere [x,y,z]) Crossing 0.3 THE (P’sphere [x]) Crossing - THE (P’sphere [x,y,z]) Crossing 0-0.2
Table 6.4: Sequence of the I-V curves (displacement in voltage)
THA (M’spere; SDT-1 [x,y,z]) Boom 4 Boom 3 Boom 2 Boom 1 THA (M’sphere; SDT-2 [x,y,z]) Boom 4 Boom 3 Boom 2 Boom 1 THB (Solar wind [x,y,z]) Boom 4 Boom 3 Boom 2 Boom 1 THB (M’sphere [x]) - - Boom 2 Boom 1 THC (M’sheath [x,y,z]) Boom 4 Boom 3 Boom 2 Boom 1 THC (Solar wind [x]) - - Boom 2 Boom 1 THD (M’sphere [x,y,z]) Boom 4 Boom 3 Boom 1 Boom 2 THD (P’sphere [x]) - - Boom 1 Boom 2 THD (P’sphere [x,y,z]) Boom 4 Boom 3 Boom 1 Boom 2 THE (M’sphere [x,y,z]) Boom 4 Boom 3 crossing crossing THE (P’sphere[x]) - - crossing crossing THE (P’sphere [x,y,z]) Boom 4 Boom 3 crossing crossing
6.1.4 Sheath impedance, (the linear part)
From the slope of the I-V curves the sheath impedance in the linear part can be derived as explained earlier, with help of IDL’s ladfit, which is only a linear fitting tool. The results are shown in figure similar as the key figure, fig. 6.12. The bars
54 are divided into five groups, one for each guard setting. In each group five different usher settings are tested. In the plots in which the data is presented, the top two
figures represent data from booms 1/2, the ones below booms 3/4 and the bottom ones booms 5/6 (i.e. the axial booms).
Figure 6.12: Key figure showing the pattern over the following bar plots over the sheath impedance.
55 Magnetosphere
Figure 6.13: Data from THEMIS Alpha’s measurements in the magnetosphere the sheath impedance does not vary too much with the guard- and usher setting for any of the radial booms and have a value of about 6 MΩ. But the axial booms show a dependency of the usher setting. The sheath impedance increases with higher usher voltage. For boom 5 the sheath impedance spans from about 8 to 11 MΩ and for boom 6 from 9 to 12 MΩ.
56 Figure 6.14: Data from THEMIS Alpha’s measurements the radial booms show a sheath impedance of about 6 MΩ. As for the previous measurement there is no dependency regarding the guard- and usher setting for boom 1/2. However, from these measurements we can see a slight dependency of the usher voltage in the result from boom 3/4. There is a small increase with higher usher voltage, a couple of kΩ. Regarding the axial booms, they shows the same dependency of the usher setting as in the other measurement by THEMIS Alpha. Here the sheath impedance span from about 6 to 11 MΩ for both boom 5 and 6.
57 Figure 6.15: Data from THEMIS Delta’s measurements in the magnetosphere shows a slight dependency of the usher settings for all radial booms. Compared to the data from THEMIS Alpha the overall sheath impedance is lower. The values rise from about 4 MΩ for the lowest usher voltage to about 5 MΩ for the highest one. Regarding the data from the axial booms, they show the same dependency of the usher setting as in the other measurement from THEMIS Alpha. Here the sheath impedance span from about 5 to 9 MΩ for both boom 5 and 6.
58 Figure 6.16: Data from THEMIS Echo’s measurements in the magnetosphere shows a slight dependency on the usher settings for all radial booms. Also here the values for the sheath impedance are lower. The values rise from about 4 MΩ for the lowest usher voltage to about 5 MΩ for the highest one. Regarding the data from the axial booms, they show a dependency on the usher setting, but not as clear as for previously presented data. We still see some trend of increasing sheath impedance with higher usher settings, but with some exceptions. However the values for the sheath impedance are consistent with previous presented results, i.e. span from about 5 to 9 MΩ.
59 Solar wind
Figure 6.17: From THEMIS Bravo’s measurements in the solar wind we can see a slight dependency of the usher settings for all radial booms. The values rise from about 5 MΩ for the lowest usher voltage to about 5.5 MΩ for the highest setting. Regarding the data from the axial booms, as well as the measurement in magnetosphere, they show a clear dependency on the usher setting. The sheath impedance increase, with higher usher voltage, for a total increase from about 5.5 to 10 MΩ.
60 Magnetosheath
Figure 6.18: From THEMIS Charlie’s measurements in the magnetosheath we can see rather random fluctuation within the data from all booms, radial and axial. There seems not to be any clear correlations between these variations and any guard- or usher setting. With maybe the exception of the axial where we can see similar behavior as for the measurements with the axial booms in the magnetosphere and solar wind. The pattern is not as clear, but there seems to be a general trend that the sheath impedance increases with usher voltage. The values for the sheath impedance for the radial booms lie between 5-6 MΩ. For the axial we can see an increase from 5 to 8 MΩ.
61 Plasmasphere
Figure 6.19: From THEMIS Delta’s measurements in the plasmasphere. The val- ues for the sheath impedance is in general much lower than for the magnetosphere, solar wind and magnetosheath. For the radial booms the values are around 1.8-2 MΩ. The possible dependency of the guard- and usher setting is much harder to see for these measurements. We can see a small increase between the first and last bar of about 200 kΩ. But if this increase is a small increase for each usher increase in usher voltage or a general increase with increased guard voltage is hard to see since the total increase is so small. Regarding the axial boom we can also see a general increase, this time of the order of approximately 1 MΩ. The increase seems to be a combination between guard- and usher dependency, and the sheath impedance increase from about 2.8 to 3.5 MΩ.
62 Figure 6.20: THEMIS Echo’s measurements in the plasmasphere. In these data we can see a slight dependency of the usher setting. The value for the sheath impedance increases from around 2 MΩ for the lowest usher voltage to 2.4 MΩ for the highest usher voltage. Regarding the axial booms there are fluctuation, but with no clear dependency of the guard- or usher settings. The values vary from about 3 to 4 MΩ.
63 6.1.5 Sheath impedance, (the entire sweep)
As mentioned in the section 5, we also retrieve the sheath impedance with another method. Here we get the sheath impedance through the entire sweep, not only the linear part as represented in the bar plots. As said in the analysis section, this was mainly done to give an idea of how much the bias settings needed to be changed to receive a noticeable only between the two relative transfer functions. We aimed for a increase of the sheath impedance of about a factor of ten, based on the accuracy possible with the frequency data and possible limitations of the instruments. From the results sweeps in the magnetosphere, magnetosheath and solar wind we choose to change the bias setting to -50 nA, giving a difference from around 5-6 MΩ to about
25 MΩ. One interesting observation is that the data from the plasmasphere does not have the same trend. Here the sheath impedance is lowered with less negative bias current, figure 6.24.
Figure 6.21: Shows the sheath impedance throughout the entire sweep, data collected in the magnetosphere with satellites THEMIS Alpha, Delta and Echo. In all plots we see an increase in the sheath impedance with higher bias.
64 Figure 6.22: Shows the sheath impedance throughout the entire sweep, data collected in the solar wind with satellites THEMIS Bravo. Also here we see an increase in the sheath impedance with higher bias current.
Figure 6.23: Shows the sheath impedance throughout the sweep, data collected in the magnetosheath with satellite THEMIS Charlie. Also here we see an increase in the sheath impedance with higher bias current.
65 Figure 6.24: Shows the sheath impedance throughout the sweep, data collected in the plasmasphere with satellites THEMIS Delta and Echo. Here we see a com- pletely different behavior compared to the data from the magnetosphere, magne- tosheath and solar wind. Here we instead see a decrease in the sheath impedance with an increased bias current, in contrary to the behavior in the magnetosphere, magnetosheath or the plasmasphere.
6.2 Relative transfer functions
In section 5 we discussed relative transfer functions with the different radial boom pairs set to different bias settings. We in the experiment changed the bias setting on booms 1/2, and we plot the amplitude ratio of G1,2/G3,4. The expected behavior is therefore that we will see a dip in the relative transfer curve at low frequency and that the curve reunites with the baseline at some higher frequency. For all plots showing the relative transfer functions, the black line with triangles shows the baseline and the black line with stars shows the relative transfer function. In each plot, seven theoretical lines are also included, for sheath impedances of 3, 4, 5, 6,
10, 15 and 20 MΩ, and a frequency span of zero to 4 kHz.
G 1 + jω · R · C 1 + jω · R · (C + C ) 1,2 = | 1,2 s | · | 3,4 s i | (6.1) G3,4 1 + jω · R1,2 · (Cs + Ci) 1 + jω · R3,4 · Cs
66 6.2.1 THEMIS Alpha
In figure 6.25 showing the relative transfer function for THEMIS Alpha we can clearly see a decrease in the relative transfer function, starting around 100 Hz. The curves reunite somewhere between 2200-3000 Hz. There are several theoretical rel- ative transfer functions added into the plot. There is a general correlation between the experimental and theoretical results, even if the experimental curve starts de- creasing at lower frequency than the theoretical curves. But the general is the shape consistent between the two curves. The best match between theoretical and exper- imental calculations is obtained with a sheath impedance values of 6 MΩ. This is in very good agreement with the value we see in the barplots showing the sheath impedance for THEMIS Alpha in the lower density regions, see figures 6.13 and 6.14.
The majority of the sweep during the experimental phase was made in low-density plasma conditions.
Figure 6.25: Shows the baseline and the relative transfer function for THEMIS Alpha.
67 6.2.2 THEMIS Delta
Shows similar behavior as figure 6.25, i.e. a separation which starts around 100
Hz and an rejoining of the two curves somewhere between 2500-3000 Hz. However, the analysis of where the curves reunite is harder to determine from this plot since the baseline has more fluctuations and noise. Looking at the comparison with the theoretical curves, we here see the best match at a sheath impedance values between
5-6 MΩ. Also this is in agreement with the results of the I-V curve analysis, see
figure 6.19, where we saw slightly lower sheath impedance value compared with the results from THEMIS Alpha.
Figure 6.26: Shows the baseline and the relative transfer function for THEMIS Delta. Shows similar behavior as fig. 6.25.
68 6.2.3 THEMIS Echo
THEMIS Echo shows similar behavior as figures 6.25 and 6.26. A small difference is that the curves seem to reunite at a lower frequency, around 1500-2800 Hz. As for the measurement with THEMIS Delta, figure 6.26, the baseline shows more fluctu- ations which makes it harder to see where the two curves reunite. Looking at the comparison with the theoretical curves, we see the best match between theoretical and experimental calculations at a sheath impedance values between 4-6 MΩ, de- pending on where in the frequency range we are. Compared to the barplots, figure
6.20, we see a consistency since the sheath impedance in the barplots is about 4-5
MΩ.
Figure 6.27: Shows the the baseline and the relative transfer function for THEMIS Echo. Shows similar behavior as 6.25 and 6.26. But here we can see the two curves seem to join somewhere around 1500-2800 Hz, i.e. at slightly lower frequencies than the previous two figures. As in figure 6.26, the baseline shows more fluctuations. Looking at the comparison with theoretical line, we here see the best match between theoretical and experimental calculations at a sheath impedance values between 4-6 MΩ, depending which frequency range.
69 Chapter 7
Discussion
7.1 I-V curves
7.1.1 Voltage corrections
As can be seen in figures 6.1, 6.3 and 6.2, showing I-V curve before and after the different corrections, it is clear the sweep voltage must be corrected for changes in the spacecraft floating potential and for the potential offset caused by the nearby spacecraft. The corrections for spacecraft floating potential are particularly vital.
Without the corrections the analysis would give a sheath impedance of about 30
MΩ, where as the true impedance is only 4-6 MΩ.
7.1.2 Voltage separation between I-V curves
As seen in the plots with I-V curves there are some voltage separation between I-V curves from different booms. Probe pair 1/2 (black/blue) is consistently at a lower voltage than probe pair 3/4 (red/green) for the same bias current. This is expected because how we do the corrections. From boom 1/2 we subtract a value measured with boom 3/4 which are 5 meters shorter. This will result in a slightly too small correction. For boom 3/4 the opposite is true. Here we instead subtract too much of the signal. This results in that the curve for boom 1/2 is moved slightly to the right and the curve for boom 3/4 slightly to the left.
70 There are also a voltage offset between the probes in a pair (e.g. probe 1 vs. probe
2), which cannot be explained by intended constructions. From table 6.3 we see that there is a pattern relating the separation to the satellites, instead of the plasma conditions. For all spacecraft the I-V curve from boom 4 is located slightly to the left of boom 3. For boom 1/2 there the placement differs between the satellites.
For THEMIS Alpha, Bravo and Charlie, are the I-V curve from boom 2 located slightly to the left of boom 1, irrespective of the region. In the data from THEMIS
Delta the I-V curves are opposite organized, i.e. boom 1 is slightly to the left seen to boom 2. For THEMIS Echo are all the I-V curve cross somewhere around zero volts.
The correlation between placement and a specific spacecraft exists, while there does not seem to be any correlation between the region in which the data have been collected. We therefore make the conclusion that it is either a construc- tion/manufacture imperfection, or due to what the spacecraft has experienced during its mission in space. This could for example be small imperfections or coating on one of the spheres which would yield slightly different work functions. It is important to remember that all these separations are small. For the separation between the pairs it is of the order of a 0.2-0.4 volts and within the boom pair about 0.02-0.05 volts.
7.1.3 Differences in the maximum photocurrent
We have also seen a difference in the maximum photocurrent (when the photocurrent becomes saturated, i.e. the knee point) between different measurements. We cannot say where this point occurs for all measurements since the knee-point is not reached in many of the sweeps. This is especially true for the I-V curves in the plasmasphere where only a limited part of the linear part of the curve can be seen. From the I-V curves where we can see the knee-point, we see some interesting features, especially for THEMIS Alpha. The maximum difference between the probe saturation current is about 60nA. If this is pattern exists in all regions it might create a problem when measuring the electric field since all probe are biased to the value, so called opera-
71 tion bias, which is as of now -185 nA. And as we see boom 4 has a value of -192 nA, which is within a worrying limit.
7.2 Sheath impedance
7.2.1 Variations depending on region
We see a clear dependence on the region in the values for the sheath impedance.
In the magnetosphere, magnetosheath and the solar wind the sheath impedance is approximately 4-6 MΩ for the radial booms, and ranges from 5-12 MΩ for the axial booms, increasing with usher voltage. This dependence will be discussed in the next section. The clearest difference in the sheath impedance is between the plasmas- phere and the remaining regions. In the plasmasphere the sheath impedance are significantly lower, approximately 2-3 MΩ.
The complete description of how different plasma properties affect the sheath impedance is complex and involves the properties and material of the sensors, interacting ef- fect with the plasma, and general conditions in the plasma (e.g. the Debye length, electron- and ion temperature, density etc). But looking at the data in section 6 we seem to be able to use the density as an indicator. A clear correlation can be seen between the sheath impedance and the density in the different regions. As can be seen in table 6.1, the density varies considerably between the different measure- ments, even for data collected in the same region. The correlation between density and sheath impedance can be seen both on the big scale between the regions, and within the high- and low density groups in each region. Regions with low density
(approximately 0.01-100 cm−3) show a sheath impedance of 4-6 MΩ, compared to regions with high density (104-106 cm−3) with a sheath impedance of about 2 MΩ.
The values for the sheath impedance in the high- and low density group within each region follows the same pattern, but since the differences in density are smaller, the variations in sheath impedance are smaller.
72 However, to explain the difference between the plasmasphere and the other low- density regions we might need to consider the different plasma conditions. The plasmasphere is much denser and colder than the magnetosphere, magnetosheath and solar wind region (see table 6.1). There is a high possibility that this will affect the electron current (see equ. 3.1 and 3.3). To give an estimate we calculate the values with the different density and electron temperature when VB = 0, the point in which the photo current starts influence the I-V curve.
r kbTe Ie = −Aneqe (7.1) 2πme
Typical values given by the plasmasphere:
r 1.6 · 10−19 I = 50 ∗ 105 ∗ 1.6 · 10−19 ' 100nA (7.2) e 2π ∗ 3.11 · 10−31
Typical values given by the magnetosphere:
r 104 ∗ 1.6 · 10−19 I = 50 ∗ 0.1 ∗ 1.6 · 10−19 ' 10pA (7.3) e 2π ∗ 3.11 · 10−31
As we can see it there a huge difference in the electron current between the plasma- sphere and the magnetosphere. This means that in the plasmasphere the electron current is comparable to the photo current, and will therefore influence the shape
73 of the I-V curve. More precisely the linear part of the I-V curve will become much steeper, yielding a lower sheath impedance. So the difference in the electron current likely explains the lower sheath impedance values we see in the plasmasphere.
For the axial booms it is hard to make conclusions about the density dependence of the sheath impedance. For these booms, the dependence on the usher settings dominates (see next section).
7.2.2 Variations depending on guard- and usher settings
As mentioned, we also see a dependence between the sheath impedance and the usher settings in the results for the axial booms (data collected in the magnetosphere, mag- netosheath and the solar wind). We see a clear increase of the sheath impedance with higher usher voltage. The difference is of the order of 4-5 MΩ between usher setting
-8 and +8 volts. This is almost a doubling of the sheath impedance, so it is defi- nitely an effect that needs to be taken into consideration during other measurements.
A smaller increase of the sheath impedance with higher usher setting can also can be seen for most measurements with the radial booms. We see what seems to be an upper limit where this dependency no longer exists, or at least so small that it is not detectable by the EFI. The limit seems to be around 103 cm−3, since we see signs of dependency in the data from THEMIS Echo’s measurements (density of 102 -
103 cm−3, table 6.1), but no visible dependency for THEMIS Delta’s measurements
(density of 103-104 cm−3). One possible explanation for this upper limit is that with these densities the typical Debye length is around one meter. With a distance between the probes and the usher of three meters, and a Debye length of about one meter, the probes would be isolated from any influence of the usher.
There are no signs of dependence of the guard setting, with one possible excep- tion of the data collected in the plasmasphere by THEMIS Delta. But from the
74 summary plots we see THEMIS Delta during this measurement is on the way out from the plasmasphere into the magnetosphere (see summary plots in the Appendix
B). The density will then be lowered which might explain the increase of sheath impedance for this particular sweep.
A possible explanation why we see a dependence on the usher setting but not on the guard setting might be that the relative distance between the two photoelectron sources matters. The spacecraft is 15-20 meters from the guard and another 5 more to reach the sphere. The photoelectrons created on the preamplifier only have to travel 0-3 meters, corresponding to the distance to the fine wire or sphere. If this argument is true, the majority of the photoelectrons creating disturbance for the measurements are from the preamplifier and the spacecraft photoelectrons are effec- tively deflected from reaching the sensors without any need for a guard. However, it is hard to test this hypothesis since we cannot eliminate the guard- and usher when in space.
7.2.3 Lower resistance than expected
There is a clear difference between the expected and the measured values for the sheath impedance. From earlier calculations the impedance was estimated at about
20-30 MΩ [1]. The results from this thesis analysis show consistently lower values, independent of the regions or satellite. To investigate the discrepancy we calcu- lated the sheath impedance using the OML approximation. For current collection by a biased probe (i.e. equations 3.1-3.6) we assumed a single-temperature exponen- tial distribution for the photoelectron distribution with values for the photoelectron temperature and photoelectron current from Laako et al. [3]. The bias current for the four fixed sensors were set to -185 nA. The photoelectron current was set
2 to 5 nA/cm , based on observations of the maximal photocurrent j0 (value of the knee-point) and dividing by the sphere’s total area. This gives 250 nA/50 cm2 =
5 nA/cm2. Values for the plasma density, electron- and ion temperature are from
75 table 6.1. The resulting sheath impedance was around 25 MΩ, consistent with the previous believed value for the sheath impedance. The OML approximation only has a limited amount of parameters which we can adjust. The ones that are ad- justable are the electron density (ne), electron- and ion temperature (Te,Ti) and the maximum photocurrent (j0). All these have been measured at the same time as collecting the voltage data, and the calculations using these values did not reproduce the obtained results for the sheath impedance.
To explain the discrepancy with the measured values, we therefore tried testing the assumptions in our calculation. We assume the actual OML approximation is valid, leaving the assumptions made by Laako’s et al. The weakest is that the photoelectron temperature relies on the assumption that the spheres have the same photoelectron temperature as an entire spacecraft [3]. To see if this is a reasonable approximation, we lowered the photoelectron temperature from 1.5 eV to 0.5 eV.
With this change we obtained values for the sheath impedance of around 5 MΩ, which is consistent with the results we see from the SDTs runs. We therefore make the conclusion that the probe photoelectron temperature is less than that of the spacecraft, and probably near to 0.5 eV.
7.3 Transfer functions
The EFI have a transition from a resistive low-frequency coupling to a capacitive high-frequency coupling. The transition is known as the RC roll-off, and the curve describing the whole frequency range gives the transfer function.
We have collected data with different bias settings on the two boom pairs, boom
1/2 at -50 nA and boom 3/4 at -185 nA. Taking the ratio of the signals received on each pair as a function of frequency gives a relative transfer function, where the position of the RC roll-off for the two function depends on the sheath impedance
76 which is connected to the bias setting. The result should look similar to the figure
7.1. If the ratio of the gain of these two signals is plotted, the data with equal bias setting should give a linear response with a value of 1, the so called baseline. With the changed bias setting, plotting boom 1/2 over boom 3/4, the function will roll down at the point corresponding to f = 1 and roll back up at f = 1 . 2πR1/2Cs 2πR3/4Cs From the data in figure 6.25 - 6.27, we can see that the baselines are overall flat, with some fluctuation without a trend. We therefore do not do any further analysis of the baseline, or consider them in the analysis of the relative transfer function.
Figure 7.1: Sketch of the relative transfer function if we draw less bias current from boom pair 1/2, and plotted this data over the one obtain for the unchanged boom pair.
With the decreased bias current for boom 1/2, we see a clear decrease in the in- strument response from a couple of hundred Hz to somewhere between 2-3 kHz.
These results are similar for all three satellites (THEMIS Alpha, Delta and Echo).
The low-frequency roll-off is connected to the RC roll-off at the higher bias setting,
(-50 nA) and the high-frequency roll-off to the lower bias setting (-185 nA).
77 From the values we obtained for the sheath impedance, we could give a prediction of where the roll-offs should occur. In section 4.2 we obtain a formulae to calculate the roll-off, equation 4.8. Using the values for the sheath impedance, analyzing the I-V curves, we expect the two points to be around 450 Hz (for -50 nA and 25 MΩ) and 2 kHz (for -185 nA and 6 MΩ) using the measured capacitance of 14 pF for both cases.
1 = 455Hz (7.4) 2π(25 · 106)(14 · 10−14)
1 = 2274Hz (7.5) 2π(6 · 106)(14 · 10−14)
We can clearly see consistency between the predicted value based on the sheath impedance from the I-V curves and the result seen in the plots of the relative trans- fer function. However, the relative transfer function does not give such an exact value as calculating the roll-off from the sheath impedance given by the I-V curves.
Where the two curves reunite is somewhat difficult to decide exactly since there is some noise in the data. But one important conclusions can be made, we can for sure rule out that the RC-roll-off occurs around 400-500 Hz for the normal bias setting,
(-185 nA). From all the baselines we instead see the roll-off somewhere between 2-3 kHz.
One other thing is that there seems to be a trend for both the baselines and rela- tive transfer function to rise with higher frequency. But we must be a bit careful to make conclusions from this part of the data since the amount of data points decrease drastically with the increase of frequency. In the first points we take an average of around 100 000-150 000 data points per bin, while in the last bins only a couple of
78 hundred. The is due to the amount of zero-valued data points at higher frequencies for which a ratio is meaningless.
The frequency data collected is both autocorrelated and non-Gaussian, which make a proper error analysis rather complex. We would need to use bootstrapping anal- ysis, which was assumed exaggerated for this thesis considering the time constrain.
But even if we cannot give the possible error for the datapoint, and with the decrease in data points, we see the increase of the relative transfer function/baseline for all six measurements. This makes it highly unlikely that this just a coincidence, and we assume the increase is a real physical phenomena.
A possible explanation for the rise with higher bin number could be so called boom shortening. Data have been collected in multiple plasma regions, but the higher fre- quencies are not collected evenly over all regions. In contrary, these high frequency waves are mostly associated with whistler mode waves close to Earth. Closer to
Earth the density goes up, which shorten the Debye length. The phenomena known as boom shortening arises in large Debye length plasmas where the conducting wire booms partially short-circuit the applied electric field and the booms become ”elec- trically shortened”. With the lower Debye length, (i.e. when the probes collect the data for the highest frequencies), the booms are at their full ”length”. Since we plot boom 1/2 over 3/4 this extended electrical length will give a rise of the base- line/relative transfer function.
79 Chapter 8
Conclusions
From this analysis we have learned that the value for the sheath impedance and the transfer function is not consistent with what was previously assumed. The sheath impedance is only about a sixth of what was expected. Previous calculations had predicted values of about 30 MΩ, while the results of this thesis show values around 5-6 MΩ for lower density regions (magnetosphere, magnetosheath and the solar wind), and 2 MΩ in regions with higher density (plasmasphere). We believe that the lower sheath impedance is due to a smaller than expected photoelectron temperature for the probes. Our analysis indicates a value of 0.5 eV instead of the previous assumed 1.5 eV.
From the results in this thesis we can see a correlation between the sheath impedance and density of the plasma. The results indicate that a lower plasma density gives higher sheath impedance and vise versa. However, when it comes to the big differ- ences between region with largely different plasma conditions (e.g. magnetosphere vs. plasmasphere), our analysis has shown that the difference is due to the change of the electron current. In the plasmasphere the plasma conditions are such that the electron current is large and therefore strongly influence the I-V curve, while the photocurrent dominates for the regions with low-density, hot plasma.
80 We also found that the sheath impedance is dependent on the usher setting. This is especially visible in the regions with lower density, and most pronounced for the axial booms. For the axial booms we see an increase from 5-6 MΩ for usher setting
-8 volts to 12 MΩ for +8 volts. Both the dependence on the usher setting and the plasma features (i.e. the change of the electron current), are effects which need to be considered for experiments relying on precise knowledge of the sheath impedance.
We have also shown that the RC roll-off in the transfer function occurs between 2-3 kHz. This was shown in both calculation of the roll-off from the sheath impedance, based on the I-V curves, and from the relative transfer functions. Both analyses show the roll-off in a region around 2-3 kHz at the nominal operation bias of -185 nA.
This is a big difference when compared to the earlier assumed roll-off around 400-
500 Hz. The results from this thesis are therefore of large importance for research preformed at intermediate frequencies, and will impact the results from such mea- surements. For example a lot of research today is using THEMIS EFI data to look at different wave phenomena, especially Chorus emissions. These occurs in a fre- quency range from a couple hundreds of hertz to 5 kHz, and will therefore be directly affected by this new transfer function.
81 Chapter 9
Appendix
9.1 Appendix A - Spikes in the voltage data
During the analysis we noticed spikes in the voltage data when we reach saturation of the photocurrent. Spikes could always occur in this part of the I-V curve since small
fluctuations in the bias current may result in big changes to the voltage, i.e. spikes.
The puzzling thing is that the spikes appear when the sensor is facing away from the sun which is not the expected behaviour. The figures in this section are from IDL:s tplot and show examples of these voltage spikes. The top panel represents boom 1, next panel boom 2 and so on. The bottom panel shows the phase data, measured onboard the spacecraft.
9.1.1 THEMIS Alpha - Magnetosphere
In all sweeps we can see that all six booms show voltage spikes during a longer period when sweeping boom 3/4, compare fig. 9.2/9.4 with 9.1/9.3. Further observations are that when we see spikes in boom 2 and 4 voltage data, spikes are occurring simultaneously in the other boom’s data. This we do not see in the data for boom
1 or 3. We cannot see any spikes when the axial booms were swept, neither in its own or other boom’s voltage data. The spikes for boom 1/2 occur around a phase of 90◦ or 270◦ and for boom 3/4 around 0◦ or 180◦.
82 However is the slit from which the phase measurements are placed such that we to obtain the real sun angle so we should subtract 45◦ from the results seen in the phase data. So the sun angles are 90◦, 270◦, 0◦ and 180◦. As mentioned there are some difference in the data from the early and later sweeps. For the earlier sweeps does all spikes in the data from the radial boom have a depth of around -70 to -80 volts, and the spikes from the axial of about -40 volts. For the later sweeps we see the same depth, i.e -70 to -80 volts, when sweeping boom 1/2. However, are there no spikes in the other booms data, as we could see in figure 9.1. Further, when sweeping boom 3/4 the depth of these booms are -70 to -80 volts, while the depth for boom 1/2 is only about -20 volts. And finally are the spikes when sweeping the axial booms are not deeper than -10 volts.
Figure 9.1: Shows the spikes occurring in THEMIS Alpha’s voltage data. This data is from the earlier sweep. The figure shows data collected when boom 1/2 were swept. The spikes occur around a phase of 135◦ or 315◦, with a depth of around -70 to -80 volts for the radial and -40 volts for the axial.
83 Figure 9.2: Shows the spikes occurring in THEMIS Alpha’s voltage data. This data is from the earlier sweep. The figure shows data collected when 3/4 were swept. We can see that all six booms show voltage spikes during a longer period when sweeping boom 3/4. The spikes occur around a phase of 45◦ or 225◦, with a depth of around -70 to -80 volts for the radial and -40 volts for the axial.
Figure 9.3: Shows the spikes occurring in THEMIS Alpha’s voltage data, data collected during the second run that day. The figure shows data collected when boom 1/2 were swept. In consistent with fig. 9.1, the spikes occur around a phase of 135◦ or 315◦, and at similar depth, duration and phase.
84 Figure 9.4: Shows the spikes occurring in THEMIS Alpha’s voltage data, data collected during the second run that day. The figure shows data collected when boom 3/4 were swept. In consistent with fig. 9.2, the spikes occur around a phase of 45◦ or 225◦. The difference is that the depth of the spikes for boom 1/2 and 5/6 are lower than in the early measurements.
9.1.2 THEMIS Bravo - Solar wind
In figure 9.5 can we see the result when boom 1/2 were swept and in figure 9.6 when boom 3/4 were swept. These sweeps occur in the solar wind region. We can see that when one boom is swept, we only see spikes within its own data, which is true for all radial booms. However, we can see some kind of reaction in boom 1/2’s voltage data when sweeping boom 3/4. Once again we see no spikes when sweeping the axial booms. The duration of spikes are much shorter than that for THEMIS
Alpha data, but once again does the longest duration occur for boom 4. As for all previous results the spikes for boom 1/2 occur around a phase of 90◦ or 270◦ and for boom 3/4 around 0◦ or 180◦. The depth for boom 1 and 3 is about -50 volts and for boom 2 and 4 -80 volts.
85 Figure 9.5: Show the spikes occurring in THEMIS Bravo’s voltage data when boom 1/2 were swept. The duration of spikes are much shorter that for THEMIS Alpha data in the magnetosphere. The spikes occur around a phase of 135◦ or 315◦, which a depth of -50 volts for boom 1 and -80 volts for boom 2.
Figure 9.6: Shows the spikes occurring in THEMIS Bravo’s voltage data when boom 1/2 were swept. The duration of spikes are much shorter than that for THEMIS Alpha data in the magnetosphere. The spikes occur around a phase of 0◦ or 225◦, which a depth of -50 volts for boom 3 and -80 volts for boom 4.
86 9.1.3 THEMIS Charlie - Magnetosheath
In figure 9.7 can we see the result in THEMIS Charlie’s voltage data when boom
3/4 were swept in the magnetosheath. Here we cannot see any spikes for any booms except boom 4, this is when boom 3/4 were swept. We see one spike, occurring at about 45◦ and with a depth of about -40 volts.
Figure 9.7: Shows the spikes occurring in THEMIS Charlie’s voltage data, swept in the magnetosheath. We see only one clear spike, occurring in boom 4’s data when boom 3/4 were swept. The phase when the spike occur is about 45 degrees and with a depth of about -40 volts.
9.1.4 Conclusions regarding the voltage spikes
In the part of the I-V curves where the photocurrent is saturated we see spikes in the voltage data. There is always a possibility that those spikes occur in this part of the I-V curve since small fluctuations in the bias current may result in big changes in the voltage, i.e. spikes. But with help of the phase data we observed that the spikes occur in an anti-sunward direction, instead of the more expected sunward
87 direction. This almost completely rule out the possibility for this to be a shadow effect, due to that the narrow sun angle required would imply that the spacecraft shadowing the anti-sunward boom itself, and therefore result in bad data. However, it is clear from the data collected that the spikes are correlated to the anti-sunward angle. For all sweeps where we reach saturation of the photocurrent, we see spikes when the probe in question is facing away from the sun. But with the data available for this thesis, we unfortunately have not come to an exhaustive explanation why they occur at this angle.
88 9.2 Appendix B - Summery plots
Figure 9.8
89 Figure 9.9
90 Figure 9.10
91 Figure 9.11
92 Figure 9.12
93 Figure 9.13
94 Figure 9.14
95 Figure 9.15
96 Figure 9.16
97 Figure 9.17
98 Figure 9.18
99 Figure 9.19
100 Figure 9.20
101 Figure 9.21
102 Figure 9.22
103 Figure 9.23
104 Figure 9.24
105 Figure 9.25
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108