MASTER'S THESIS. Spacecraft-Plasma Interaction Modelling of Future Missions to Jupiter. Tobias Rudolph

Transcription

1 MASTER'S THESIS Spacecraft-Plasma Interaction Modelling of Future Missions to Jupiter Tobias Rudolph Master of Science Space Engineering - Space Master Luleå University of Technology Department of Computer Science, Electrical and Space Engineering

2 Spacecraft-plasma interaction modelling of future missions to Jupiter A thesis written at the Institut de Recherche en Astrophysique et Planétologie, Toulouse, France by Tobias Benedikt Rudolph in partial fulfilment of the requirements for the degree of MSc with a Major in Space Technology at the Luleå University of Technology, Luleå, Sweden Toulouse, October 2011

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4 ABSTRACT As an orbiter cruising to Jupiter will encounter different plasma environments, variety of spacecraft surface charging is expected. This surface potential can lead to inaccurate and wrong in-situ plasma measurements of on-board sensors, which explain the interest in simulating the charging. In this thesis the spacecraft-plasma interactions for a future mission to Jupiter are modelled with the help of the Spacecraft Plasma Interaction System, taking the case of a Jupiter Ganymede Orbiter (JGO) and a Jupiter Europa Orbiter (JEO) as an archetype for a future mission. It is shown that in solar wind at Earth and Jupiter, spacecraft potentials of about 8 V for the JEO, and 10 V to 11 V for the JGO are expected. Furthermore, at a distance of 15 Jupiter radii from Jupiter, the JGO is expected to charge to an electric potential of 2 V, except in the planetary shadow, where it will charge to a high negative potential of -40 V. Moreover, close to the orbit of Callisto, JGO will charge to 12 V in the sun and to 4.6 V in eclipse, due to a high secondary electron emission yield. KEYWORDS: spacecraft charging, Jupiter Ganymede Orbiter, Jupiter Europa Orbiter, Europa Jupiter System Mission - Laplace, Spacecraft Plasma Interaction System, Jupiter Icy Moon Explorer iii

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6 PREFACE I planned to write this master thesis in Japan, but due to the earthquake on 11th March 2011 it was not possible. Therefore it was done at the Institut de Recherche en Astrophysique et Planétologie, termed IRAP, in Toulouse, France, under the supervision of Dr. Nicolas André and Dr. Vincent Génot. I want to express my special gratitude to Nicolas André for the spontaneous offer of a thesis and to Nicolas André and Vincent Génot for the excellent supervision and for all helpful scientific discussions. Furthermore, I would like to say a special thank you to doctoral candidate Stanislas Guillemant for his daily help and for answering all my questions concerning the SPIS software. In addition, I would like to thank in particular Prof. Christophe Peymirat from my second year university, Université Paul Sabatier in Toulouse, France, for all administrative support after returning from Japan, for his encouragement and especially for his help to find a new thesis for me. Many thanks also to Prof. Dominique Toublanc from the Université Paul Sabatier for taking care of me after returning to Toulouse and for offering me a workplace. As mentioned, I intended to do my master thesis as a research student at the Department of Earth and Planetary Science at The University of Tokyo, Japan, under supervision of Prof. Ichiro Yoshikawa. But due to the earthquake on 11th March 2011 I had to return to Europe. Although my time in Tokyo was limited due to the catastrophe, I was very glad to get this unique opportunity offered. I would like to especially thank Prof. Masafumi Hirahara for the contact, Prof. Ichiro Yoshikawa for offer, supervision and support, my lab member Kouichi Sakai for his support and help in everydays life and Mrs. Emiko Gosho from the international student office for always having an open ear and her competent advisory. However, my special thanks go to my parents, my brothers and my sister for their help and encouragement during all my studies in every situation. In the end, I would also like to offer a special word of thanks to my wonderful girlfriend Elena for her support and for inspiring me daily. v

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8 CONTENTS Chapter 1 Introduction 1 Chapter 2 Theoretical Background Plasma Properties and parameters Solar wind and Jovian magnetospheric plasma Spacecraft-plasma interactions Current balance equation Ion wake formation Chapter 3 Spacecraft Plasma Interaction System - SPIS Background Solving mechanism Chapter 4 Europa Jupiter System Mission - Laplace Mission concept Jupiter Ganymede Orbiter Design proposal Design proposal Jupiter Europa Orbiter Chapter 5 Modelling Jupiter Ganymede Orbiter - Proposal Jupiter Ganymede Orbiter - Proposal Jupiter Europa Orbiter Chapter 6 Simulations Solar wind plasma Solar wind at Earth Solar wind at Jupiter Jovian magnetospheric plasma JGO2 at the orbit of Ganymede JGO2 at the orbit of Callisto Accuracy of simulations Chapter 7 Conclusion 47 Appendix A List of acronyms 49

9 Appendix B Simulation settings 51 Appendix C Verification of input parameters 59 C.1 Simulations and results Appendix D SPIS Guide 61 D.1 Introduction D.2 Installation and source code changes D.3 Modelling and simulation Overview Create a new project Geometry/CAD manager Import the CAD structure and load the properties catalogs Geometry property group editor Meshing, conversion into mesh groups and fields mapping Global parameters Conversion to numerical data and running the simulation Extract the data D.4 Visualisation and data analysis Appendix E Limitation of SPIS 75 E.1 Photoelectron emission in shadow viii

10 CHAPTER 1 Introduction The interplanetary space and the magnetosphere of planets is not a perfect vacuum but rather filled with plasma. A spacecraft cruising through it encounters numerous problems. One of them is spacecraft charging which is caused by the spacecraft-plasma interactions. Due to higher mobility of ambient electrons compared to ions, a spacecraft is subjected to a higher flux of electrons and can charge to a negative potential. However, in case of high emission of secondary electrons by particle impact and especially photoelectrons, a spacecraft can also charge positive. Spacecraft charging can lead to various destructive effects. First of all it complicates plasma measurements by space instruments, due to reflection or acceleration of low energetic charged particles [15, 19, 14]. Also focusing and exclusion of charged particles can lead to disturbed measurements [21]. In addition to that, measurements can be contaminated by emitted photoelectrons and secondary electrons, as well as by backscattered electrons [21]. Moreover, different surface conductivities of conductors and dielectrics lead to differential charging. If the potential difference exceeds a given threshold, arc discharges occur. This effect is known to have caused several spacecraft operational anomalies and failures [6, 48, 38], which strongly explains the economical interests to do research in this field. In 1979 the first spacecraft charging research satellite P-78-2, known as SCATHA, was launched, starting an era of advanced research. It has led to an increased interest and knowledge in spacecraft charging and to the development of numerous computational tools to simulate spacecraft-plasma interactions. One of them is the Spacecraft Plasma Interaction System, termed SPIS. In this master thesis spacecraft-plasma interactions for a future mission to Jupiter are modelled. To do so, we estimate average surface potentials with SPIS for the case of the Jupiter Ganymede Orbiter and the Jupiter Europa Orbiter of the Europa Jupiter System Mission. The orbiters will cruise through different plasma environments as the solar wind at Earth and Jupiter, the inner Jovian magnetosphere and the magnetosphere of Ganymede, which will lead to variety of charging. Furthermore, the huge solar panels of the Ganymede orbiter may lead to critical charging, whereas the Europa orbiter is powered by a radioisotope 1

11 2 Introduction source. Because the resistances and capacities between subsystems are confidential information of the satellite provider, the problem of differential charging cannot be addressed here. The thesis is organized in the following way. In Chapter 2 plasma theory, plasma environments and spacecraft-plasma interactions, taking into account charging and ion wake formation, are introduced. Chapter 3 deals with the background and solving mechanism of the Spacecraft Plasma Interaction System, which is the simulation software used in this thesis. Then, chapter 4 addresses the overall concept of the Europa Jupiter System Mission and gives information about the Jupiter Ganymede Orbiter and the Jupiter Europa Orbiter. Afterwards, in chapter 5 the models of the orbiters used within this thesis are described. In chapter 6 spacecraft-plasma interactions in solar wind at Earth and Jupiter, and in the Jovian magnetosphere are simulated. Finally, chapter 7 provides a summary, concluding remarks and an outlook.

12 CHAPTER 2 Theoretical Background 2.1 Plasma Plasma physics is widely used to describe a huge amount of solar, stellar and interplanetary physical processes. Moreover, more than 99 % of the observed matter in the universe is believed to be plasma [44, p. 115] stating the importance of plasma theory. In the following subchapters plasma theory is introduced and specific plasma environments are described Properties and parameters A plasma is often loosely defined as an ionized gas. However, this is not a sufficient condition because all gases have a given degree of ionization 1. A more specific definition is the one used by Koskinen: Plasma is quasi-neutral gas with so many free charges that collective electromagnetic phenomena are important to its physical behaviour [32, p. 59]. Quasi-neutrality implies that the number density of ions n i is approximately equal to the number density of electrons n e on macroscopic length scales for single ionized atoms, thus n 0 n i n e, (2.1) where n 0 is defined as the plasma density. Compared to particles in neutral gas, plasma particles do not interact mainly by mechanical collisions but by electromagnetic forces because moving charged particles induce electric and magnetic fields. This obviously means that each charged particle interacts with a lot of other particles due to the long-range characteristic of the Coulomb force 2. Therefore multi-body interaction is important for the collective behaviour of a plasma. In the following, the fundamental parameters of plasma physics are explained. The characteristic spatial scale in plasma theory is the Debye length. On scales larger than 1 The degree of ionization is given by the Saha ionization equation. 2 The Coulomb force is r 2, whereas the Van-der-Waals force between neutral atoms and molecules is r 6. 3

13 4 Theoretical Background the Debye length the electric field induced by a charged particle or a charged surface of a spacecraft is screened. The Debye length for electrons (index e) respectively ions (index i) is defined as [44, p. 125] ɛ0 kt e,i λ e,i = n 0 e, (2.2) 2 with ɛ 0 the permittivity of free space, k the Boltzmann constant, T e,i the temperature of electrons or ions and e the elementary charge. The total Debye length λ D is then given by [44, p. 125] 1 = (2.3) λ 2 e λ 2 i λ 2 D If the Debye length is much bigger than the spacecraft dimension, the spacecraft-plasma interaction is called electrically coupled, whereas in the other case it is called electrically uncoupled [23, p. 33]. The electric potential φ induced by a charge Q within a plasma as a function of distance r is dependent on the Debye length and is known as the Debye-Hückel potential [22, p. 8] φ(r) = Q r exp ( ). (2.4) 4πɛ 0 r λ D Therefore quasi-neutrality of a plasma is fulfilled on macroscopic scales larger than the Debye length. If electrons are displaced from the ions, for example by an external electromagnetic wave, the resulting electric field will pull them back towards their equilibrium position 3. But due to their inertia, the electrons will be driven behind the equilibrium position and will be displaced in the opposite direction [44, p. 126]. The resulting equation of motion is the one of a harmonic oscillator [44, p. 127]. The electrons will therefore oscillate around the ions with the electron plasma frequency [23, p. 33] where m e is the electron mass. ω pe = n e e 2 ɛ 0 m e 56.4 n e, (2.5) In the presence of an electromagnetic field, the corresponding force on a charged particle is given by the Lorentz force [23, p. 28] F L = q( E + v B), (2.6) where q is the particle charge, v the particle velocity and E and B the electric and magnetic field, respectively. In case a velocity component of the charged particle is perpendicular to the magnetic field, the particle will gyrate around the field lines with the Larmor radius [23, p. 28] 3 The ions are assumed to be stationary due to their higher inertia. r L = mv qb, (2.7)

14 2.1. Plasma 5 where m is the particle mass and v the velocity component perpendicular to the magnetic field. Finally, to interact as an ideal plasma, the following three conditions have to be fulfilled [8, p. 10]: 1. The Debye length has to be much smaller than the extension of the plasma. 2. The number of particles within a Debye sphere 4 has to be large to assure collective behaviour. 3. The plasma frequency has to be bigger than the collision frequency of neutral atoms and molecules, so that electromagnetic forces determine the motion within the plasma system Solar wind and Jovian magnetospheric plasma Different from Earth atmosphere, the solar corona is due to its high temperature unstable and therefore emits corpuscular radiation into the interplanetary space [30, p. 150]. This radiation consists mainly out of electrons and protons and is known as solar wind. Less than 5 % of the ions are alpha particles [42, p. 12]. The solar wind has a fast component with speeds between 400 km/s to 800 km/s and a slow component with speeds between 250 km/s to 400 km/s [30, p. 150 f.]. However, average solar wind parameters at Earth and Jupiter location are given in table 2.1. Table 2.1: Average solar wind plasma environment at Earth orbit and Jupiter orbit. The values at Jupiter orbit are not measured but derived by scaling [42, p. 12] At Earth (1 AU) At Jupiter (5.2 AU) Density [cm 3 ] Speed [ km ] s T p [ev] T e [ev] Jupiter s magnetosphere is the largest planetary magnetosphere within the solar system and is formed by interaction with the solar wind. In figure 2.1 a schematic view of the magnetosphere is displayed. The surface where the solar wind approaches the magnetospheric environment of Jupiter and drops to subsonic speed is called bow shock [30, p. 225]. Its distance from Jupiter is varying between 55 to 125 Jupiter radii (R J = km) and is strongly dependent on the solar activity [18]. The magnetosheath is a transition region between bow shock and magnetopause, whereas the magnetopause separates the planetary plasma from the solar wind and is the outer boundary of the magnetosphere [30, p. 221]. 4 The number of particles within a Debye sphere is the so called plasma parameter and can be calculated 4 with N D = n 0 3 πλ3 D [8, p. 8].

15 6 Theoretical Background Figure 2.1: Noon-midnight cross-section through the Jovian magnetosphere. [7, p. 594] On the opposite side, the so called nightside, a long magnetotail extends over more than 700 Jupiter radii 5 [7, p. 595]. Jupiter s magnetosphere can roughly be divided into three regions, termed inner, middle and outer magnetosphere [7, p. 593]. The satellite Io is orbiting at 5.9 R J within the inner region, which is extending up to 10 R J [7, p. 593]. Due to Io s volcanic activity, it is blowing a lot of mass into its atmosphere. When it reaches the Jovian magnetosphere, ionization process arise producing plasma which is mainly consisting of sulphur and oxygen ions. This phenomenon is believed to be the origin of most of the plasma [7, p. 561 and 597]. The plasma in the inner magnetospheric region is very dense and is corotating with the planet [7, p. 516]. Due to centrifugal forces, the plasma is slowly distributed also in the middle magnetospheric region, which is placed between 10 and 40 R J [7, p. 593]. Densities within this region are considerably lower and the plasma azimuthal velocity is smaller than the corotational speed [7, p. 593]. At a distance greater than 40 R J the outer magnetospheric region is placed [7, p. 593]. Here the plasma azimuthal velocity is less than half of the corotational velocity and plasma densities are further decreasing [7, p. 595]. 5 The magnetotail was observed to extend even to Saturn s orbit [7, p. 595].

16 2.2. Spacecraft-plasma interactions 7 Specific data of the plasma environments such as densities, ion types, energies and azimuthal velocities within the Jovian magnetosphere can be found in references [7, p. 593] and [10]. 2.2 Spacecraft-plasma interactions Current balance equation Depending on the environmental plasma, solar flux and spacecraft geometry and material, a spacecraft charges to a specific equilibrium potential, termed floating potential. In this subchapter the current balance equation of a spacecraft is derived and discussed. If the spacecraft potential is in equilibrium, the net current I net of the spacecraft is zero and therefore the emitted and collected currents I emitted and I collected of the spacecraft are balanced, so I net (V floating ) = I collected I emitted = 0, (2.8) where V floating is the floating potential. The emitted current is composed by secondary electron emission current I sec 6, which is caused by electron and ion impacts, backscattered electron current I be, photoelectron current I phe and artificial generated current I a, for example from charged particle emitter or ion thrusters. This gives I emitted = I sec + I be + I phe + I a. (2.9) The collected current is given by the incidental environmental electron (index e) and ion (index i) current I e and I i, respectively. The energy of emitted photoelectrons and secondary electrons is given by a Maxwellian distribution with characteristic energies of 2 ev for secondary electrons [49, p. 1211] and 3 ev for photoelectrons [42, p. 14]. Due to these low energies, the emitted electrons can be recollected by the spacecraft, which gives a third collected current term I re. Therefore the total collected current is I collected = I e + I re I i. (2.10) Putting equation 2.9 and 2.10 in equation 2.8, the net current at floating potential is given by I net (V floating ) = I e + I re I i I sec I be I phe I a = 0. (2.11) 6 Secondary electron emission due to ion impact is not active in SPIS v [29] although the function exists already in the global parameters. Because secondary emission by electron impact is more efficient [39, p. 23] the error by neglecting secondary emission by ion impact is in general small.

17 8 Theoretical Background Ion wake formation In space plasmas the flow is usually considered to be mesosonic, which is mathematically defined as [23, p. 35] u e u i 1 and 1, (2.12) v the v thi where u is the electron (index e) and ion (index i) drift speed and v th their thermal speed. Therefore, in mesosonic plasma flow the plasma speed relative to the spacecraft exceeds the thermal speed of the ions but not the thermal speed of the electrons. This will cause an ion wake behind the spacecraft which is filled with electrons. For a theoretical description of the wake formation in mesosonic flow we have to distinguish between a positive and a negative charged spacecraft. Two different wakes can be caused by a positive charged spacecraft, namely narrow and enhanced wakes. Both wake types are displayed in figure 2.2. Figure 2.2: Schematic figure of a narrow (a) and an enhanced ion wake (b) in mesosonic flow. [9]

18 2.2. Spacecraft-plasma interactions 9 Narrow wakes form if the conditions [9] m i u 2 i 2 > kt i and mu 2 i 2 ev sc (2.13) are fulfilled, with m i the ion mass, k the Boltzmann constant, T i the ion temperature, e the elementary charge and V sc the spacecraft potential. On the other side, enhanced wakes form if [9] kt i < m iu 2 i 2 < ev sc. (2.14) In case of an enhanced wake, the size and shape is not preliminary determined by the spacecraft structure. Since the potential energy of the spacecraft exceeds the ion drift energy, ions cannot reach the spacecraft. Therefore the ion wake is dependent on the equipotential surface at which the plasma potential reaches m iv i 2e [9]. Compared to a positive charged spacecraft, a negative one leads to a decreased wake region [9]. Dependent on spacecraft voltage and ratio of electron to ion temperature, ions are focused behind the spacecraft and fill the wake region [24].

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20 CHAPTER 3 Spacecraft Plasma Interaction System - SPIS In this chapter an introduction to SPIS is given and the solving mechanism is explained. Anyway, a guide how to use SPIS can be found in appendix D. 3.1 Background In order to exchange knowledge regarding spacecraft-plasma interactions and spacecraft charging between experts all over Europe, the Spacecraft Plasma Interaction Network in Europe, termed SPINE, was founded. The community was interested in a tool to simulate spacecraft-plasma interactions. Due to this reason, the prototype simulation software PicUp3D was developed in the object-oriented programming language Java, sponsored by ESA, IRF, CNRS and CNES [13, 12]. To fully meet the requirements of the SPINE community, the next generation software Spacecraft Plasma Interaction System, termed SPIS, was developed in Java on behalf of the European Space Agency by ONERA, Artenum and the Université Paris Diderot - Paris VII in 2002 [4]. As PicUp3D, also SPIS is an open source project and is released under the terms of the GNU General Public Licence. 3.2 Solving mechanism Two different matter models are currently implemented in SPIS: A particle-in-cell (PIC) model as well as a model using Maxwell-Boltzmann distribution of the particles. The kinetic PIC plasma model is simplifying the complexity of the simulation by using so called superparticles. A huge number of real physical particles are placed into charged superparticles which are then moved due to the electromagnetic forces within the simulation box. It is the classical approach to solve charging problems and is therefore used for all simulations performed in this thesis. 11

21 12 Spacecraft Plasma Interaction System - SPIS The equations of motion which have to be solved are [11, 13] d p dt = F L = q( E + v B) and d x dt = v, (3.1) where p is the momentum, t the time, F the Lorentz force, q the charge, E the electric field, v the velocity, B the magnetic field and x the place. Two different particle trajectory integration methods are implemented in SPIS to derive place and velocity of the superparticles. An exact integration is used in case of a uniform electric field and in absence of a magnetic field in each cell [45]. In all other cases the Runge- Kutta Cash-Karp method is used [45]. A uniform external magnetic field, e.g. from a planetary magnetosphere, within the simulation box can be given as an input in the global parameter editor in SPIS-UI, whereas the electric field is calculated with the help of the Poisson equation [13, 11] φ = ρ ɛ 0 = q in i en e ɛ 0 and E = φ, (3.2) where φ is the potential, ρ the charge density, ɛ 0 the vacuum permittivity, q i and e the ion respectively the electron charge and n i and n e the ion (index i) and electron (index e) density. Note that in case of a Maxwell-Boltzmann matter model, a non linear Poisson equation has to be solved. It is given by [46] φ = q in i en e exp( eφ kt e ) ɛ 0, (3.3) where k is the Boltzmann constant and T e the electron temperature. To derive charge densities, the real physical particles which are placed within a superparticle are deposit linearly to the four nodes of the meshing tetrahedron 1 in which the particular superparticle is placed [45]. 1 The meshing with tetrahedrons is explained in appendix D.

22 CHAPTER 4 Europa Jupiter System Mission - Laplace 4.1 Mission concept The Europa Jupiter System Mission (EJSM-Laplace) was a planned collaboration between ESA and NASA to investigate the entire Jovian system. Due to NASA s financial budget the proposed common mission is likely to be dropped [1]. Nevertheless, in the following EJSM-Laplace is explained in more detail, because future missions to Jupiter will be based on it. The three main scientific objectives were [43, p. 4]: 1. Characterize Ganymede as a planetary object including its potential habitability 2. Explore Europa to investigate its habitability 3. Explore the Jupiter system as an archetype for gas giants However, the four Galilean moons Callisto, Europa, Ganymede and Io were the main points of interest and especially the first three, since they contain large amount of ice and are suspected to have subsurface oceans in which life could exist [33, 17, 31]. Their supposed internal structures can be seen in figure 4.1. EJSM-Laplace consisted of two sister satellites which are termed Jupiter Ganymede Orbiter (JGO) and Jupiter Europa Orbiter (JEO). Both satellites would have been independently developed, manufactured, launched - probably in and operated [43, p. 3], JGO under the responsibility of ESA and JEO led by NASA. After 6 years cruise and Venus-Earth-Earth fly-bys to save power and propellant mass, JGO would have been inserted into an elliptical orbit around Jupiter and would have performed measurements of atmosphere and inner magnetosphere of the gas giant [43, p. 69]. Afterwards, in the so called Callisto phase, JGO would have performed during about 13 13

23 14 Europa Jupiter System Mission - Laplace months 10 fly-bys of the moon Callisto at an altitude of about 200 km and 1200 km (last flyby) [43, p. 96] allowing to investigate its structure, surface and exosphere [43, p. 69]. Since Ganymede has an intrinsic magnetic field, which was discovered by the Galileo spacecraft [16], the transfer to Ganymede (about 240 days) would have been used to determine its interaction with the much stronger magnetic field of Jupiter in which it is buried [43, p. 69]. During all those phases also investigations of further moons were planned. Finally, JGO would have been inserted into an orbit around Ganymede [43, p. 68ff.], which would have allowed to make a detailed investigation of this icy moon. Figure 4.1: Supposed internal structures of Io (top left), Europa (top right), Ganymede (bottom left) and Callisto (bottom right). One can clearly see the suspected subsurface oceans (blue colour) of the last three. [2] Due to expected synergistic science, also JEO was planned to be launched in early 2020 and would have cruised within 6 years to Jupiter by using Venus-Earth-Earth fly-bys [5, p ]. A lot of possible trajectories were investigated [5, p ]. After orbit injection around Jupiter at least three Io encounters to monitor its high temperature volcanic activity, which is induced by tidal heating [5, p ], and several encounters of the other three Galilean moons Europa, Ganymede and Callisto were planned [5, p ]. The final orbit around Europa would have been at very low altitude of 100 km to 200 km with an inclination of 95 to 100 degrees because of scientific instrument requirements and mission constraints [5, p ].

24 4.2. Jupiter Ganymede Orbiter 15 Due to operation of both spacecraft together in the Jovian environment, complementary and synergistic science would have lead to an enhanced and remarkable science return [43, p. 26] which would have significantly increased the current knowledge of gas giants and their habitability. Currently ESA investigates possibilities to achieve science goals of the EJSM-Laplace mission by a new ESA-led mission. For this new mission an orbiter called JUpiter ICy moon Explorer (JUICE) is planned. It might be similar to the Jupiter Ganymede Orbiter discussed earlier, therefore JGO is used as a model for the upcoming simulations. To see the impact of the huge solar panels of JGO, modelling of JEO is also performed. 4.2 Jupiter Ganymede Orbiter The Jupiter Ganymede Orbiter design was not completely fixed. Out of three different proposed designs, two were still in competition [27]. Those two will be explained in more detail in the next upcoming subsections. Due to confidential reasons, the configurations of the orbiters are not published in very detail, just main dimensions and simplified illustrations were available Design proposal 1 A simplified illustration of the first design proposal can be seen in figure 4.2. Figure 4.2: Simplified illustration of the first proposed design of the Jupiter Ganymede Orbiter. [43, p. 105]

25 16 Europa Jupiter System Mission - Laplace On the spacecraft main structure, which has dimensions of 2.25 m 1.70 m 3.13 m (x y z), two huge solar arrays with a total area of 64 m 2 (2 32 m 2 ) are mounted (±Y-side) and are able to rotate around the Y-axis [43, p. 104]. Each solar array consists of four panels, their configuration can be seen in figure 4.2 [43, p. 104 ff.]. The maximum width of an array is m and the total span of the whole satellite is m [43, p. 104]. A high gain antenna with a diameter of 3.2 m is fixed on the -X-side, whereas on the opposite side (+X) the remote-sensing and in-situ instruments are placed [43, p. 104 f.]. The main engine is situated on the -Z-side and the cold plate on the +Z-side [43, p. 105] Design proposal 2 The second design proposal of the Jupiter Ganymede Orbiter can be seen in figure 4.3. Figure 4.3: Simplified illustration of the second design solution of the Jupiter Ganymede Orbiter. [43, p. 108] The satellite consists of a main body with a size of 1.56 m 1.56 m 2.68 m (x y z) [43, p. 108 ff.]. Remote-sensing instruments (+X-side), in-situ instruments (-X-side), main engine (-Z-side) and a high gain antenna with a diameter of 3.5 m (+Z-side) are mounted on the different sides of the satellite [43, p. 108 ff.]. Electric power is generated by two huge rectangular solar arrays (±Y-side) which have a total area of 72 m 2 (2 36 m 2 ) and are moveable around the Y-axis [43, p. 108]. Two service modules on the ±X-side have tilted surfaces which have high emissivity white paint of an area of 1.44 m 2 to provide temperature stability [43, p. 110].

26 4.3. Jupiter Europa Orbiter Jupiter Europa Orbiter About the Jupiter Europa Orbiter which is displayed in figure 4.4 even less information are publicly available than for the Jupiter Ganymede Orbiter. Figure 4.4: Design configuration of the NASA led Jupiter Europa Orbiter. [5, p ] Specific dimensions about the spacecraft are not given, therefore the following spacecraft size is estimated from pictures given in reference [5, p ]. The JEO main body has a length of about 3.5 m and a maximum and minimum diameter of 2.3 m and 1.4 m, respectively. A two axes steerable 3 m high gain antenna [5, p ] is fixed to the main structure by a 2.8 m long retractable boom [5, p ]. On the nadir facing side (bottom in the picture 4.4) a magnetometer and a low gain antenna are placed, whereas on the opposite spacecraft side the main engine is fixed. The power is generated, in opposite to the solar cells on the Jupiter Ganymede Orbiter, by a radioisotope power source [5, p ].

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28 CHAPTER 5 Modelling Before running a simulation, the Jupiter Ganymede Orbiter and the Jupiter Europa Orbiter have to be modelled. Their model is built with the help of Gmsh, an open source CAD and 3D meshing tool which is implemented in SPIS. In the upcoming sections the realisation of the models of the different orbiters is explained in more detail. The displayed coordinate systems and facing sides of the solar panels may differ from chapter 4. Those displayed in this chapter are the coordinate systems used in the simulations. 5.1 Jupiter Ganymede Orbiter - Proposal 1 The model of the first proposed Jupiter Ganymede Orbiter (see chapter 4.2.1) is shown in figure 5.1. The spacecraft is placed within three simulation boxes. The outer box is used to set the boundary of the simulated plasma volume in SPIS and the two inner ones are needed to improve the resolution and to control the growing of the mesh within the plasma volume, near the spacecraft. This is done by setting a characteristic length (as explained in appendix D) to limit the tetrahedron size used for the meshing. The outer simulation box is chosen to be always at least some Debye length away from each spacecraft part. Mesh size and simulation box have to be always adjusted to the particular simulation. In figure 5.2 a two dimensional mesh of the Jupiter Ganymede Orbiter is displayed. One can clearly see the growing of the mesh when going from the spacecraft surface to the outer simulation box. However, for better visualisation not the whole outer simulation box is displayed and a 2D instead of a 3D mesh, which is used during simulations, is chosen. The dimensions of the model are derived from the dimensions given in chapter and are as follow. The main body has a size of 2.25 m x 1.70 m x 3.13 m. The 3.2 m high gain antenna is not directly connected to the spacecraft main structure due to modelling limitations of Gmsh, but by assigning the same electrical node to structure and antenna the surface charge is distributed equally, setting both to the same electric potential. The solar panels are connected to the main body by a 0.1 m m 0.1 m long boom. They have a length of m, a minimum width of m (extending over m length), 19

29 20 Modelling and a maximum width of m (extending over m length). Furthermore, they are 10 cm thick. Figure 5.1: Model of the first design proposal of the Jupiter Ganymede Orbiter (see chapter 4.2.1) placed in a simulation box (outer box). The two inner boxes are used to control the mesh size. Figure 5.2: 2D mesh of the first proposal of the Jupiter Ganymede Orbiter within its simulation box. The outer simulation box is due to better visualisation not completely displayed.

30 5.2. Jupiter Ganymede Orbiter - Proposal 2 21 Instrumentation, low gain antennas and magnetometer are neglected in the model because their size and placement on the spacecraft are unknown. Furthermore, their influence on the charging of the spacecraft is small compared to the huge solar panels, the main body and the high gain antenna. In addition, they would significantly increase the complexity of the simulation which would lead to an increased simulation time. The sun facing side of the solar panels (-Z-side) is modelled with CERS (cerium doped silicon with MgF 2 coating), whereas all other surfaces are coated with conductive ITO (indium tin oxide). 5.2 Jupiter Ganymede Orbiter - Proposal 2 In figure 5.3 the second designed model of the Jupiter Ganymede Orbiter (see chapter 4.2.2) is displayed. The simulation box and the two other boxes used during simulations (as described in chapter 5.1) are not displayed for better visualisation. Figure 5.3: 2D meshed model of the second design proposal of the Jupiter Ganymede Orbiter (see chapter 4.2.2). The model consists of a 1.56 m 1.56 m 2.68 m main body and a 3.5 m high gain antenna as the proposed design configuration which is described in chapter As described in chapter 5.1, here also the antenna is not connected to the main body, but both have the same electrical node. The solar panels facing to the ±X-side have a size of 0.1 m 18 m 2 m. This is derived from the total area given in chapter The solar panels are connected by a 0.1 m 1.12 m 0.1 m boom to the main structure. Instruments, low gain antennas and magnetometer are neglected in the model. The sun facing side of the solar panels (-X-side) is modelled with CERS. On the ±X-side of the main structure two areas of a size of 1.44 m 2 each are modelled with conductive white paint PCB-Z. All other surfaces of the spacecraft are coated with conductive ITO.

31 22 Modelling 5.3 Jupiter Europa Orbiter The model of the Jupiter Europa Orbiter is very rough because information about the spacecraft are rare. It is modelled as a 3.5 m long cylinder with a diameter of 1.4 m, which extends after a length of 2.9 m linearly to a diameter of 2.3 m. A 2.8 m long boom is modelled between the 3 m high gain antenna and the main structure with small spaces between structure and boom, as well as between boom and antenna due to modelling reasons. But all elements are assigned to the same electrical node setting everything to the same surface potential. Instrumentation, magnetometer and antennas are neglected in the model. The model of the Jupiter Europa Orbiter is displayed in figure 5.4, neglecting the simulation box and two other boxes used for improvement of the mesh. The surface of the model is covered with conductive ITO. The Sun is modelled in the -X-direction. Figure 5.4: 2D meshed model of the Jupiter Europa Orbiter.

32 CHAPTER 6 Simulations In this chapter the charging and wake formation of the two Jupiter Ganymede Orbiters (JGO1 1 and JGO2 2 ), and the Jupiter Europa Orbiter (JEO) in solar wind plasma at Earth and Jupiter are discussed. Moreover, simulations of the JGO2 are performed in the Jovian magnetosphere. Finally, an error estimation is given. The complete simulation inputs are attached in appendix B. 6.1 Solar wind plasma Solar wind at Earth Simulations in average solar wind plasma conditions at Earth orbit are performed, taking into account a plasma density of 8.7 cm 3, an electron temperature of 8.6 ev, a proton temperature of 10.3 ev and a proton drift velocity of 468 km/s (see table 2.1 in chapter 2.1.2). This corresponds to a Debye length of 5.5 m. Secondary electrons and photoelectrons are emitted with 2 ev and 3 ev, respectively. In figure 6.1 the plasma potential around the JGO1 is displayed [Simulation name: TR3001b]. The solar UV is directed towards +Z direction, in the same direction as the plasma flow. The spacecraft is charged to a potential of 9.98 V. Behind the spacecraft in the opposite direction of the Sun, within the ion wake, a negative potential barrier is placed. This can be better seen in figure 6.2, where the displayed potential is limited to 0.5 V, so every higher potential is shown as 0.5 V. It is found that photoelectron emission is the most important charging factor at 1 AU, driving the floating potential of the spacecraft positive. The negative potential barrier behind the spacecraft is due to the ion wake. As the protons flow in +Z direction, the density of protons behind the spacecraft is much lower than the electron density due to their smaller thermal speed compared to their drift speed. This leads to a maximum negative potential of V behind the main body. The proton charge density is displayed in figure JGO1 corresponds to the model out of chapter JGO2 corresponds to the model out of chapter

33 24 Simulations Figure 6.1: Plasma potential around the JGO1 in solar wind plasma at Earth orbit. Solar UV is directed towards +Z direction, in the same direction in which the plasma flows. [Simulation name: TR3001b] Figure 6.2: Plasma potential around the JGO1 in solar wind plasma at Earth orbit. For better visualisation the displayed potential is limited to 0.5 V, which means that every higher potential is displayed as 0.5 V. Solar UV is directed towards +Z direction, in the same direction in which the plasma flows. One can clearly see the negative potential barrier behind the spacecraft. Its form is caused by the spacecraft shape. [Simulation name: TR3001b]

34 6.1. Solar wind plasma 25 Figure 6.3: Proton charge density around the JGO1 in solar wind plasma at Earth orbit. Solar UV is directed towards +Z direction, and also the protons flow in +Z direction, leading to an ion wake behind the spacecraft. In front of the spacecraft small accumulations of protons with densities of up to m 3 can be found, but for better visualisation the legend is limited to a maximum proton density of 10 7 m 3. [Simulation name: TR3001b] The ion wake extends far into space and has at a distance of 45 m behind the spacecraft main body an ion density of 6.6 cm 3 and behind the huge solar panels a minimum ion density of 5.1 cm 3 (compared to ambient ion density of 8.7 cm 3 ). However, the wake does not increase significantly in width and a constant density can be found in front of the spacecraft, therefore it can be described as narrow. Furthermore, it satisfies formula out of chapter for narrow wakes. Similar results compared to the JGO1 in solar wind at Earth orbit are obtained for the JGO2 [Simulation name: TR1001b] due to the related design. The JGO2 is expected to charge to a surface potential of V. In the JGO2 simulation, the solar UV and plasma flow is directed towards +X direction. The plasma potential around the orbiter is displayed in picture 6.4 and 6.5, whereas the ion charge density can be found in figure 6.6. As it can be seen, the ion wake behind the spacecraft is of narrow type because it does not increase in width and a maximum negative potential behind the main body of V can be found. 3 m iu 2 i 2 = J > J = kt i and mu2 i 2 = J J = ev sc

35 26 Simulations Figure 6.4: Plasma potential around the JGO2 in solar wind plasma at Earth orbit. Solar UV and plasma flow are directed towards +X direction. [Simulation name: TR1001b] Figure 6.5: Plasma potential around the JGO2 in solar wind plasma at Earth orbit. For better visualisation the displayed potential is limited to 0.5 V, which means that every higher potential is displayed as 0.5 V. Solar UV and plasma flow are directed towards +X direction. One can clearly see the negative potential barrier behind the spacecraft. [Simulation name: TR1001b]

36 6.1. Solar wind plasma 27 Figure 6.6: Proton charge density around the JGO2 in solar wind plasma at Earth orbit. Solar UV is directed towards +X direction, and also the protons flow in +X direction, leading to an ion wake behind the spacecraft. In front of the spacecraft small accumulations of protons with densities of up to m 3 can be found, but for better visualisation the legend is limited to a maximum proton density of 10 7 m 3. [Simulation name: TR1001b] Compared to both Jupiter Ganymede Orbiters, the Jupiter Europa Orbiter [Simulation name: TR2002b] charges in solar wind at 1 AU to a lower potential of about 8.11 V because photoelectrons are emitted from a smaller surface area relative to the overall spacecraft surface area. The plasma potential around the JEO in solar wind at Earth orbit is displayed in figure 6.7 and 6.8. Solar UV and plasma flow are directed in +X direction. In picture 6.9 the ion charge density is displayed. Since the spacecraft dimension is much smaller than the one of the Jupiter Ganymede Orbiters, the extension of the narrow ion wake is smaller and therefore the potential drop behind the JEO is not as significant as in previous cases. However, still a maximum negative potential wake barrier behind the spacecraft main body of V can be found.

37 28 Simulations Figure 6.7: Plasma potential around the JEO in solar wind at 1 AU. Solar UV and plasma flow are directed in +X direction. [Simulation name: TR2002b] Figure 6.8: Plasma potential around the JEO in solar wind at 1 AU. For better visualisation the displayed potential is limited to 0.5 V, so every higher potential is displayed as 0.5 V. Solar UV and plasma flow are directed in +X direction. [Simulation name: TR2002b]

38 6.1. Solar wind plasma 29 Figure 6.9: Proton charge density around the JEO in solar wind plasma at Earth orbit. Solar UV and plasma flow are directed towards +X direction, which leads to an ion wake behind the spacecraft. In front of the spacecraft small accumulations of protons with densities of up to m 3 can be found, but for better visualisation the legend is limited to a maximum proton density of 10 7 m 3. [Simulation name: TR2002b] A summary of all performed simulations in solar wind at 1 AU is displayed in table 6.1. Table 6.1: Summary of obtained results for JGO1, JGO2 and JEO in solar wind plasma environment at Earth JGO1 JGO2 JEO Spacecraft average surface potential [V] Potential barrier in wake behind main body [V] Wake description narrow ion wake narrow ion wake a narrow ion wake b Simulation name TR3001b TR1001b TR2002b a Condition(formula 2.13) satisfied with evsc = J m i u2 i 2 b Condition(formula 2.13) satisfied with evsc = J m i u2 i 2 = J > J = kt i = J > J = kt i

39 30 Simulations Solar wind at Jupiter As the EJSM orbiters will also encounter the solar wind plasma environment close to Jupiter orbit, charging in solar wind at 5.2 AU is simulated. The average solar wind plasma at Jupiter orbit has a density of 0.32 cm 3, which is more than 27 times smaller compared to the solar wind density at Earth orbit. The electron temperature of 8.6 ev, the proton temperature of 10.3 ev and the proton drift velocity of 468 km/s (see table 2.1 in chapter 2.1.2) stay the same. This leads to a Debye length of 28.5 m. Secondary electrons and photoelectrons are emitted with 2 ev and 3 ev, respectively. In figure 6.10 the plasma potential around the JGO1 is displayed [Simulation name: TR3000b]. The solar UV is directed towards +Z direction, in the same direction as the plasma flow. The spacecraft charges to V. Although the distance towards the Sun is bigger compared to simulations in chapter 6.1.1, and therefore the emission of photoelectrons is lower, photoelectron emission is still the main charging factor because the ambient plasma density is very low. The potential drop-off along the Z-axis is plotted in figure Compared to the charging of the JGO1 in solar wind at Earth, no negative potential wake is visible within the simulation box, although a narrow ion wake is observed in figure This can be explained by the low plasma density. The electrons within the wake shield the spacecraft potential, but are not dense enough to introduce a negative potential wake. As in solar wind at Earth, also at Jupiter the ion wake is narrow. Similar results as for the JGO1 are obtained for the JGO2 and the JEO, and are displayed in table 6.2. In all cases no negative potential barrier in the wake can be observed, but the spacecraft potentials are similar to the results obtained in solar wind at Earth (compare with table 6.1). However, in all cases slightly higher positive potentials are observed. Those can be explained by the absence of the negative potential barrier in wake direction, which leads to less recollected secondary electrons and photoelectrons.

40 6.1. Solar wind plasma 31 Figure 6.10: Plasma potential around the JGO1 in solar wind at Jupiter orbit. The solar UV is directed towards +Z direction, in the same direction as the plasma flow. The potential distribution around the JGO1 is symmetric and no negative charged wake is visible due to the low ambient plasma density. [Simulation name: TR3000b] Figure 6.11: Plot of the potential along the Z-axis of figure 6.10 for the JGO1 in solar wind at Jupiter orbit. [Simulation name: TR3000b]

41 32 Simulations Figure 6.12: Ion charge density around the JGO1 in solar wind at Jupiter. The solar UV is directed towards +Z direction, in the same direction in which the plasma flows. The legend is limited to an ion charge density of 0.4 cm 3, and therefore very small accumulations of ions up to 2.2 cm 3 are neglected in front of the spacecraft for better visualisation. [Simulation name: TR3000b] Table 6.2: Summary of obtained results for JGO1, JGO2 and JEO in solar wind plasma environment at Jupiter JGO1 JGO2 JEO Spacecraft average surface potential [V] Potential barrier in wake behind main body [V] Wake description narrow ion wake a narrow ion wake b narrow ion wake c Simulation name TR3000b TR1000.2b TR2000b a Condition(formula 2.13) satisfied with evsc = J m i u2 i 2 b c Condition(formula 2.13) satisfied with evsc = J m i u2 i 2 Condition(formula 2.13) satisfied with evsc = J m i u2 i 2 = J > J = kt i = J > J = kt i = J > J = kt i

42 6.2. Jovian magnetospheric plasma Jovian magnetospheric plasma JGO2 at the orbit of Ganymede The EJSM orbiters will also enter the Jovian magnetosphere. Therefore, simulations of the JGO2 at a radial distance of about 15 Jupiter radii from Jupiter, at the orbit of the satellite Ganymede are performed. For simulation of the plasma environment just the cold electron population is taken into account. Taking into account also the hot electron population would increase significantly the simulation time. Furthermore, taking an average would give too much weight for the electron temperature to the hot population. Thus, the following plasma parameters are used: The plasma density is 4.5 cm 3 [10], the electron temperature 20 ev [10], the ion temperature of the oxygen ions [7, p. 516] is 60 ev [7, p. 516] and the plasma azimuthal speed 150 km/s [7, p. 516]. This corresponds to a Debye length of 13.6 m. Secondary electrons and photoelectrons are emitted with 2 ev and 3 ev, respectively. Depending on the local time, four different charging cases with respect to plasma velocity direction and photoelectron emission are simulated. Those are displayed in figure Figure 6.13: Plasma and radiation environment of the JGO2 in an orbit at a radial distance of 15 R J around Jupiter dependent on the local time. At midnight and noon local time, the plasma velocity direction is parallel to the solar panels. Contrary to the noon case, at midnight the spacecraft cruises through the planetary shadow and hence no photoelectrons are emitted. At 6 h and 18 h, the plasma flux is perpendicular to the solar panels. At 6 h the photoelectrons are emitted within the ion wake because photon velocity vector and ion velocity vector have

43 34 Simulations opposite directions, whereas at 18 h they have the same direction and therefore photoelectrons are emitted in ram direction. In figure 6.14 and 6.15 the plasma potential around the spacecraft at 6 h [Simulation name: TR1007b] and 18 h [Simulation name: TR1005.1b] local time are displayed. In both cases the solar UV is directed in +X direction, but at 6 h the plasma flows in -X direction, whereas at 18 h it flows in +X direction. Figure 6.14: Plasma potential around the JGO2 at a radial distance of 15 R J from Jupiter within Jupiter s magnetosphere at 6 h local time. The solar UV is directed towards +X direction and the incidental plasma flows in -X direction. [Simulation name: TR1007b] The spacecraft charges at 6 h to an electric surface potential of 1.96 V and at 18 h to 1.97 V, but due to different ion flow directions a negative potential wake can be found on opposite sides of the spacecraft. However, also in ram direction a small negative potential barrier is placed due to photoelectron and secondary electron emission. For both cases, the plasma potential along the X-axis (out of figure 6.14 and 6.15) is plotted in figure Although wake and ram direction in both cases changes, the potential shape and amplitude stay similar. The negative potential barrier in ram direction behind the spacecraft main body is for both cases V, whereas the maximum negative potential in wake direction is V at 6 h and V at 18 h. The corresponding ion wake for the 6 h and 18 h case is displayed in picture 6.17 and 6.18, respectively. In both cases it is of narrow type.

44 6.2. Jovian magnetospheric plasma 35 Figure 6.15: Plasma potential around the JGO2 at a radial distance of 15 R J from Jupiter within Jupiter s magnetosphere at 18 h local time. The solar UV and the plasma flow are directed towards +X direction. [Simulation name: TR1005.1b] Figure 6.16: Plasma potential along the X-axis out of figure 6.14 (6 h case) and 6.15 (18 h case). The spacecraft are placed at X=0.

45 36 Simulations Figure 6.17: Ion charge density around the JGO2 at a radial distance of 15 R J from Jupiter within Jupiter s magnetosphere at 6 h local time. The solar UV is directed towards +X direction and the incidental plasma flows in -X direction. The legend is limited to an ion charge density of 5 cm 3, and therefore very small accumulations of ions up to 28 cm 3 are neglected in front of the spacecraft for better visualisation. [Simulation name: TR1007b] Figure 6.18: Ion charge density around the JGO2 at a radial distance of 15 R J from Jupiter within Jupiter s magnetosphere at 18 h local time. The solar UV and the plasma flow are directed towards +X direction. The legend is limited to an ion charge density of 5 cm 3, and therefore very small accumulations of ions up to 10 cm 3 are neglected in front of the spacecraft for better visualisation. [Simulation name: TR1005.1b]

46 6.2. Jovian magnetospheric plasma 37 At noon local time, the spacecraft charges to an electric potential of 1.88 V [Simulation name: TR1008.3b]. The potential barrier in ram direction is V and hence similar to the 6 h and 18 h case, whereas the potential barrier in wake direction is smaller with V, because the ions flow parallel to the solar panels in +Z direction, and therefore the ion wake is not well developed. This can be seen in figure 6.19 in which the narrow ion wake is displayed. Solar UV is directed towards +X direction. Figure 6.19: Ion charge density around the JGO2 at a radial distance of 15 R J from Jupiter within Jupiter s magnetosphere at noon local time. The solar UV is directed towards +X direction and the incidental plasma flows in +Z direction. The legend is limited to an ion charge density of 5 cm 3, and therefore very small accumulations of ions up to 20 cm 3 are neglected in front of the spacecraft for better visualisation. [Simulation name: TR1008.3b]

47 38 Simulations The spacecraft potential at midnight differs from previous simulations. As the spacecraft is in the planetary shadow, no photoelectrons are emitted. Due to the higher mobility of ambient electrons compared to oxygen ions, the spacecraft charges to a very high negative spacecraft potential of V [Simulation name: TR1006.2b]. The potential is symmetric around the spacecraft, slowly decreasing to 0 V in distance. As the cold electron population has a characteristic temperature of 20 ev, these low energetic electrons are reflected and deflected by the highly negative charged spacecraft, which will consequently cause inaccurate plasma density measurements. The drop in electron charge density around the negative charged JGO2 is displayed in figure The plasma flows in -Z direction. Figure 6.20: Electron charge density of incidental cold electron population around the JGO2 at a radial distance of 15 R J from Jupiter within Jupiter s magnetosphere at midnight local time. The incidental plasma flows in -Z direction. [Simulation name: TR1006.2b]

48 6.2. Jovian magnetospheric plasma 39 A summary of the obtained results in Ganymede orbit is given in figure Once again, we can observe similar spacecraft potentials at 6 h, noon and 18 h of 1.8 V to 2 V, whereas at midnight high negative charging of V occurs. All ion wakes for positive charged spacecraft are narrow 456. Figure 6.21: Summary of obtained simulation results in an orbit around Jupiter at 15 R J, showing expected spacecraft potential V S/C and potential barrier in wake (V wake ) and ram (V ram ) direction behind the spacecraft main body for the case of the JGO2. 4 Condition(eq. 2.13) satisfied for 6 h: ev sc = J miu2 i 2 = J > J = kt i 5 Condition(eq. 2.13) satisfied for 12 h: ev sc = J miu2 i 2 = J > J = kt i 6 Condition(eq. 2.13) satisfied for 18 h: ev sc = J miu2 i 2 = J > J = kt i

49 40 Simulations JGO2 at the orbit of Callisto Simulations of the JGO2-plasma interactions at a radial distance of about 26.3 Jupiter radii from Jupiter, at the orbit of the satellite Callisto are performed. For simulations of the plasma environment just the cold electron population is taken into account to reduce the complexity. Since its temperature is unknown, it is estimated with 100 ev [28]. The temperature of the atomic oxygen ions is set to 60 ev [7, p. 516], the plasma density to 0.15 cm 3 [7, p. 516] and the plasma azimuthal speed to 200 km/s [7, p. 516]. This corresponds to a Debye length of m. Secondary electrons and photoelectrons are emitted with characteristic energies of 2 ev and 3 ev, respectively. As seen in chapter 6.2.1, similar charging results are obtained at 6 h, noon and 18 h local time at a radial distance of 15 Jupiter radii. Therefore, for the Callisto case just two simulations are performed, one at 18 h and one at midnight local time (see picture 6.13 in chapter 6.2.1). In figure 6.22 the plasma potential around the JGO2 at 18 h local time is displayed [Simulation name: TR1205.1b]. Plasma flow and solar UV are directed towards +X direction. The spacecraft charges to an average surface potential of V. Figure 6.23 shows the ion charge density around, and the narrow ion wake behind the JGO2. Due to the low plasma density no negative potential wake is introduced, because the electrons within the ion wake shield the spacecraft potential but are not dense enough to introduce a negative potential wake. Photoelectron emission is the most important charging factor. Nevertheless, it should be noticed that the incidental thermal electrons charge the spacecraft rather positive than negative, because the secondary electron emission yield of ITO for isotropic flux of electrons with energies of 100 ev is [37]. The secondary electron emission yield of ITO for isotropic flux as a function of electron energy is displayed in figure Picture 6.25 shows the normalized photoelectron, secondary electron and thermal electron densities along the X-axis out of figure It can be seen that near the spacecraft surface (close to X=0), photoelectron and secondary electron densities exceed the thermal electron density, but fall off rapidly, whereas the thermal electron density stays constant. Photoelectrons can also be found behind the spacecraft in the shadow (positive X). This is because the emitted photoelectrons distribute around the spacecraft and can be recollected due to the high positive spacecraft potential.

50 6.2. Jovian magnetospheric plasma 41 Figure 6.22: Plasma potential around the JGO2 at a radial distance of 26.3 R J from Jupiter within Jupiter s magnetosphere at 18 h local time. Solar UV and the plasma flow are directed towards +X direction. [Simulation name: TR1205.1b] Figure 6.23: Ion charge density around the JGO2 at a radial distance of 26.3 R J from Jupiter within Jupiter s magnetosphere at 18 h local time. The solar UV and the plasma flow are directed towards +X direction. The legend is limited to an ion charge density of 0.18 cm 3, and therefore very small accumulations of ions up to 1.3 cm 3 are neglected in front of the spacecraft for better visualisation. [Simulation name: TR1205.1b]

51 42 Simulations Figure 6.24: Secondary electron emission yield for ITO as a function of electron energy considering isotropic flux. [37] Figure 6.25: Normalized photoelectron, secondary electron and thermal electron densities along the X-axis out of figure 6.23 for a simulation of the JGO2 at a radial distance of 26.3 R J from Jupiter within Jupiter s magnetosphere. Solar UV and the plasma flow are directed towards +X direction. Photoelectrons and secondary electrons rule the electron density near the spacecraft (close to X=0), whereas the thermal electron density is more important at distances bigger than 15 m from the spacecraft.

52 6.2. Jovian magnetospheric plasma 43 At midnight local time, during the eclipse, no photoelectrons are emitted from the spacecraft. However, as discussed above the secondary electron emission yield exceeds one, and hence also in the planetary shadow a positive spacecraft potential is expected. Simulation confirm this theory and show that the spacecraft charges at midnight local time to a positive average surface potential of 4.61 V [Simulation name: TR1206.2b]. A picture of the plasma potential around the JGO2 at midnight local time is displayed in figure The plasma flows in -Z direction parallel to the solar panels. Therefore the ion wake, which is shown in figure 6.27, is small and narrow. A summary of all simulations performed at 26.3 Jupiter radii is displayed in table 6.3. Figure 6.26: Plasma potential around the JGO2 at a radial distance of 26.3 R J from Jupiter within Jupiter s magnetosphere at midnight local time. The plasma flows in -Z direction parallel to the solar panels. [Simulation name: TR1206.2b]

53 44 Simulations Figure 6.27: Ion charge density around the JGO2 at a radial distance of 26.3 R J from Jupiter within Jupiter s magnetosphere at midnight local time. The plasma flows in -Z direction. The legend is limited to an ion charge density of 0.18 cm 3, and therefore very small accumulations of ions up to 3.5 cm 3 are neglected in front of the spacecraft for better visualisation. [Simulation name: TR1206.2b] Table 6.3: Summary of obtained results for the JGO2 at 18 h and midnight local time at 26.3 Jupiter radii distance from Jupiter 18 h midnight Spacecraft average surface potential [V] Potential barrier in wake behind main body [V] - - Wake description narrow ion wake a narrow ion wake b Simulation name TR1205.1b TR1206.2b a Condition(formula 2.13) satisfied with evsc = J m i u2 i J = kt i b Condition(formula 2.13) satisfied with evsc = J m i u2 i J = kt i = J > 9.6 = J > 9.6

54 6.3. Accuracy of simulations Accuracy of simulations To perform simulations within a reasonable amount of time, the complexity had to be decreased. This was done by neglecting hot electron populations especially in the Jovian magnetosphere, and by setting the interplanetary and planetary magnetic fields to zero. Hot electrons have usually a secondary electron emission yield bigger than one, which would drive the spacecraft potential to more positive values compared to our results. For the magnetic field, no impact on the simulations in solar wind are expected because the Larmor radii for thermal electrons and ions, as well as for secondary electrons and photoelectrons are several times bigger than the spacecraft and simulation box size for the simulated cases 7 (compare with [9]). The magnetic field strength in Jupiter s magnetosphere at 26.3 Jupiter radii distance from Jupiter, at the orbit of Callisto, is about 20 nt [7, p. 516], which leads to Larmor radii for photoelectrons and secondary electrons of m and m, respectively. Even closer to Jupiter, at about 15 Jupiter radii distance, the magnetic field is approximately 80 nt [7, p. 516], leading to Larmor radii for the photoelectrons of 73.0 m and for the secondary electrons of 59.6 m. These values are closer to the computation box size but still bigger than the spacecraft dimension, therefore the influence is expected to be small (compare with reference [9]). Besides the mentioned assumptions, several possible error sources have to be taken into account for estimating the accuracy of the simulations. One error source is the numerical noise, which is the main noise factor in PIC simulations. Theoretically, for a Maxwell-Boltzmann distribution, the particle density noise is proportional 1 to σ = NavP art, where N avp art is the average number of superparticles per cell [12]. Reducing the numerical noise by increasing N avp art is very expensive in terms of computing resources. Results for the spacecraft potential are fluctuating statistically in a maximum range of 200 mv for all simulations performed. The last problem which may influence the obtained results, is the introduced Fourier (mixed Dirichlet-Neumann) boundary condition at the simulation box boundary. It is used to simulate a potential decay with r 2 at the boundary, where r is the distance. To see the impact of the boundary, the simulation of the JGO2 at a radial distance of 15 Jupiter radii from Jupiter in the Jovian magnetosphere at 18 h local time (see chapter 6.2.1; [Simulation name: TR1005.1b]) is performed again within a bigger simulation box 8 [Simulation name: TR1005.4b]. Differences in average surface potential (1.97 V for simulation TR1005.1b and 1.99 V for simulation TR1005.4b), and potential barrier in ram (-0.33 V for simulation TR1005.1b and V for simulation TR1005.4b) and wake (-0.95 V for simulation TR1005.1b and V for simulation TR1005.4b) direction are very small and in the range of statistical fluctuations. Thus, no significant impact of the chosen boundaries on the simulations is expected. 7 Taking into account an interplanetary magnetic field strength of 1 nt at Jupiter orbit [7, p. 605] and of 5 nt at Earth orbit [26, p.196]. 8 The simulated plasma volume is increased by a factor of 5.8.

55

56 CHAPTER 7 Conclusion In this master thesis the spacecraft-plasma interactions for a future Jupiter mission were modelled. To do so, simulations with the help of the Spacecraft Plasma Interaction System (SPIS) for the cases of the Jupiter Ganymede Orbiter (JGO) and the Jupiter Europa Orbiter (JEO) of the Europa Jupiter System Mission in solar wind and in Jupiter magnetospheric plasma were performed. At the very beginning, research about the relevant plasma environments had to be conducted and information about the sizes and surface materials of the orbiters gathered and evaluated. With those information the orbiters were modelled with Gmsh, an open source CAD and 3D meshing tool. Since two different designs of the JGO were in competition, both proposals were modelled (JGO1 and JGO2). Afterwards, the simulations were performed and following results obtained: 1. The JEO charges in solar wind at Earth to an electric potential of 8.11 V and in solar wind at Jupiter to 8.29 V. At Earth, a negative potential wake is observed behind the spacecraft main body of V. 2. The JGO1 and the JGO2 charge to similar potentials in solar wind at Earth of 9.98 V and V, respectively. Moreover, a potential barrier in wake direction of V (JGO1) and V (JGO2) behind the spacecraft main body can be observed. In solar wind plasma at Jupiter, electric potentials of V (JGO1) and V (JGO2) are expected. 3. At a radial distance of 15 Jupiter radii from Jupiter, close to the orbit of Ganymede, simulations with the JGO2 in the Jovian magnetosphere, neglecting a hot electron population, are showing at a local time of 6 h, noon and 18 h, electric potentials of 1.88 V to 1.97 V. A negative potential barrier is not just observed in wake direction (-0.55 V to V) but also in ram direction (-0.27 V to V) due to photoelectron and secondary electron emission. At midnight local time, in the planetary shadow, the JGO2 is expected to charge to a very high negative potential of V. 47

57 48 Conclusion 4. At a radial distance of 26.3 Jupiter radii from Jupiter, at the orbit of Callisto, in the Jovian magnetosphere, simulations at 18 h and midnight local time were performed. In both cases the spacecraft charges positive, at 18 h local time to an average surface potential of V and at midnight local time to 4.61 V. The positive potential in the planetary shadow is observed in the absence of photoelectron emission due to a high secondary electron emission yield. Thus, the incidental thermal electrons rather charge the spacecraft positive than negative. 5. In all simulated cases narrow ion wakes were observed in the presence of a positive charged spacecraft. As mentioned, spacecraft charging can significantly influence in-situ plasma measurements of on-board sensors. Acceleration and deflection of charged particles can cause shifts in energy spectrums, and enhanced or reduced particle fluxes. One has to be aware of the spacecraft-plasma interactions in order to interpret measurements always with respect to the spacecraft potential and not to take them as absolute measurements. For our simulations the average spacecraft surface potential of V in the planetary shadow at 15 R J distance from Jupiter may significantly influence the plasma measurements, in particular of the low energetic populations. Putting everything into a nutshell, one can say that open issues concerning the expected spacecraft charging for the EJSM were answered. Simulations in solar wind and at the orbit of Ganymede and Callisto within the Jovian magnetosphere were performed successfully. However, advanced issues as the influence of hot electron populations and heavy ions on spacecraft charging in the Jovian magnetosphere, charging at the orbit of Europa, and charging in the magnetosphere of Ganymede have to be simulated in the future. For further improvement of the performed simulations differential charging should be addressed by taking into account resistances and capacities between spacecraft subsystems.

58 APPENDIX A List of acronyms AU - Astronomical Unit CNES - Centre National d Études Spatiales (National Centre of Space Research, France) CNRS - Centre National de la Recherche Scientifique (National Center for Scientific Research, France) EJSM - Europa Jupiter System Mission ESA - European Space Agency GUI - Graphical User Interface IRF - Institutet För Rymdfysik (Institute of Space Physics, Sweden) JEO - Jupiter Europa Orbiter JGO - Jupiter Ganymede Orbiter JGO1 - Jupiter Ganymede Orbiter design proposal 1 (see chapter and 5.1) JGO2 - Jupiter Ganymede Orbiter design proposal 2 (see chapter and 5.2) NASA - National Aeronautics and Space Administration (USA) ONERA - Office National d Études et de Recherches Aérospatiales (The French Aerospace Lab, France) PIC - Particle-In-Cell SPINE - Spacecraft Plasma Interactions Network in Europe SPIS - Spacecraft Plasma Interaction System 49

59

60 APPENDIX B Simulation settings In this chapter all simulations and global parameter inputs are listed. Furthermore, the simulation box size, the number of tetrahedrons used for meshing and the mesh quality (best mesh quality = 1) are given. If default is written in the table, the default value of SPIS were not changed. Simulations performed with the JEO can be found in table B.1, and simulations with JGO1 in table B.2. SPIS simulations for JGO2-plasma interactions are summarized in table B.3, B.4, B.5 and B.6. 51

61 52 Appendix B Table B.1: Simulations of the JEO Simulation name TR2000b TR2002b TR2003b CSat electrondensity iondensity electrontemperature iontemperature iontype H+ H+ H+ ionvx ionvy ionvz electronsecondaryemission photoelectrontemperature photoemission sunx suny sunz avpartnbpercell itergradient default default default tolgradient default default default plasmadt electrondt elctronduration iondt ionduration duration Simulation box size (x [m] y [m] z [m]) x 155 x x 32.2 x x 32.2 x 56.3 number of tetrahedra mesh quality factor S/C average surface potential [V]

62 53 Table B.2: Simulations of the JGO1 Simulation name TR3000b TR3001b CSat electrondensity iondensity electrontemperature iontemperature iontype H+ H+ ionvx 0 0 ionvy 0 0 ionvz electronsecondaryemission 3 3 photoelectrontemperature 3 3 photoemission 3 3 sunx 0 0 suny 0 0 sunz avpartnbpercell itergradient default default tolgradient default default plasmadt electrondt elctronduration iondt ionduration duration Simulation box size (x [m] y [m] z [m]) 159 x x x 49.3 x 61.6 number of tetrahedra mesh quality factor S/C average surface potential [V]

63 54 Appendix B Table B.3: Simulations of the JGO2 - part 1/4 Simulation name TR1000.2b TR1001b CSat electrondensity iondensity electrontemperature iontemperature iontype H+ H+ ionvx ionvy 0 0 ionvz 0 0 electronsecondaryemission 3 3 photoelectrontemperature 3 3 photoemission 3 3 sunx suny 0 0 sunz 0 0 avpartnbpercell itergradient default default tolgradient default default plasmadt electrondt elctronduration iondt ionduration duration Simulation box size (x [m] y [m] z [m]) x x x 69 x 32.5 number of tetrahedra mesh quality factor S/C average surface potential [V]

64 55 Table B.4: Simulations of the JGO2 - part 2/4 Simulation name TR1005.1b TR1005.4b CSat electrondensity iondensity electrontemperature iontemperature iontype O+ O+ ionvx ionvy 0 0 ionvz 0 0 electronsecondaryemission 3 3 photoelectrontemperature 3 3 photoemission 3 3 sunx suny 0 0 sunz 0 0 avpartnbpercell itergradient tolgradient plasmadt electrondt elctronduration iondt ionduration duration Simulation box size (x [m] y [m] z [m]) 82 x x x x number of tetrahedra mesh quality factor S/C average surface potential [V]

65 56 Appendix B Table B.5: Simulations of the JGO2 - part 3/4 Simulation name TR1006.2b TR1007b TR1008.3b CSat electrondensity iondensity electrontemperature iontemperature iontype O+ O+ O+ ionvx ionvy ionvz electronsecondaryemission photoelectrontemperature photoemission sunx suny sunz avpartnbpercell itergradient default tolgradient default plasmadt electrondt elctronduration iondt ionduration duration Simulation box size (x [m] y [m] z [m]) x x x x x x number of tetrahedra mesh quality factor S/C average surface potential [V]

66 57 Table B.6: Simulations of the JGO2 - part 4/4 Simulation name TR1205.1b TR1206.2b CSat electrondensity iondensity electrontemperature iontemperature iontype O+ O+ ionvx ionvy 0 0 ionvz electronsecondaryemission 3 3 photoelectrontemperature 3 0 photoemission 3 0 sunx suny 0 0 sunz 0 0 avpartnbpercell 8 6 itergradient default default tolgradient default default plasmadt electrondt elctronduration iondt ionduration duration Simulation box size (x [m] y [m] z [m]) x x x x number of tetrahedra mesh quality factor S/C average surface potential [V]

67

68 APPENDIX C Verification of input parameters In order to verify the correct usage and the simulation control of SPIS version 4.3.1, which is used in this thesis to improve the simulation time, simulations of the Cassini orbiter performed by Nilsson with SPIS version 3.7RC09 [35, p. 48] are redone. In the next chapter the simulation inputs and results are presented. C.1 Simulations and results In table C.1 the input parameters and the corresponding spacecraft ground potential of simulations performed with SPIS v.3.7rc09 (by Nilsson [35, p. 48]) and SPIS v are listed. It should be noticed that for all simulations performed, the source code of the Cassini orbiter written by Nilsson is used [34]. In total, two simulations are rerun. The first one (see comparison 1 in table C.1) shows a derivation of the spacecraft ground potential of 0.03 % compared to the simulation done by Nilsson, whereas the second one (see comparison 2 in table C.1) derivates by 1.26 %. In other simulations it was verified that running several times the same simulation with the same SPIS version give exactly the same results. However, the small derivations can be explained by source code changes of the different SPIS versions and by changes of the global plasma control parameters 1 which change the plasma dynamics. The derivations are small compared to the uncertainties of the plasma environments used in this thesis. As a result, it can be stated that the correct usage of SPIS is verified by comparison with Nilsson. 1 Global plasma control parameters are plasmadt, electrondt, electronduration, iondt and ionduration in table C.1. 59

69 60 Appendix C Table C.1: Simulation input and output of Cassini orbiter. Comparison 1 Comparison 2 SPIS version RC RC09 Debye length [m] Density [ # ] cm 3 T=T e =T i [ev] Avg. part./cell Duration [s] C [nf] Model file name [34] case C case C case D case D plasmadt [s] no input no input electrondt [s] no input no input electronduration [s] no input no input iondt [s] no input no input ionduration [s] no input no input Spacecraft ground potential [V] [35, p. 48] [35, p. 48]

70 APPENDIX D SPIS Guide Learning SPIS is very time-consuming and should not be underestimated. Therefore this guide should help novice users to run and analyse first simulations. It is strongly recommended to follow it step-by-step. The guide is specifically written for SPIS version running on Linux operating system. D.1 Introduction In addition to this guide it is recommended to read carefully the SPIS documentation which can be found by pushing Help Online help in the upper right corner of the SPIS menu bar. Especially, the technical documentation TN 1.0: SPIS-UI User Manual (UM): Quick Start and general user manual of SPIS [20] is useful for beginners. Other useful guides of older SPIS versions and further information can be found in references [35, 36, 40, 25]. D.2 Installation and source code changes To download SPIS, first do an online user registration to the SPINE community on the SPIS website [4]. After a short time you will receive an with the access code. Take into account that this can take few days because the is not automatically generated. It is recommended to run SPIS rather on a Linux than a Windows operating system due to improved performance and stability. Several SPIS source codes are available and are depending on the installed C standard library. Therefore carefully check the installed glibc version before downloading SPIS. This can be done by using the command ldd --version in the Linux terminal. Finally download and unpack the correct SPIS source code and run runspis.sh which can be found in the SPIS ROOT/Bin directory. For a better meshing and to avoid out of memory errors, which are quite common due to the amount of random access memory needed by SPIS, it is recommended to do the following two changes of the source code. 61

71 62 Appendix D A better meshing can be achieved by optimising the Gmsh meshing with the help of the Netgen mesh generator. For this, the following changes have to be done. Open the file SPIS ROOT/SpisUI/Bin/Mesher.py and change the line self.cmd = GL_CMD_GMSH + + self.mesh_output_format_flag self.filename1_geo+ -o +self.filename4out+ > + self.filename3_out to self.cmd = GL_CMD_GMSH + + self.mesh_output_format_flag optimize_netgen +self.filename1_geo+ -o + self.filename4out+ > +self.filename3_out SPIS addresses a maximum of 1000 MB RAM by default. If the Java Virtual Machine runs out of memory the simulation breaks and a java.lang.outofmemoryerror: Java heap space error is thrown. To avoid this error one can increase the JVM heap size in the file SPIS ROOT/SpisUI/BinLinux/spis-ui.properties by changing export JVM_XMX=1000m to a higher value dependent on the available RAM of the used computer.

72 D.3. Modelling and simulation 63 D.3 Modelling and simulation Overview SPIS has an excellent Graphical User Interface (GUI) in which further subguis are integrated. The main GUI is displayed in figure D.1. It includes the workspace, a Jython console, a log and a toolbar. To perform the modelling, simulation and data extraction chain, the toolbar is in general used from the left to the right. Figure D.1: Graphical User Interface of SPIS with toolbar (top), workspace (center), log and Jython console (bottom). [37] Create a new project Before starting the modelling with Gmsh, a new project has to be created. This is done with the help of the Save Project button in the SPIS GUI toolbar. It is recommended to use the button during the development phase as often as possible to ensure that the updated project is always saved in case SPIS crashes Geometry/CAD manager As mentioned in chapter D.4.3.1, the toolbar in the SPIS GUI is used from the left to the right. Therefore, at the beginning call the Gmsh CAD and meshing generator by pushing the Call the CAD tools button in the toolbar. A new window pops up, you have to create a

73 64 Appendix D New file, mark it and push CAD tool to open Gmsh. A short introduction into Gmsh should be given in this chapter. For further information, refer to tutorial Gmsh User Tutorial for CAD and Meshing [41] which can be found in the SPIS documentation. Gmsh uses a bottom-up method to help the user to develop the geometry. First, define the points of the model which are the edges of the geometry. If this is done, connect the points to lines, the lines to surfaces and the surfaces to volumes. In order to create the points, choose in the Gmsh menu window Geometry and Elementary entities Add New Point. The point can now be entered in the new opened window by giving a X, Y and Z coordinate 1. An important parameter is the field Characteristic length which defines the size of the meshing tetrahedrons at this point and thus the resolution of the simulation. After meshing, the length of each tetrahedron edge is smaller or equal to the defined characteristic length [40, p. 74]. Besides the points for modelling the spacecraft, also the points of the computational volume in which the simulation is run in SPIS have to be defined. Therefore, points for the simulation box have to be entered, which should be some Debye length away from each spacecraft part. Their characteristic length can be bigger than the one at the spacecraft because a high resolution is not needed at the boundary 2. Depending on the needed resolution, it can make sense to introduce one or even more intermediate boxes between spacecraft and simulation box. By choosing a specific characteristic length for the points of the intermediate boxes one can influence the resolution around the spacecraft and smooth the meshing. After having defined all needed points, connect those for example to straight lines. This is done by pushing the Straight line button and clicking on the points in the visualisation window which should be connected. Afterwards connect the lines to plane surfaces by pushing Plane surface and marking the lines which define a surface. Finally, the different surfaces can be used to define the volume by pushing Volume and marking them. If the model is defined properly, one has to define the Gmsh Physicals. Those are needed as boundary conditions later in the SPIS processing chain in order to give the different surfaces and volumes different physical properties. To define the physical surfaces, go back to default configuration of the Gmsh menu window and choose Physical groups Add Surface. At least two different physical surface groups and one physical volume group are needed. The spacecraft surfaces, the external outer boundary surfaces of the simulation box and in addition to that, the plasma computational volume itself. In case all surfaces of the spacecraft are out of the same material, mark all of them and group them together. Same procedure has to be done for outer boundary surfaces of the simulation box. It is useful to change the Physical Surface ID which is written in the Gmsh output.geo file. This can be done by pushing the Edit button in the default configuration of the menu window. With the help of an editor one can now have a look at the code produced by Gmsh. 1 The used unit is meter. 2 Choose for example one third of the Debye length.

74 D.3. Modelling and simulation 65 At the end of the code Physical Surface(ID) should be written (since this was given as the last input), where ID is a number. It is recommended to change this ID number to for example 3000 upwards for spacecraft surfaces and 4000 for the outer boundary surfaces for better recognition later on. Furthermore, add the plasma volume, the volume in which the plasma is placed, in the file by adding Physical Volume(ID) = {ID_volume1, ID_volume2,...} to the code. Again, ID has to be a number and ID volume1, ID volume2 et cetera are the volume ID s of the volumes in which the plasma is placed 3. When all of this is done, recheck that the connections are made properly because in case it is not no error message appears. One way to check is to close Gmsh and open it again. In case something is not in order, an error message will appear now. Besides, it might be helpful to display points, lines, surfaces and/or volumes numbers. This can be done in the Gmsh menu window under Tools Options Geometry Visibility. If no error message appears, the geometry works and one can close Gmsh again and push the Set as main button to mark the file as the one which should be used and Update project in the Geometry/CAD manager because modification of files are just saved in the temporary folder. Hint: For experienced users it might be useful to do some changes to the code. The user can for example define characteristic lengths and the Debye length in the top of the code by writing reslocalsatellite = a; reslocalboundary = b; debyelength = c; where a, b and c are lengths given in meter. The now defined variables reslocalsatellite, reslocalboundary and debyelength have to be written also at the required positions within the code. Advantage is that just the values of a, b and/or c have to be changed in case the user wants to change all characteristic lengths and/or the simulation box size 4 and not every single characteristic length entered for each point Import the CAD structure and load the properties catalogs To import the CAD model into the SPIS framework push the Load the defined geometry into the framework button in the SPIS GUI toolbar. Afterwards you have to load different physical and numerical properties for materials, electrical nodes and the plasma into the framework to define the local parameters such as boundary 3 The volumes ID volume1 and ID volume2 are added together which is different to the other defined non physical volumes in the code where ID volume2 is subtracted from ID volume1. 4 The variable debyelength should be used for changing the simulation box size.

75 66 Appendix D conditions or physical surface materials. This is done by pushing the Load the default catalogues of material, electrical and numerical properties button in the toolbar and by clicking Load in the new opened window. A huge amount of default properties are available, nevertheless also external NASCAP based material properties can be loaded if needed Geometry property group editor Now the imported properties of chapter D have to be assigned to the Physicals of the model which were defined in Gmsh and are described in appendix D To do so, call the Call the GEOM-property groups editor in the toolbar of the SPIS GUI. Here in addition to the Physicals defined earlier, also three IDs with the name DEFAULT POINT GROUP, DEFAULT SURFACE GROUP and DEFAULT VOLUME GROUP are displayed. Those can be deleted [35, p. 31] or at least have to be moved to the bottom of the list with the help of the Move down button since the list is a priority list. Moreover, it is very important to rank the volume group which corresponds to the plasma volume defined in Gmsh under all physical surfaces to avoid errors and crashes of the system. A screenshot of the GroupEditor is shown in figure D.2. After having ranked the different groups, one has to assign the material, electrical node and plasma properties to the spacecraft surfaces and just the specific plasma properties to the plasma volume and simulation box boundary. By default, following properties which are shown in table D.1 should be set. Table D.1: Default properties of the group editor. [20, p.26] Physical Material ElecNode Plasma Spacecraft surface ITO, default Spacecraft ground Spacecraft, default (ElecNode-0) Boundary surface None None Boundary, default Plasma volume None None Plasma Model in Volume, default In case different groups of physical surfaces of the spacecraft in the.geo file of Gmsh are defined, for example to model solar panels, you have to subscribe each surface group, material, electrical node and plasma properties. Indium tin oxide (ITO) in table D.1 is chosen as an example for a conductive surface. For the sun facing side of the solar panels for example CERS, default can be chosen as solar cell material. If different electrical nodes are modelled, the electric circuit with resistances, capacitors and voltages between the nodes has to be given as an input in the file circuit.txt. More detailed information can be found in the SPIS documentation SPIS/NUM Controlling NUM from UI [46].

76 D.3. Modelling and simulation 67 Figure D.2: Group editor of SPIS which is used to rank the Physicals and to assign those different material, electrical node and plasma properties. [37] After the different properties are assigned to the Physicals, confirm this by clicking the OK button Meshing, conversion into mesh groups and fields mapping For the next steps three different buttons in the SPIS GUI toolbar are available. Those are Call the mesher, Convert the GEOM (CAD) groups into mesh groups and Map (deploy) the fields on the mesh according to groups. But by pushing just the last button all three tasks will be executed one after the other. First the meshing is performed. This can take a long time depending on the simulation box size and the chosen characteristic lengths of the model. You can check the number of tetrahedrons in the logging of the SPIS GUI. It is indicated as nbcell. For a modern computer to tetrahedrons are reasonable in order to keep a good equilibrium between simulation time and resolution. If the number of tetrahedrons is too small or too big, it is recommended to change the characteristic lengths and/or the simulation box size as described in chapter D The mesh quality can be checked with the mesh inspector, which is implemented in SPIS, by

77 68 Appendix D clicking on Mesh Mesh Inspector in the menu bar. In the Mesh Inspector first load the mesh file.msh from the project folder, mark it in the Inspector and finally add four different analysers by clicking on Mesh Add Analyser. An analysis is done by marking the analyser and clicking on Analyse and Histogram in the Mesh Inspector control panel. The analysers are explained in more detail in reference [20, p. 40 ff.]. It is also possible to display the mesh with the help of Cassandra by clicking on Mesh Mesh Viewer in the SPIS menu bar Global parameters With the help of the global parameter editor which is displayed in figure D.3 and which can be called with the Call the Global Parameters editor button in the SPIS GUI toolbar, it is possible to set the physical parameters of the plasma and radiation environment, and the numerical parameters of the simulation control. Figure D.3: Global Parameter Editor. [37] Numerous settings are possible and each of it is explained in the SPIS documentation SPIS/NUM Controlling NUM from UI [46]. It can be accessed by pushing Help Online help in the SPIS menu bar. A short description is also given in the Global Parameters Editor itself. The global parameters are divided into eleven subsections. Those are Spacecraft, Poisson equation, MultiZone, Simulation control, Plasma, Scenario, Volume Interactions, Sources, Outputs, Surface Interactions and B Field. In the following, the most important ones which were also used during this master thesis are explained in more detail and advices are given. If changes of the global parameters are done, they have to be confirmed by pushing Enter, otherwise they will not be applied in the simulation. After all settings are done, the Global Parameters Editor has to be left by pushing save and quit.

78 D.3. Modelling and simulation 69 Spacecraft The global parameter CSat defines the spacecraft capacity. To save computational power it is recommended to calculate the capacity first by using the global parameter exactcsat. If exactcsat is turned on by putting its value > 0, the exact spacecraft capacity is calculated while running the simulation. Following procedure should be used. First run a simulation with exactcsat turned on and wait until the calculated capacity converges. Then stop the simulation and give the calculated capacity as an input for the global parameter CSat and turn exactcsat off to save computing time. Simulation control Settings of the global parameters of the simulation control are quite tricky. The parameter duration sets the total time of the simulation. It should be noticed that the value entered in seconds is not the real time needed to finish the simulation. To estimate the good duration time, calculate the time for the ions to cross the simulation box. This can be done by knowing the ion speed relative to the spacecraft and the simulation box size. Multiply this value for example by 10 and enter it for the duration. Carefully check after the simulation was run, that the duration was chosen sufficient and the spacecraft potential converged to a given value. The simulation control is divided into three different layers [47], which are displayed in figure D.4. Figure D.4: Simulation control structure used within the code. [46] The uppermost layer is the simulation level which takes the satellite-plasma interaction into account. The next level is the plasma (matter field coupling) and spacecraft (electric circuit) level, and the lowest one the particle level. Those levels are connected by different nested loops which can be controlled by various global parameters as simulationdt, plasmadt, plasmaduration, electrondt, electronduration, iondt and ionduration, where Dt stands

79 70 Appendix D for the time steps and Duration for the integration time 5. First, the default settings can be tried to obtain the values automatically. If those do not lead to sufficient results in a reasonable amount of time, it is recommended to enter the values manually as explained in reference [47, 46] and shortly in the next paragraph. The global parameter plasmadt should be smaller than a plasma period [46]. For this the plasma periods of all populations have to be calculated 6. A sufficient condition to calculate each time step is populationdt = π ω population, where ω population is the plasma frequency in rad/s for a specific population. If all are calculated, set plasmadt to the lowest populationdt obtained, which limits all other populationdt. Except in very special cases the integration duration should be the same as the time step [47]. Plasma In this subsection the global parameters for the plasma environment are set. With electrondensity and iondensity the electron and ion densities are defined and with electrontemperature and iontemperature their specific temperatures. Different ions are supported by SPIS up-todate namely H+, O+, H2O+, Xe+, Xe++, Ar+, Cs+ and In+. They can be set in the parameter iontype. The ion drift velocity and its direction can be defined with the help of the parameters ionvx, ionvy and ionvz 7. The vector points in the ion velocity direction. With avpartnbpercell, the average number of superparticles per meshing tetrahedron is set. Remember that in a PIC simulation superparticles are used in which physical particles are placed. Increasing this number will significantly increase simulation complexity and time. The global parameters electrondt, electronduration, iondt and ionduration were already discussed in the Simulation Control subsection. Surface Interactions Here surface interactions such as emission of photoelectrons and secondary electrons can be set. With the help of the global parameter electronsecondaryemission, the secondary emission of several electron populations, their dynamics and secondary emission from secondary electrons can be controlled. If set to 3, the secondary emission from electron population 1 is turned on with secondary electron dynamics modelling, but without secondary emission from secondary electrons 8. The temperature of the secondary electrons from electron impacts can be controlled with secondarytemperature. There is also a parameter called secondaryfromprotontemperature which should set the secondary electron temperature from proton impacts. But secondary emission from proton impact is not active in SPIS version [29]! Photoelectron emission with photoelectron dynamics modelling can be turned on by setting photoemission to the value 3. With photoelectrontemperature the energy of the photoelectrons 5 Not all simulation control parameters can be find in the Simulation Control. Some are included in the Plasma section, such as electrondt, electronduration, iondt and ionduration. 6 As there are thermal electrons and ions, but also secondary electrons and photoelectrons. 7 Other ions can be included by doing source code changes. 8 For more detailed information have a look at SPIS ROOT\Doc\DocSpisNum\HowTo\Controlling NUM from UI.html [46].

80 D.3. Modelling and simulation 71 can be set. Very important global parameters are sunx, suny and sunz, which define the solar flux. If 1 set to 1, it is the solar flux at 1 AU. Therefore, it has to be scaled with to the spacecraft d[au] 2 position 9. The vector points towards the Sun in opposite photon velocity direction which is different from ionvx, ionvy and ionvz. B Field This subsection includes just three global parameters namely Bx, By and Bz. A uniform magnetic field can be applied by entering the field strength of the different components Conversion to numerical data and running the simulation After the global parameters are defined properly, data and model have to be converted to the SPIS-NUM data structure. This is done by clicking on Convert data from UI to NUM data structure. Afterwards the simulation can be run by pushing the Launch the numerical kernel and performs the simulation button in the GUI toolbar. The simulation can either be run internal in the framework or external. Advantages of an internal simulation run is that the user can control the simulation in the log of the SPIS GUI and extract data during the simulation by pushing Solvers SPIS-NUM Extract data. Disadvantages can be a loss in computational power and higher memory costs. The simulation time is depending on the model and the global parameters and can take from seconds up to days. The first step to do after the simulation has finished is to save it. This is done by clicking on Save the current project in the SPIS toolbar. Reason for saving is not just to ensure that the data are not lost in case SPIS crashes, but also for creation of the final data. If this is done, the data can be accessed at any time again by loading the project in SPIS with the help of the Open a existing project button in the GUI toolbar after having launched SPIS Extract the data Once the simulation is finished and data are saved, they have to be extracted. For this push the Call the DataFields manager for data analysis, extraction and conversion button in the toolbar. The DataField Manager will pop up and the data one is interested in can be selected. Mark View on Cell for volume data or View on Face for surface data (e.g. to display emitted currents from spacecraft surfaces). Do not press the button Export to Cassandra which will load the data in Cassandra in the SPIS framework because this is a quite unstable operation. Rather click on Export to VTK which will export the data in VTK format to the temporary directory. Afterwards, copy them from /tmp/ to the project folder or save the project again which will automatically copy them into the project name.spis/vtk directory. 9 Where d is the distance between the Sun and the spacecraft in astronomical units.

81 72 Appendix D D.4 Visualisation and data analysis For visualisation of the data it is strongly recommended to use ParaView instead of Cassandra although Cassandra is more intuitive. Nevertheless, ParaView has the advantage of much more functions and advanced visualisation possibilities. Since ParaView is an open source software, the newest version can be downloaded easily. A screenshot of ParaView version is displayed in figure D.5. Figure D.5: ParaView software v including toolbar (in the top), Pipeline Browser (top left), Object Inspector (bottom left) and visualisation window (right). [3] To visualise the results of the simulation, import the VTK files and press Apply in the Object Inspector. Under Filters in the menu bar different filters can be applied to the loaded file. One interesting filter is called Slice. It can be used for displaying a plane in a volume, whereas Plot Over Line can be used for example to display densities in a graph as a function of place. By clicking on Toggle Color Legend Visibility in the ParaView toolbar, a legend is displayed. Next to it, with the Edit Color Map button you can open the Color Scale Editor and change the colours of the legend. This is done by pushing Choose Preset and selecting and importing the right one as Blue to Red Rainbow in HSV colour space. This should be done for an improved visualisation. The legend automatically ranges from the minimum to the maximum value of the figure. It might be useful to rescale it in case of outliers. This can be done by turning Automatically

82 D.4. Visualisation and data analysis 73 Rescale to Fit Data Range off, pushing Rescale Range and entering the new range. The name of the legend can be changed by changing to the Color Legend window in the Color Scale Editor and entering a name in the Text field. Afterwards close the window. A coordinate system and the coordinate axis can be turned on by pushing the buttons Show Orientation Axes and Show Center in the toolbar. Finally, save the created image by clicking on File Save Screenshot in the menu bar.

83

84 APPENDIX E Limitation of SPIS SPIS is still under development and improvement. Therefore, in special cases the software has significant limitations. One of those is photoelectron emission in shadow. It is explained in more detail in the next chapter. E.1 Photoelectron emission in shadow SPIS v cannot model the shadow of objects for solar flux up-to-date. This leads to photoelectron emission from surfaces which are in the shadow, causing false results. An example of photoelectron emission in shadow is shown in figure E.1. In the following case of the Jupiter Europa Orbiter, the solar UV is directed towards -Z direction, perpendicular to the antenna surface [Simulation name: TR2003b]. Due to the dimensions of the antenna, a significant decrease of the photoelectron emission current behind the antenna on the spacecraft main body is expected. This is not the case. A maximum photoelectron emission current of A/m 2 is emitted from the antenna surface and from the main body behind the antenna. The problem is known and written down in the SPIS documentation ( no shadowing for now [46]). However, it has a significant impact on the usage of SPIS, because different spacecraft configurations with respect to the Sun cannot be addressed in this thesis. It is therefore a point which should be urgently improved in upcoming SPIS versions. 75

85 76 Figure E.1: Photoelectron emission current of the Jupiter Europa Orbiter. The solar UV is directed towards -Z direction, nevertheless photoelectrons are emitted in the shadow of the antenna from the main body, leading to wrong results. [Simulation name: TR2003b]