Interaction with the magnetic field: the magnetospheres

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Past and future scientific missions aiming at analysing low energy plasma

A scientific satellite is a great opportunity for loading on board various instruments, each dedicated to a specific physical interest. Among all past, present or future scientific missions, several carry on-board payload dedicated to low energy plasma measurements.
The NASA Ranger 1 ’s mission, launched in 1961, was to test performance of the new technologies intended for operational Ranger flights and to study the nature of particles and fields in interplanetary space. It carried on-board an electrostatic analyser, but re-entered Earth’s atmosphere three days later, because of the loss of its telemetry. The same year its successor Ranger 2, with the same objectives, flew only one day, due to a malfunction in its booster rocket. Pioneer 6, launched in 1965, was the first of four American spacecraft designed to study interplanetary phenomena in space: Pioneer 7, 8, 9 were respectively launched every year starting in 1966. Each one carried on-board a plasma analyser and constituted the first solar monitoring network. They provided simultaneous scientific measurements at widely dispersed locations in heliocentric orbit.
Helios, a joint German-American deep-space mission, including two twin spacecraft Helios 1 and Helios 2 launched respectively in 1974 and 1976, aimed at studying the main solar processes and solar-terrestrial relationship. Its instruments investigated the solar wind, magnetic and electric fields, cosmic rays and dust in regions between Earth’s orbit at 1 AU and the closest region from the Sun never reached by any other spacecraft of its generation: 0.29 AU from the Sun. The charged particle experiments covered various energy ranges from 0.15 eV to 1 GeV.
Voyager 1 and Voyager 2 left the Earth in 1977, aiming at exploring Jupiter and Saturn, thanks to a specific alignment of the outer planets that occurs only once in 176 years. Both spacecraft, still in flight, are carrying among others the following experiments: plasma particles, low-energy charged-particles and plasma wave instruments. In 2013 both orbiters have reached a distance from the Sun greater than 100 AU and are still travelling away at a speed of about 523.6 million km (3.5 AU) per year.
ISEE-3/ICE, launched in 1978, was the third of three International Sun-Earth Explorers (ISEE) designed and operated by NASA in cooperation with the European Space Agency. NASA built the first and third spacecraft, while ESA built the second. The three spacecraft were to simultaneously investigate a wide range of phenomena in interplanetary space. Carrying several experiments to study, for example, solar X-rays, solar wind protons and electrons, and plasma composition, it is the first mission to monitor the solar wind approaching Earth. It also detected an impressive plasmoid of electrified gas ejected from Earth’s magnetosphere.
The Ulysses spacecraft (NASA/ESA), launched in 1990, was equipped with a wide range of scientific instruments. These were able to detect and measure magnetic fields, energetic particles, radio and plasma waves, dust and gas, X-rays and gamma rays. But mainly it carried the SolarWind Observations Over the Poles of the Sun (SWOOPS) which measured solar wind ions and electrons in energy ranges between 0.8 and 814 eV [Issautier et al. (2001)]. Ulysses flew above the Sun’s southern and northern poles, regions never studied before which allowed the survey of the solar wind from all angles, producing the first three-dimensional picture of the heliosphere.
In 1997, the NASA Advanced Composition Explorer (ACE) left the Earth to investigate the matter ejected from the Sun to establish the commonality and interaction among the Sun, Earth, and the Milky Way galaxy. ACE brought many scientific experiments: (SWIMS) solar wind ion mass spectrometer; (SWICS) solar wind ion composition spectrometer; (ULEIS) ultra-low-energy isotope spectrometer; (SEPICA) solar energetic-particle ionic charge analyser; (SIS) solar isotope spectrometer; (CRIS) cosmic-ray isotope spectrometer; (SWEPAM) solar wind electron, proton, and alpha monitor; (EPAM) electron, proton, and alpha particle moni-tor; (MAG magnetometer) and (RTSW) real-time solar wind experiment. This mission is still in progress and keeps providing space weather reports (i.e. about the changes of environmen-tal conditions in near-Earth space) and warnings of geomagnetic storms that might disrupt communications on Earth and harm astronauts in space.

Grey areas for a quantitative measurement

Even though analytical models combined with numerical solvers exist and provide consistent results in estimating plasma measurement biases, they remain valid for the consideration of only few perturbations induced by spacecraft/plasma interactions. Key elements for a complete space environment understanding through plasma instrument data analysis are still neglected, as their analytical modelling are difficult.
It is shown in the previous section that perturbations induced by all the spacecraft/plasma interactions are obviously a subject of interest for plasma physicists and modellers, but the issues are usually studied independently from each others, despite their inter-correlation. Analytical models are rapidly overwhelmed or more simply impossible to establish when dealing with several interdependent sources of perturbations. Moreover an analytical expression of a complex physical process implies different assumptions and approximations that drastically limit the range and the validity of this formulation. This simplification is of course necessary to set the theory but avoids some critical issues.
A blatant example is the consideration of 3D aspects of the spacecraft/plasma interactions. Considering the particles coming purely radially to the detector (as in [Génot et al. (2004)]) or based on a plane-parallel approximation ([Scime et al. (1994)]) ignores all of the spacecraft relevant aspects of the sheath, solar illumination (shadowing, booms), three dimensioned ion wake, and also different material properties depending on the satellite surfaces considered, etc. Particle deflections due to local surface (and eventually differential) potentials can lead to misinterpretations of the local plasma parameters. Authors are perfectly aware of this charged spacecraft focussing issue and admit that the analytical method reached its limits. Global PIC simulations should help analysing the interactions network as they handle 3D geometries with adequate material properties plus the computation of individual particle trajectories.

Anticipating the problems: help to design spacecrafts and instruments

There is no need to harp on about the global advantage provided by computers in the prelimi-nary studies concerning all the possible engineering fields. From the space engineering point of view, numerical simulations are obviously essential to conceive a satellite and anticipate mechan-ical, thermal, electrostatic, and many other issues in the final probe design. Several powerful softwares are available to compute and solve (more or less independently) these problems and configure efficient and robust satellites for telecommunication, military or scientific use. Simu-lating a satellite within its expected environment allows the anticipation of the possible charging that can occur (in case of arcing risks between several elements if the potentials reached are hazardous), the rates of secondary emission, the ion wake dimension and orientation, etc. If all the problematic interactions aforesaid were modelled through numerical simulations one would have a comprehensive understanding of the complex satellite/environment system.
Numerical studies even when performed after that the satellite has been practically designed are essential to the plasma physicists. Modellers wish to conceive particle detectors that will analyse specific physical environments, knowing that the instruments themselves will respond to the environment (through secondary emission and charging), in the vicinity of a satellite structure which will also react to the environment. Once a scientific probe orbit has been defined and the expected encountered space environment conditions have been determined, simulations are not only useful to conceive an instrument that will correctly measure the expected ambient plasma (in terms of energy range, scanning frequency, aperture angle, field of view) but also to anticipate the instrument constraints generated by the interacting system « satellite + instrument + plasma ». Some issues have been described in the previous sections and are hardly avoidable but it is still possible to limit the impact of the interactions on plasma measurements by choosing adapted materials at key locations, which can for example emit fewer parasite particles in certain environment conditions, or generate fewer disturbances owing to lower charging potential level. Some technical designs on the satellite are often mandatory and scientists who submit the instrument proposals have no choice but to yield to the constraints imposed by thermal, electrical or mechanical considerations. However there is practically no interest in embedding an instrument that will be blind most of the time. Numerical simulations provide insight on leeways and compromises for optimizing the correlation of the « satellite + instrument + plasma » system and providing more accurate evaluations of the space environment.
In this context the Spacecraft Plasma Interactions Network in Europe (SPINE) community has been initiated in 2000 by the European Space Research and Technology Centre (ESTEC) in Noordwijk, Netherland. The objective of this network is to share resources and to coordinate efforts in all domains related to the interaction of Spacecraft with the space plasma, including spacecraft charging. The SPINE Web site1 is an advanced platform for information exchange and collaborative work, a kind of Virtual Laboratory dedicated to studies of spacecraft/plasma interactions. SPINE provides guidance for the SPIS software development and participates to the software development and testing.
Concurrently with this PhD study, I am also a young scientist member of the Interaction of Satellites with Space Environment team2, hosted by the International Space Science Institute (ISSI – Bern, Switzerland). The objective of this group is to advance knowledge and under-standing in targeted areas in ways that would not be possible without the level of collaboration considered in this team. Research activities concentrate on five basic and interdependent aspects of satellite interaction with the space environment. These are: 1/ charging, 2/ sheath effects, 3/ particle emission from surfaces, 4/ transient responses and 5/ wake dynamics. The group uses a combination of computer models (EMSES, iPic3D, LASP, PTetra and SPIS – references about those numerical codes will be cited in Section 4) and, where possible, detailed measurement results. Different plasma conditions are considered including the ionosphere, Earth magneto-sphere and the interplanetary solar wind. Studies are also conducted by considering specific cases or missions of direct interest to group members including for example, Solar Probe, Solar Orbiter, Rosetta, Cluster or Swarm.

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Kappa distribution functions

The Solar wind plasma at thermal equilibrium is usually modelled through a Maxwellian dis-tribution function. However, other types of distribution functions are useful to describe the Solar wind. Indeed in the plasma particle velocity distribution of the measured Solar wind, observations were made of some non-Maxwellian suprathermal tails [Maksimovic et al. (2005)]. Those non-thermal populations can be well modelled thanks to the so-called Kappa (κ) distri-bution function, also called generalized Lorentzian, as explained in [Pierrard and Lazar (2010)] and also [Summers and Thorne (1991)]: n 1 Γ(κ + 1) v2 −(κ+1) fκ(v) = 1 + (2.11) π 3/2 θ3 κ 3/2 Γ(κ − 1/2) κθ2 with θ2 = 2κ−3 T κ m κ is the parameter that, when approaching infinity, makes the Kappa distribution function approach a Maxwellian (as illustrated on Figure 2.2). Note that κ > 3/2 and Γ(x) is the Gamma function. According to [Montgomery et al. (1968)], [Feldman et al. (1975)], [Štverák et al.(2009)], the Solar wind electron velocity distribution function can be considered as the sum of three distinct populations (Figure 2.3): an isotropic Maxwellian Core plus an isotropic Lorentzian Halo plus a drifting isotropic Lorentzian Strahl. f (v) = fc(v) + fh(v) + fs(v) (2.12).

Plasma scales: Debye length and plasma frequency

A plasma, sometimes described as the fourth state of matter, is defined as a set of charged par-ticles whose behaviour is ruled by collective particle interactions [Bittencourt (1986)]. Looking on a large enough scale a plasma at equilibrium is electrically neutral. The characteristic length over which the neutrality is established is called « Debye length » and is expressed as: λD = ε0kT (2.16) n0e2 with ε0 being the permittivity of free space, n0 the plasma density and T the characteristic temperature of the plasma.
The Debye length is thus the scale over which mobile charge carriers (usually electrons) screen out electric fields. It is the distance over which significant charge separation can occur. If a material surface is in contact with a plasma and in the presence of electrical fields: the characteristic thickness of the region in front of the surface is λD , and this region is known as the sheath. Inside the sheath charged particles behave as individual particles dominated by electromagnetic forces and the plasma may not be in necessarily locally neutral (especially near the satellite surfaces where particle emission and collection are important). Considering the satellite dimension LSC : if λD ≫ LSC the system « satellite/plasma » is considered as electrically coupled, meaning that a potential on one spacecraft element will be felt all over the satellite.

Interaction with the magnetic field: the magnetospheres

The Solar wind interacts with any Solar system body endowed with a magnetic field. The structure resulting from the encounter between the Solar wind and the magnetized object is known as the magnetosphere. The Earth, Jupiter, Saturn, Uranus and Neptune own their proper magnetosphere. They can also be found around Mercury, Ganymede (one of the Jupiter’s moon), Mars and Venus (those two last planets have induced magnetospheres). The best example to describe the structure that region is the Earth case as its magnetosphere is now well known. Note the magnetosphere environment will not be treated in this work as it focusses on low energy particles and those regions are usually populated with particles well beyond a hundred of eV.
The magnetosphere around Earth is composed of the terrestrial magnetic field lines immersed in the wind. Its configuration is quite deformed: compressed by the flow on the day side, towards the Sun (it extends up to ∼ 10 RE with RE being the Earth radius) and highly elongated on the night side (as far as several hundreds of Earth radii). A schematic view of the Earth magnetosphere structure is displayed on Figure 2.10 and its main components are described hereafter:
• The Solar wind is slowed down at the bow shock, the outermost layer of the magneto-sphere. The magnetic field is increased and some particles are accelerated. It represents the boundary between the magnetosheath and the interplanetary environment.
• Downstream of the bow shock is the magnetosheath, mainly formed from shocked solar wind, with high particle energy fluxes and strong variations of the magnetic field.
• The magnetopause is the region beneath in which the pressure from the planetary magnetic field is balanced with the pressure from the Solar wind.
• On the night side, the extended region is the magnetotail, containing two lobes. In the northern lobe the magnetic field points towards the Earth and in the southern tail it points away from Earth. The lobes have a relatively low density (< 5 cm−3) with temperatures of about 100 eV for electrons and 300 eV for ions.

Table of contents :

1 Introduction 
1.1 Introduction générale en français
1.2 English introduction: Principle of in flight plasma measurement
1.2.1 Past and future scientific missions aiming at analysing low energy plasma
1.2.2 Description of particle instruments
1.3 Sources of perturbations
1.4 Measurements analysis methods
1.4.1 Partial consideration of perturbations
1.4.2 Grey areas for a quantitative measurement
1.5 Interest of numerical simulations
1.5.1 Anticipating the problems: help to design spacecrafts and instruments
1.5.2 Analysing in-flight measurements
1.6 Objectives of this work
1.7 Plan and sum up
2 The Solar wind plasma 
2.1 Plasma physics
2.1.1 Distribution functions
2.1.2 Plasma scales: Debye length and plasma frequency
2.1.3 Magnetic field
2.2 The Solar wind
2.2.1 Properties and observations
2.2.2 Interaction with the magnetic field: the magnetospheres
3 Interactions with a satellite 
3.1 Equilibrium potential and currents
3.2 Differential charging
3.3 Space charge effects and ambient current estimations: probe theory
3.3.1 The Boltzmann factor
3.3.2 The thick sheath regime
3.3.3 The thin sheath regime
3.3.4 Concluding remark
3.4 Ideal collected distribution functions
3.5 Secondary electron emission / electron impact: SEEE
3.5.1 SEEE Principle
3.5.2 SEEE Modelling
3.6 Secondary electron emission under proton impact: SEEP
3.7 Photoemission
3.8 Ion wake
3.9 Potential barriers
3.10 Viewing factor
3.11 Other phenomena
4 Numerical simulation of Solar wind/satellite interaction 
4.1 The SPIS numerical code
4.1.1 Presentation of the software
4.1.2 SPIS basic principles
4.1.3 Utility of the SPIS code for simulations
4.2 Illustration of Solar wind impacts on spacecraft
4.2.1 Article 1: Solar wind plasma interaction with Solar Probe Plus spacecraft
4.2.2 Article 2: Simulation study of spacecraft electrostatic sheath changes with the heliocentric distances from 0.044 to 1 AU
4.2.3 Possible effects on plasma measurements
5 Numerical particle instruments 
5.1 Definition of scientist’s needs
5.2 The SPIS-SCI Instruments
5.3 Measurement principle
5.4 Measurement of a undisturbed Maxwellian plasma: Case 1
5.5 Measurement of a disturbed Maxwellian plasma
5.5.1 Positive potential effect: Case 2
5.5.2 Negative potential effect: Case 3
5.5.3 Photoemission: Case 4 and 5
5.5.4 Secondary electron emission: Case 6
5.5.5 Combined effect of SEEE and photoelectrons: Case 7
5.6 Undisturbed non isotropic Maxwellian plasma: Case 8
5.7 Conclusion
6 Applications 
6.1 Solar Orbiter
6.1.1 Solar Orbiter simulations: configurations
6.1.2 Results analysis of SOLO at 1AU
6.1.3 Results analysis of SOLO at 1AU with a Fast Solar Wind
6.1.4 Results analysis of SOLO at 0.28AU
6.1.5 Solar Orbiter cases conclusion
6.2 Cluster
6.2.1 Cluster simulation: configuration of the CLUS@1AU case
6.2.2 Results analysis of CLUS@1AU
6.2.3 Cluster simulation conclusion
6.3 Conclusion on scientific applications and engineering
7 Conclusion and perspectives 
7.1 Achievements (English)
7.2 Critical analysis of this PhD and Perspectives (English)
7.3 Conclusion générale (français)
A Appendix 209
A.1 Physical and Geophysical Constants
A.2 Basic concepts of the distribution function
A.3 Cluster in-flight data
A.4 Article 1 – Guillemant et al. (2012): Solar wind plasma interaction with Solar Probe Plus spacecraft
A.5 Article 2 – Guillemant et al. (2013): Simulation study of spacecraft electrostatic sheath changes with the heliocentric distances from 0.044 to 1 AU
Bibliography 

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