Rosetta Langmuir probe

performance

Fredrik Johansson

IRF Uppsala

Uppsala University

A thesis submitted for the degree of

MSc

2013 June

Abstract

Several Langmuir probe voltage sweeps by a model of the ESA spacecraft

Rosetta was simulated in a plasma with solar wind parameters using the

ESA open source software SPIS 5. The simulations were carried out to in-

vestigate the features of the spacecraft’s environment in the solar wind and

the effect of photoemission from the spacecraft surface on the measurements

made by the Langmuir probes on board Rosetta. We report a best fit to an

existing probe sweep result in the solar wind near the Earth at 1 AU from

9 Nov 2009 for a 4 million particle simulation in SPIS of an 8 V positively

charged spacecraft with the following parameters: Tph = 2 eV, Te = 12 eV,

Ti = 5 eV, ne = 5 cm−3. We also report that the spacecraft is shielding the

Langmuir probes on Rosetta from plasma electrons, and particularly low

energy electrons. In one instance, this blocking is shown to lead to an over-

estimation of solar wind electron temperature by 12% and underestimate

the plasma density by 24% by the Langmuir Probe for a +10 V charged

spacecraft in ne= 5 cm−3, Te = 12 eV solar wind. Two models used in lit-

erature on photoemission, one for isotropical emission from a plane and the

other for radial emission from a point, was used and compared. We report

a clear preference to the approximation of a Maxwellian energy distribution

of photoelectrons emitted radially from a point source model with our sim-

ulation result on the Langmuir Probe aboard Rosetta. We also report the

solar aspect angle dependence on the plasma potential and plasma density

result, which are in overall agreement with Rosetta measurements from the

second Earth fly-by.

Popularvetenskaplig sammanfattning

Ett av de kraftfullaste verktygen for att simulera hur en rymdfarkost paverkas

och paverkar sin omgivning i rymden, SPIS 5, har nyligen utokats med

mojligheten att simulera vetenskapliga experiment precis sasom de gors i

verkligheten. Rymden mellan solsystemets planeter ar inte tom utan fyllt

av plasma, det vill saga, elektriskt laddade partiklar. Nar en rymdfarkost

fardas genom rymden sa paverkas den av plasma och solljus och kan bade

ge ifran sig och absorbera partiklar. Detta forandrar plasmat nara rymd-

farkosten vilket ocksa paverkar de resultat vi far fran de vetenskapliga in-

strumenten ombord.

I denna rapport undersoker vi rymdfarkosten och kometjagaren Rosetta,

som ar 2014 ska observera och landa pa kometen Churuymov-Gerasimenko.

Ombord finns tva stycken svenskutvecklade Langmuirprober som mater

densiteter och laddningar pa plasmat for att undersoka vad kometen bestar

av, och hur en komet beter sig i den starka stralningen fran solen. Nagot

liknande har aldrig gjorts forut och eftersom kometer ar lika gamla som sol-

systemet sa hoppas man bland annat fa reda pa vad solsystemet skapades av

nar det foddes. For att kunna forsta de varden Langmuirproben uppmater

pa sin plats pa rymdfarkosten under sin resa, sa maste vi jamfora plasmat

innan rymdfarkosten paverkat det och efterat, och vad Langmuirproben

faktiskt uppmater.

Vi rapporterar har resultatet av simuleringar av en solbelyst modell av

rymdfarkosten Rosetta i ett plasma pa vagen till kometen, och vilka effekter

resultatet har pa vara matningar fran Langmuirproberna. Detta kan sedan

anvandas for att uppskatta vad ett ostort plasma har for egenskaper bara

med hjalp av vara matningar fran Langmuirproberna pa Rosetta. Med

hjalp av SPIS 5 sa kan vi ocksa visualisera resultatet och rymdfarkostens

omgivning pa ett vackert och lattillgangligt sett.

Acknowledgements

I would like to thank Anders Eriksson for invaluable and enthusiastic guid-

ance during the course of this master thesis work. I would also like to thank

Thomas Nilsson for teaching me the never-changing and problem-free life

that is making simulations in SPIS.

Contents

1 Background 1

1.1 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 The Rosetta mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 Plasmas and the Solar wind . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3.1 Debye shielding and Debye length . . . . . . . . . . . . . . . . . 3

1.3.2 Particle motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3.3 Photoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Langmuir probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.5 Theoretical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5.1 Probe theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5.2 Photoelectron current . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5.3 Photoelectron cloud . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.5.4 Magnetic effects . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.5.4.1 v × B . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.5.4.2 Larmor radius . . . . . . . . . . . . . . . . . . . . . . . 11

2 Simulations 13

2.1 SPIS - Spacecraft Plasma Interaction System . . . . . . . . . . . . . . . 13

2.1.1 SPIS 5 and theory . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.1.2 SPIS materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 Geometrical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2.1 Mesh resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

v

CONTENTS

3 Validation 19

3.1 Densities and potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Previous work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4 Theoretical model performance 23

4.1 Plasma electron current . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2 Photoelectron current in wake . . . . . . . . . . . . . . . . . . . . . . . . 24

4.3 Photoelectron current to a sunlit Langmuir probe . . . . . . . . . . . . . 26

4.4 Problematic zones for applying the model fit . . . . . . . . . . . . . . . 28

4.5 Electrostatic potential geometry . . . . . . . . . . . . . . . . . . . . . . 29

4.6 Second derivate of Langmuir probe sweep . . . . . . . . . . . . . . . . . 29

5 Comparison with probe sweep on Rosetta 35

6 Solar aspect angle dependence 39

6.1 Plasma potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

6.2 Density profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

7 Conclusions 47

7.1 Theoretical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

7.2 Rosetta Langmuir probe sweep . . . . . . . . . . . . . . . . . . . . . . . 48

7.3 SAA dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

7.4 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

References 51

vi

1

Background

———————————————————————-

1.1 Problem Definition

Rosetta is a spacecraft from the European Space Agency (ESA), on its way to the

comet 67P/Churyumov-Gerasimenko for a first of its kind in situ investigation, as well

as the most detailed environment investigation of a comet ever attempted. Comets

are believed to be the primitive building blocks of the planets in the Solar system

and seeded the Earth with water and possibly even life[12]. By studying a comet’s

dust and gas, its structure and abundances, the Rosetta Mission will help further the

understanding of the evolution of the Solar system and the role of comets therein.

The purpose of this report is to investigate the plasma environment around the

spacecraft and the effect of photoelectron emission from the Rosetta orbiter on the

measurements made on one of the instruments on board, the Langmuir probe instru-

ment. This is done by simulating the spacecraft environment and the data measured

by the Langmuir probe instrument, which is used to investigate the properties of the

plasma in the solar wind and surrounding the plasma, and compare it to real data from

the S/C.

1.2 The Rosetta mission

The Rosetta spacecraft consists of a 2.8×2.1×2.0 meter orbiter with two 32 m2 solar

panels and carries a smaller spacecraft, the lander, which will land on the comet.

1

1. BACKGROUND

Launched in March 2004, the Rosetta spacecraft is currently undergoing a ten year long

journey to comet 67P/Churyumov-Gerasimenko, having already completed three Earth

fly-bys and one Mars fly-by. The purpose of the fly-bys were twofold: providing the S/C

with the gravitational boost needed to reach its destination at correct angle of approach

as well as creating an opportune moment to test its instruments and investigate the

planets’ surroundings. The Rosetta mission is now less than a year from reaching the

same orbit and position as the target comet at 4 AU, and the start of its mission. The

duration of the mission is scheduled for at least a year from January 2014 until the

comet reaches its perihelion (the point closest to the Sun) at 1.2 AU[13].

Rosetta carries a multitude of instruments including two Langmuir probes designed,

manufactured and operated by the Swedish Institute of Space Physics (IRF) in Uppsala,

Sweden.

1.3 Plasmas and the Solar wind

As Rosetta travels to its destination, it is traversing through a medium dominated by

plasma (a collection of ions and electrons) ejected from the Sun, called the Solar wind.

The parameters of the plasma are depending on the condition of the Sun at the time

of its emission.

The fourth state of matter, plasma, as defined by Francis F. Chen, is a:

”quasineutral gas of charged and neutral particles, which exhibits collec-

tive behaviour” [1].

• For an ordinary neutral gas, the force of gravity between individual particles is neg-

ligible and the motion is usually controlled by collisions between individual particles.

This can also be true for a plasma, but as most of the particles in a plasma are charged,

the dominant motion driver is instead the total electric and magnetic field force on the

plasma. The term ”Collective behaviour” is reflecting on the movement of the charged

particles and the currents and fields thereby induced in the plasma, which influences

other plasma particles at a distance and thus drives the motion of the plasma as a

whole. If the plasma is sufficiently tenuous, we can speak of a collisionless plasma, and

disregard collisions completely for calculating the motion of the particles. This is the

case for all plasmas discussed in this work.

2

1.3 Plasmas and the Solar wind

Quasineutrality is a feature of the plasma of how the macroscopic picture of a plasma

is overall neutral, but the microscopic picture of individual plasma particles is far from

neutral. The scale length of this effect and other implications of quasineutrality deserve

a further explanation.

1.3.1 Debye shielding and Debye length

Debye shielding [1] is an innate ability of the plasma to shield out local potentials

within. If a body such as a probe, is put into a plasma, it will attract ions or electrons

depending on the relative potential difference. In doing so, it creates a small volume

sheath around the body with opposite charge of that body, which reduces the potential

of the body as it is felt by particles outside this volume. This phenomenon is known as

Debye shielding and the characteristic thickness of the sheath is known as the Debye

length.

This is also proven mathematically[1] by considering an electrostatic potential of a

single point particle of charge q at a distance r:

V (r) =q

4πε0r, (1.1)

where constants such as ε0,kB, etc. have their usual meaning in the body of this report.

It can then further be shown[1] that the effective potential seen when in a plasma will

be reduced to

V (r) =q

4πε0re− rλD , (1.2)

where λD is the Debye length, given by

λD =

√ε0kBTenee2

, (1.3)

where Te is the temperature of the electrons and ne is the density of electrons.

For mechanisms working at much larger distances than the characteristic scale

length λD, the potential is effectively shielded out. At such distances, the position

and motion of individual charges are therefore not important, and only collective ef-

fects of all particles need be considered. This is the main regime of consideration in

plasma physics.

3

1. BACKGROUND

1.3.2 Particle motion

The solar wind plasma is a very tenuous plasma, and thus assumed to be collisionless.

However it can still be assumed to follow a Maxwell-Boltzmann distribution of the

particle velocities, where the particles have a thermal motion with a mean thermal

velocity vth, given by:

vth,i =

√kBTimi

, (1.4)

where T and m is the temperature and mass of particle species i.

The bulk motion of the solar wind is assumed to be a uniform non-varying plasma

flow speed, vSW , taken to be the typical value of 400 km/s, flowing radially outward

from the Sun.

1.3.3 Photoelectric effect

To complete the picture of the spacecraft-plasma environment, we must also take the

photoelectric effect into account. When electrons in a molecule are hit by photons,

the molecule may absorb photons of specific energy intervals to excite and possibly

emit electrons. For metal surfaces exposed to photons, such as the spacecraft body in

sunlight, this effect has a measurable result in terms of overall charge of the surface,

and also creates a photoelectron cloud around the spacecraft body, moving with the

spacecraft.

It is also important for comets like comet 67P/Churyumov-Gerasimenko, where it is

responsible for ionizing the comet plasma tails, and to a smaller extent, the immediate

surroundings of the comet, called the comet coma.

The photoelectric effect, and the photoelectrons emitted by the effect is thus very

much depending on the solar spectrum and flux, the emission and absorption properties

of the material of the surface subjected to photons, such as the photoemission saturation

current, jf0, and the angle of incidence.

1.4 Langmuir probes

The Langmuir probe was invented by Nobel laureate Irving Langmuir (1881 − 1957). It

is used to determine various properties of a plasma such as temperatures and densities

4

1.5 Theoretical model

of different particle species. The underlying principle is that of an electrode immersed

in a plasma with a variable voltage being applied to it from a power supply, attracting

positive ions at a negative voltage and attracting electrons e.t.c. at a positive voltage.

The current flowing to the probe is then measured and will depend on the parameters

of the plasma measured.

The Langmuir probe instrument (LAP) on Rosetta consists of two sensors mounted

on two booms and associated electronics inside the spacecraft body, and was developed

by the Swedish Institute of Space Physics (IRF) in Uppsala, Sweden. It is part of the

Rosetta Plasma Consortium (RPC) on board Rosetta. The booms are of lengths 2.24

and 1.62 m and the probes themselves are 50 mm diameter titanium spheres covered

by titanium nitride (TiN) mounted on 15 cm stubs, see fig. 1.1[5][3].

Figure 1.1: Langmuir probe - Identical copy of Langmuir probe on Rosetta, image

courtesy of A. Eriksson

By investigating the plasma density, electron temperature and flow speed as well

as the time and space variations of these parameters, the LAP will give us an un-

precedented view of cometary outgassing and plasma environment, and will study the

evolution and activity of the comet 67P/Churyumov-Gerasimenko as it approaches its

perihelion. Some of the quantities measured and the operational ranges is listed in

fig. 1.2. The LAP can also be used in conjunction with the other RPC instruments on

board the Rosetta spacecraft to investigate phenomena none of them could do on its

own, such as magnetohydrodynamical waves [4].

1.5 Theoretical model

1.5.1 Probe theory

To quantify the probe current and separate it into its different particle contributions,

we use a theory first developed by Mott-Smith and Langmuir[10] called Orbital motion

5

1. BACKGROUND

Figure 1.2: Table of parameters accessible to LAP - The LAP has several different

modes of operation that collectively are capable of producing all parameter and their

ranges, but not individually or at the same time and every plasma [4].

limited theory (OML). It regards the plasma as a particle distribution moving in a

vacuum field from the probe, and obtains trajectories solely based on energy and angular

momentum conservation. This approach can only be adopted when the radius of the

probe is much smaller than the Debye length. For larger probe radii, a separate theory

called sheath limited theory (SL) need to be used, but for the plasmas considered and

the instruments used for this report, we can safely assume

rprobe � λD, (1.5)

where typical values of the Debye length in the Solar wind is ∼ 10 m and the probe

radius is 25 mm.

As a starting point, OML examines the current, I, to a body of zero net charge with

particle motion dominated by the particles thermal velocity. The particles are also

assumed to follow a Maxwellian energy distribution, which gives the thermal current

Ith, given by[17]:

Ith =∑i

Apqini

√kBTi2πmi

∀ particle species i, (1.6)

where Ap is the surface area of the probe. For convenience, temperatures will hereafter

be measured in units of eV, where 1 eV = 1.16× 104 K.

This is the random current to a neutral probe, but during a Langmuir probe voltage

sweep, the current varies as a function of the probe potential. This is complicated

further by that the potential applied to the probe, the bias voltage, is not the absolute

6

1.5 Theoretical model

voltage of the probe itself. Instead, the voltage of the spacecraft is often non-zero and

not known before the measurement. i.e:

Vp = Vb + VS/C , (1.7)

where Vp is the probe potential, VS/C is the potential of the spacecraft and Vb is the

bias voltage applied to the probe. Why the potential of the spacecraft is not zero and

the implications of this is discussed further in section 2.1.

Electron current

Now, assuming all particles coming from a zero potential at infinity, and energy and

angular momentum conservation, it can be shown [2] that the OML current for electrons

follows:

Ie =

Ie0(

1 +VpTe

)for Vp ≥ 0

Ie0eVpTe for Vp < 0,

(1.8)

where Ie0 is the thermal current Ith for electrons, given by

Ie0 = Apene

√kBTe2πme

(1.9)

From the equation, we can see that the plasma electron current, dominated by

the thermal motion of electrons, increases linearly for a positive probe and decays

exponentially for a negative probe. A positive current is defined as the flow of a

negatively charged particle to the node, by convention.

Ion current

Ions in the solar wind, being heavier than the electrons, are not as influenced by

their thermal energy, but their motion is instead dominated by their drift velocity,

vd. Engwall (2006) [2] shows that the drift velocity current contribution to a charged

probe is instead

Iion =

{Iion0

(1− 2qionVp

mvd

)for vd ≥ vmin

0 for vd < vmin,(1.10)

7

1. BACKGROUND

where vmin is the minimum velocity, given by

vmin =

{√2qVpm for qVp > 0

0 otherwise,(1.11)

and

Iion0 = −Aramqionnionvd, (1.12)

where Aram is the cross-sectional area of the probe. Comparing eqs. (1.8) and (1.10),

we see that at attracting potential, the drift energy 12mv

2d has replaced the thermal

energy Te, and the drift current Aramqionnionvd has replaced Ie0 but with the area

normal to the ion flow replacing the total surface area. For a repelling potential,

eq. (1.10) is actually consistent with eq. (1.8) in the limit T → 0.

Also, as the solar wind is assumed to have a zero net charge, we can write

ne ≈ nion (1.13)

1.5.2 Photoelectron current

As discussed in section 1.3.3, the probe and the spacecraft body will emit photoelectrons

when hit by the sunlight, and this emission depends on the properties of the material

subjected to it and the potential of the probe. As the probe potential increases, fewer

electrons are emitted from the probe and more electrons are being reabsorbed.

How this photoemission behaves on the body of the Langmuir probe in space is not

easily modelled since it depends on the material of the probe, its geometry as well as

the electric field surrounding the probe. Since the electric field is highly dependent on

the plasma-spacecraft interaction, no obvious solution is known.

In this study we adopt two models suggested by J.R.L Grard[7] for two cases of

photoemission, both proven to be successful from previous studies[7][17].

Model 1

Both models consider the electrons as being emitted at certain energies somewhere in-

side the material, and through collisions within the material, exits the material with a

Maxwellian energy distribution. This was also proven to be consistent with experimen-

tal results for a wide range of materials[7]. There are however two important cases to

8

1.5 Theoretical model

consider. First, Rejean J.L. Grard et al[7] suggests the case of a Maxwell distribution

of electrons emitted isotropically from a plane surface:

If =

−If0e−VpTf for Vp ≥ 0

−If0 for Vp < 0(1.14)

where If0 is the photo emission saturation current, jf0 of the probe surface.

Here the current magnitude decreases to zero as the potential of the probe increases,

and more emitted electrons are being reabsorbed. The current reaches its maximum

negative value when the probe is highly negative and all emitted electrons are being

repelled towards infinity. This model features a very sharp transition from positive to

negative probe voltage and an example can be seen in fig. 4.4.

Model 2

Rejean J.L. Grard et al [7] also discusses a second model for the probe photoemission

current, which introduces a second linear term in the positive probe potential case. This

model describes emission from a point source, which may more accurately describe the

photoemission from the spherical probe:

If =

−If0(

1 +VpTf

)e− VpTf for Vp ≥ 0

−If0 for Vp < 0(1.15)

This model is smoother in the transition region between positive and negative probe

potentials (see fig. 4.4), but there is no obvious conclusion on which of the photoemis-

sion models is preferred in nature. The simulation software SPIS simulates isotropical

photoelectron emission from all surfaces, so naıvely, eq. (1.14) would be preferred. How-

ever the question is rather if the curvature of the Langmuir probe is large enough, and

the sphere small enough, to be approximated as a point source emission. Which would

mean that an isotropical distribution from the sphere is equal to a radial distribution

from a point. Therefore we will use both models for comparison to real data and the

simulation results until a preference is determined.

1.5.3 Photoelectron cloud

Photoelectrons are of course also emitted from the spacecraft body, booms and solar

panels, and are the source of a photoelectron cloud surrounding the spacecraft and the

9

1. BACKGROUND

Langmuir probes. If the photoelectron cloud is large enough, these electrons will be

absorbed by the probe as well. If we assume that the cloud is fairly homogeneous, we

can assume a similar current as eq. (1.8), reasonably as a function of probe bias voltage

instead:

IS =

IS0(

1 + VbTph

)for Vb ≥ 0

IS0eVbTph for Vb < 0,

(1.16)

where Tph is the temperature of the emitted photoelectron in eV and IS0 is given by:

IS0 = Apenph

√kBTph2πme

, (1.17)

where nph is the number density of photoelectrons.

This model has been proven to work well in previous studies[17].

1.5.4 Magnetic effects

So far we have disregarded some effects that complicate the motion of a charged particle

in a plasma, namely, magnetic effects. In this section we will go through two of the

most important magnetic effects to motivate why we can ignore any magnetic effects

in the model.

1.5.4.1 v × B

The interplanetary magnetic field at 1 AU is very small, about 10 nT[17], but will induce

an electric field for a moving charge in the plasma surrounding Rosetta according to:

E = v ×B (1.18)

where the solar wind velocity is about 400 - 500 km/s and the spacecraft velocity is

negligible in comparison.

The maximum induced electric field will then be for a velocity perpendicular to the

magnetic field, such that:

E = 400× 103 × 10−8 = 4× 10−3 V/m. (1.19)

Since the Langmuir probes are located on booms of one to two meters in length, the

maximum induced potential will be on the order of 0.01 V, which is so small that we

can consider it negligible.

10

1.5 Theoretical model

1.5.4.2 Larmor radius

The equations in section 1.5.1 are valid for unmagnetized plasmas, however the solar

wind is also magnetized. As a charged particle move through a magnetized plasma,

it will have a gyrating motion, and may limit the Langmuir probe sample to a small

column of particles moving perpendicular to the magnetic field if the gyro radius is

sufficiently small.

The Larmor radius, or gyroradius, is given by:

rL =mv⊥qB

, (1.20)

which for an electron of temperature 12 eV, moving in the interplanetary magnetic field

of 10 nT becomes ≈ 200 m. This is very much larger than the probe radii of 25 mm,

so we can safely disregard magnetic effects when applying our models.

11

1. BACKGROUND

12

2

Simulations

2.1 SPIS - Spacecraft Plasma Interaction System

Spacecraft charging, where a spacecraft travelling in various plasma environments is

positively or negatively charged due to interactions with the plasma, poses a real threat

for commercial and scientific spacecraft alike. Local potential differences on a space-

craft can lead to sparks that can disable entire subsystems on the S/C. One notable

example of that is Japanese satellite ADEOS, which was lost following severe space-

craft charging[11]. The problem of regulating the voltage over all the spacecraft surfaces

needs to be accounted for in the design of the spacecraft, and potential hazards iden-

tified. The only reasonable solution is then to model the design and test it through

simulations.

Also, the plasma-spacecraft-induced environment around the spacecraft perturbs

any plasma measurements by scientific instruments on-board the spacecraft, a problem

that cannot always be designed away cost-effectively and thus needs to be modelled

accurately to understand the measurements.

To combat these problems for a spacecraft of any shape, size and material and

various plasma environments, ESA started the initiative of a new simulation software

in 2002 that later became the open source software SPIS, Spacecraft Plasma Interaction

System. It has many features and capabilities (too many to list here) but essentially, it is

a Particle-In-Cell (PIC) routine that solves the Gauss’ law for electric fields,∇2φ = − ρε0,

for particles and secondary particles of many different particle distributions [9].

SPIS is built using a modular approach, so that the underlying core, the GUI or any

13

2. SIMULATIONS

open source plug-in can be updated and inserted with greater ease. Although funded

mostly by ESA, SPIS relies on an open-source license (GPL) to enable a community-

based development, and high compatibility with many systems and file formats [15].

2.1.1 SPIS 5 and theory

The study presented was made using the latest SPIS version at the a non-released

development version, SPIS 5.0.0 [16]. This latest version supports the simulation of

a particle detector experiment, such as a full Langmuir probe Sweep inside the sim-

ulation and handles the previously computationally very demanding particle detector

simulation a rather ingenious way.

SPIS is normally simulating the plasma-spacecraft interaction by solving the Poisson

equation for each macro-particle to see how the plasma around a spacecraft evolves with

time. The differential equation is solved using a Runge-Kutta step method, which is

one of the most stable and a reasonably efficient method to solve differential equations

and can be fully parallelized.

New in SPIS 5 is the ability to perform a separate particle detection experiment

at any stage of the plasma simulation, called backtracking. Liouville’s theorem for a

Hamiltonian dynamical system, states that:

” The distribution function is constant along any trajectory in phase

space.” [18].

Equivalently, we can say that the existence of a conserved current in a system implies

that the system is invariant under time translation. We can thereby freeze the system

at any point and emit test particles in the negative time direction from a particle

detector. The test particles are weighted by the value of the distribution function of

the tracked species at the surface it finally encounters, either on the spacecraft or on the

simulation boundary, to simulate particles of different species and emitted at different

energy levels.

The test particles final destination determines what particle type is detected on

the particle detector. An electron whose origin in the positive time direction is the

boundary of the spacecraft model is of course a plasma electron type, and an electron

emitted from the spacecraft is a photoelectron type, etc.

14

2.1 SPIS - Spacecraft Plasma Interaction System

This backtracking method enables SPIS to dedicate processor time to only the

particles that the particle detector detects, without losing information of the plasma

surrounding the particle detector. The implication of this is enormous as the random

noise in a particle detector result is proportional to√n, where n is the number of

particles detected. To achieve a reliable result, a particle detector experiment normally

prefers the simulation volumes to be small, particle detection areas to be large and

particle densities to be high. Any deviation from the ideal set-up will result in large

errors for short simulations, or large computational time costs for high accuracy mea-

surements. Backtracking enables SPIS to simulate the real world scenario, with tenuous

plasma in large simulation volumes. It is also enabling the use of small detection areas

and reaching a sufficient accuracy within a reasonable simulation time with the use of

quite modest modern computers.

2.1.2 SPIS materials

SPIS has a large collection of pre-defined materials, and the possibility to define your

own. Any spacecraft volume is treated as an empty space where no particles are

allowed with infinitely thin surfaces surrounding it. These surfaces can then be defined

to mimic the properties of any material of a certain thickness and can both absorb and

emit particles. This is no small a task for a spacecraft, which consists of many parts of

all kinds of materials and thicknesses. For simplicity, the entire spacecraft, solar panels

and Langmuir probes in this model is treated as Indium Tin Oxide, ITO,[6] which the

solar arrays are coated with, and whose properties are similar to the material of the

probe. While the details of the actual surfaces differ, the most important property, i.e.

that they are conductive, is the same.

One current limitation of SPIS is that the mean photoelectron temperature is de-

fined globally for each surface of the simulation. In reality, material photoemission

properties are depending on the quantum structure of the material, and thus rather

unique for each material, including but not limited to the mean photoelectron tem-

perature [7]. As this limitation is inherent to SPIS, the only additional approximation

caused by assuming all s/c surfaces are of the same material is that the photosaturation

current is set equal everywhere.

Also, we do not simulate all types of ions present in the solar wind, but only

the most abundant, H+. Regardless, we expect only a negligible contribution to the

15

2. SIMULATIONS

detected currents from any ions for the voltage ranges used in our simulations. This

is because the ions are highly energetic and scarcely affected by the relatively small

voltage ranges simulated on the S/C and the Langmuir probe.

2.2 Geometrical model

Some simplifications are made to save computational time in the making of the model.

We modelled Rosetta, see fig. 2.1 in a prolate spheroid simulation volume, which is an

ellipse with major axis b = 30 m and minor axis a = 15 m rotated around its major

axis. Rosetta itself was modelled as a 2.8 × 2.1 × 2.0 meter cuboid of Indium Titanium

Oxide (ITO) with two 32 m2 ITO solar arrays and two ITO cylindrical booms with two

probes corresponding to the Langmuir probes and booms of the same shape and size.

The model was originally created by Alexander Sjogren [14] in 2009, but was reworked

and improved upon to accommodate the new SPIS version, including the addition of

detailed models of the Langmuir probes and improved models of the probe booms on

Rosetta.

Figure 2.1: Model mesh - The 2D meshed model of Rosetta with Langmuir probes

and booms as used in SPIS. Top right: The entire simulation box, containing Rosetta and

support rendering boxes.

16

2.2 Geometrical model

2.2.1 Mesh resolution

The model mesh represents volumes by tetrahedrons and surfaces by triangles of dif-

ferent sizes to accommodate a varying resolution in the volume to make the simulation

more time efficient. The resolution is most refined near the probes, followed by the

booms, spacecraft body, solar panels and simulation box borders in decreasing order of

resolution.

One obvious source of error would be the resolution of the spherical Langmuir

probe. As a circle has infinite amount of edges, the perfect sphere surface would have

to be represented by an infinite amount of triangles, otherwise resulting in errors in the

volume and surface area of the probe, see fig. 2.2. But since the backtracking algorithm

in SPIS defines each surface of a langmuir probe as a separate particle detector, the

resolution of the probe was found to be one of the largest computational time driver,

and as such, needed to be limited.

The resolution chosen represented the probe as a surface of 124 triangles with a

surface area corresponding to 92.4% and volume of 87.2% of the actual probe. The

longest simulation time with this resolution was 24 hours.

17

2. SIMULATIONS

Figure 2.2: Probes at different resolutions - Four spherical probes meshed at a

resolution of 30 to 2624 triangles, from bottom right to top left. The probe used in the

simulations reported is pictured bottom left, consisting of 124 triangles with volume and

surface area of 87% and 92% of the actual Langmuir probe, respectively. Note that even

at the highest resolution, the probe is not quite spherical, and one would require a more

complicated model to achieve a higher volume ratio than 96.7%

18

3

Validation

3.1 Densities and potential

Many simulations were performed to test stability and correctness of the simulation

parameters. An overview of the important features of the plasma-spacecraft interaction

is given in figs. 3.1 and 3.2.

Figure 3.1: Photoelectron and ion densities visualisation - Photoelectron density

increasing from to blue to yellow in the xz-plane, ion density increases from blue to red on

the xy-plane and the Rosetta spacecraft depicted as white. The Sun is in the positive x

direction. Simulation parameters: 4 Million particle simulation, VS/C = 10 V, Te = 12 eV,

Tion = 5 eV, Tf = 2 eV, ne = 5 cm−3 solar wind at v = 400 km/s. Simulation name:

EFSRE8V1.2eV-220513-1.

19

3. VALIDATION

Figure 3.2: Electrostatic potential overview - Equipotential volume shells are shown

increasing in potential from blue to red for a +10 V charged Rosetta spacecraft. The Sun

is in the positive x direction. Simulation parameters: 4 Million particle simulation, Te =

12 eV, Tion = 5 eV, Tf = 2 eV, ne = 5 cm−3 solar wind at v = 400 km/s. Simulation

name: optimeradtest-100413-3.

We clearly detect an ion wake behind the spacecraft, shown in dark blue, due to

the ion flow velocity is much greater than the thermal velocity in nominal solar wind,

as expected. We also detect a photoelectron cloud distribution surrounding the S/C

and extending in the sunward direction. The highest densities of photoelectrons are

located in the immediate vicinity of sunlit surfaces, with a rapidly decreasing density

in the negative x direction from the S/C.

The electrostatic potential from the spacecraft decreases in magnitude rapidly with

distance from the spacecraft and reaches 1 V at approximately 10 meters from the

spacecraft in the +y and -y directions. Clearly, the solar array is the largest influence the

surrounding plasma, both in terms of photoemission and generating the photoelectron

cloud, but also in terms of dominating the electrostatic potential geometry.

3.2 Previous work

To validate the new version of SPIS, SPIS 5, a reference simulation of the same exact

parameters as Alexander Sjogren SPIS 3.7RC05 version was made, and some results

20

3.2 Previous work

are shown in fig. 3.3 below.

Figure 3.3: Photoelectron density(left column) and ion density(right column) of refer-

ence simulation in the new version of SPIS (top) and Sjogrens SPIS 3.7RC05 simulation

(bottom)[14]

In Sjogren’s geometrical model, the booms were cuboid and the Langmuir probe

itself missing, whereas in this version we have added detailed models of the probe and

used cylindrical booms. The new SPIS version also allows for much faster performance

due to parallelization and the full utilisation of multiple processors. Comparing overall

features of ion, electron and photoelectron distribution, as well as potentials at various

points we find no discrepancy more than was expected from simulation uniqueness,

where every simulation is different due to the randomness in meshing the model volume

and sourcing the plasma particles.

21

3. VALIDATION

22

4

Theoretical model performance

Simulations of the Langmuir probe sweeps were made, where the current detected on

the probe is measured at a stepwise varying potential and subsequently compared with

the theoretical model to test our understanding of the problem in the following sections.

The parameters chosen for all simulations (unless otherwise specified) were the same

as Sjogren’s reference simulation [14] of a Rosetta spacecraft in a nominal solar wind,

and detailed in Appendix A.

4.1 Plasma electron current

SPIS generates separate particle detection simulations for each particle population, and

can thus separate each contribution with ease. To test our model we separated and

simulated only the plasma electron current, from a Langmuir probe sweep and compared

with the expected result, see fig. 4.1. We also adjusted the ne and Te parameters to

the theoretical expression to obtain a good fit to the simulated sweep

The plasma electrons are repelled by the probe when the probe potential is negative

and attracted linearly otherwise. All three electron sweeps reveal identical results, with

best fits obtained for Te = 13.5(± 0.1) eV and ne = 3.83(± 0.01) cm−3. This is however

a lower current than we expected from the theoretical model and suggests that the probe

is somewhat shielded from electrons, and especially electrons with less energy, which

gives an overestimation of the plasma electron temperature and underestimation of

the plasma density. The plasma electron density is also confirmed to be lower near

23

4. THEORETICAL MODEL PERFORMANCE

Figure 4.1: Plasma electron sweep - Multiple electron sweeps with different potential

steps and VS/C = 10, 8 and 7 V (Black, red and green circles). 4 Million particle simu-

lations, Te = 12 eV, Tion = 5 eV, Tf = 2 eV, ne = 5 cm−3 solar wind at v = 400 km/s.

Theoretical result for simulation parameters(red line) and model fit fromeq. (1.8) (blue

line).

all spacecraft surfaces by investigation of the 3D-plots of the plasma, see fig. 4.2, thus

suggesting that the model is valid, and that the discrepancy has a physical origin.

4.2 Photoelectron current in wake

To further test and separate our understanding of the photoelectron current to the

Langmuir probe, a simulation was carried of a Langmuir probe sweep while in the wake

and shadowed by the spacecraft. As there is no photoemission on objects in shadow, the

only photoelectron current detected would be the absorption of photoelectrons from the

photoelectron cloud, as detailed in eq. (1.16). The result is then plotted and compared

to the theoretical result of different scenarios, see fig. 4.3.

The result was far from expected, so the simulation was redone with different poten-

24

4.2 Photoelectron current in wake

Figure 4.2: - Electron density 3D-plot of a nominal solar wind parameter simulation

EFSRE8V1.2eV-220513-1, with the Sun is in the +x direction.. The Rosetta Spacecraft

and Langmuir probe 1 visible in gray

tial steps to assure that the unexpected result didn’t arise from numerical divergence

errors in the code or incorrect circuit relaxation timescales on the particle trajectories.

Also other solar aspect angles in the shadow of the S/C was investigated and found to

yield similar results for both probes.

Quickly apparent is that the knee of the function does not occur around Vb = 0, as

expected by the model in eq. (1.16), but otherwise follows the same shape. This model

has proven useful in reality for other scenarios on Rosetta[17], but leads in this scenario

to an unrecoverable overestimation of either Tph or nph.

The photoelectrons, largely occupying a space of non-zero potential originating

from the potential of the spacecraft, will instead be attracted or repelled by the probe

depending on the relative potential of the probe to its surroundings. Similarly, pho-

toelectrons emitted by the probe is ejected into a plasma with a non-zero potential,

Vplasma, and will not be reabsorbed if the probe is more negatively charged than its

immediate surroundings. Therefore, the photoelectron current should instead be a

function of Vp − Vplasma. To accommodate this, we substitute this for Vp in eqs. (1.14)

and (1.15) and for Vb in eq. (1.16) and test it for a sweep on a sunlit probe.

25

4. THEORETICAL MODEL PERFORMANCE

Figure 4.3: Photoelectron sweep in wake - Two simulations(LP2SAA-40-270513-

1 and LP2SAA-40-270513-2) of langmuir probe sweeps with different potential steps is

plotted in blue diamonds of a nominal solar wind and Tph = 2 eV. The theoretical model

result of different scenarios is overlayed in blue, green and purple (for repelling potentials)

and a fitted red line for attracting potentials. The expected nph from 3D plots is on the

order of 10 cm−3, and the mean photoelectron temperature, Tph is 2 eV.

4.3 Photoelectron current to a sunlit Langmuir probe

In this scenario, the probe is sunlit at 180 ◦ SAA while conducting the Langmuir probe

sweep. The result is then compared with the competing models from section 1.5.1,

combined with the photoelectron emission current discussed in section 4.2 to determine

which model describes our results best.

As all plasma and photoelectron parameters are input parameters to the simulation

and hence are known, there are only two free parameters for fitting the simulated probe

sweep to the theoretical expressions: the photoelectron cloud density at probe position,

nph, and the plasma potential at probe position, Vplasma. We adjust these manually

until the best fit is obtained, with the results as shown in table 4.1.

When the absolute potential of the probe is highly negative, all emitted photo-

electrons are emitted from the probe to infinity but as the potential increases, some

26

4.3 Photoelectron current to a sunlit Langmuir probe

-­‐1.00E-­‐07  

-­‐5.00E-­‐08  

0.00E+00  

5.00E-­‐08  

1.00E-­‐07  

1.50E-­‐07  

-­‐10   -­‐8   -­‐6   -­‐4   -­‐2   0   2   4   6   8   10  

I  vs  Vb  

Backtrack  120313  

Model  1  

Model  2  

Figure 4.4: Langmuir probe sweep and theoretical models - Current vs bias volt-

age. SPIS 8.3 million particle simulation probe sweep (blue diamonds) on a sunlit Langmuir

probe with a +10 V charged spacecraft at 1 AU, in Te = 12 eV, Tion = 5 eV, Tph = 2 eV,

ne = 5 cm−3 solar wind at v = 400 km/s. The Model 1 (red line) and Model 2 fit (green

line) includes the photoelectron cloud current from the eq. (1.16) and are both offset by

some potential, Vplasma, as discussed in section 4.2.

Model 2, Equation (1.15) Model 1 Equation (1.14)

If0 (A) 6.0× 10−8 6.0× 10−8

Vfloat(V) 6.4 ± 0.1 7 ± 0.1

nph (cm−3) 14.13 ± 0.3 14.5 ± 0.3

Te (eV) 12 12

Tf (eV) 2 2

Tion (eV) 5 5

Table 4.1: Model comparison - parameter results of model fits to probe sweep from

fig. 4.4.

of the emitted photoelectrons are reabsorbed by the probe as described in eqs. (1.14)

and (1.15). Also, as the potential of the probe is positive w.r.t. the photoelectron cloud,

we observe a current linearly increasing with the potential, offset by some potential,

27

4. THEORETICAL MODEL PERFORMANCE

Vplasma, as we predicted.

The results in table 4.1 show that the models are consistent with regard to the num-

ber density of the photoelectrons, but yields significantly different results for Vplasma.

Combined with the result from fig. 4.4, we find that model 2 describes the simulation

result confidently and was then chosen to yield the experimental results of the parame-

ters Vplasma and nph in the body of this report. The final photoelectron current model,

called Model 3, then becomes:

Iph = IS + If , (4.1)

where

If =

−If0(

1 +V†Tf

)e−V†Tf for V† ≥ 0

−If0 for V† < 0,(4.2)

where

V† = Vp − Vplasma, (4.3)

and

IS =

IS0(

1 +V†Tph

)for V† ≥ 0

IS0eV†Tph for V† < 0.

(4.4)

Note that by using the model for photoemission from a point, we by no means

suggest that the probe is a point and that all photoelectrons are emitted radially in

reality (or in SPIS). We merely suggest that it seems that the probe is sufficiently small

so that we can approximate it to a point in the model.

4.4 Problematic zones for applying the model fit

The model works perfectly well for a wide range of solar aspect angles, but at certain

scenarios we find fitting the model not as straightforward, as seen in figure fig. 4.5.

The problem arises only when the probe is sunlit, in the wake and the boom is

fully or partially in the shadow of the spacecraft. At a SAA of -70◦, Langmuir probe

2 (LP2) is fully sunlit but in the ion wake and most of the boom is in the shadow of

the spacecraft. Only by erroneously using a too high photoelectron temperature do we

reach a satisfying fit, and this also yields a slight overestimate of the plasma potential

and photoelectron density.

28

4.5 Electrostatic potential geometry

4.5 Electrostatic potential geometry

The OML theoretical model for electrons and photoelectrons assumes particles coming

from a zero potential source at infinity, approaching a probe with a monotonic electro-

static potential field geometry of a plane or a point. However, as seen in fig. 4.6, the

electrostatic potential is far from spherically symmetric, and the probe is fully inside

the electrostatic potential generated by the spacecraft.

Only very close to the probe does the electrostatic potential field look spherical,

and approaches a cylinder with a spherical top as the distance to the probe increases

until the field is fully dominated by the spacecraft potential. This geometry is not

straightforward to model analytically for a probe with varying potential, but the model

works very well to yield precise results for most scenarios. When the boom is shadowed

by the spacecraft, the probe loses a large and easily accessed source of photoelectrons,

and this is exactly when the model fitting fails and yields very imprecise results, and

we need to acquire a plasma potential measurement by other means.

4.6 Second derivate of Langmuir probe sweep

Since we expect a sudden sharp increase of the gradient in the CV function around

the floating potential, we expect a peak in the second derivative of the CV function

somewhere near the floating potential. This means that the second derivative should

show a maximum around the floating potential. As differentiating a signal always

increases noise, fitting to an exact theoretical expression of the probe current can be

problematic. However, we should be able to recover the peak location, i.e. the floating

potential, by fitting to some generic function with a localized peak, e.g. a Gaussian

curve. The second leapfrog derivative was then plotted in fig. 4.7 and fitted with a

Gaussian curve.

Here we find that the first peak of the second derivative can clearly be used to

accurately deduce the potential at the probe position, and is remarkably consistent

with the model fit result of 6.4 (±0.1) V. We have no other analytical support for using

a Gaussian fit routine to the second derivative, merely other than it works very well.

This Gaussian fit routine will not work for a probe in shadow, as the electron

and photoabsorption current does not follow the same exponential function as the

photoemission current. However, it provides a means for getting a secondary estimate

29

4. THEORETICAL MODEL PERFORMANCE

whenever our theoretical model fails to produce precise results, such as the regions

discussed in the previous section

30

4.6 Second derivate of Langmuir probe sweep

(a)

(b)

(c)

Figure 4.5: CV sweep and model fits, current (A) vs Vb (V) - In the right column

we have Model 3, as detailed by eq. (4.1) fitted to the simulation result . The model is then

separated into photoelectron emission and photoelectron cloud absorption parts, where the

photoelectron emission part is subtracted from the simulation result and plotted against

the photoelectron cloud absorption model (upper left) or vice versa (lower left) on each

row.

31

4. THEORETICAL MODEL PERFORMANCE

(a)

(b)

(c)

Figure 4.6: Electrostatic potential geometry surrounding the Langmuir probe

- Equipotential shells in the plasma for a +10 V charged S/C for a +10 V probe (a), +8V

charged S/C for a +5.2 V probe (b) and -1 V probe(c).

32

4.6 Second derivate of Langmuir probe sweep

-­‐1.00E-­‐08  

-­‐5.00E-­‐09  

0.00E+00  

5.00E-­‐09  

1.00E-­‐08  

1.50E-­‐08  

2.00E-­‐08  

2.50E-­‐08  

-­‐10   -­‐9   -­‐8   -­‐7   -­‐6   -­‐5   -­‐4   -­‐3   -­‐2   -­‐1   0   1   2   3   4   5  

Leapfrog  deriva-ve  of  Probe  Sweep  

Gaussian  

Second  Deriva>ve  Deriva>ve  

Figure 4.7: Current voltage derivatives - First and second current leapfrog derivative

(red and blue diamonds) of a simulation Langmuir probe sweep and Gaussian fit (black

line) with µ = -3.6 and σ = 0.9, corresponding to a plasma potential of 6.4 V at the probe

position

33

4. THEORETICAL MODEL PERFORMANCE

34

5

Comparison with probe sweep on

Rosetta

The final test of SPIS is of course the ability to produce simulation results that are con-

sistent with actual Rosetta measurements. We therefore analyse a Rosetta spacecraft

Langmuir probe 1 (LP1) measurement from 11/9 2009, where Rosetta is at approxi-

mately 1 AU, with SAA -10◦ in the Solar wind, by fitting the Rosetta results with the

theoretical model. Thereafter we simulate iteratively until we find the best fit to the

Rosetta result and plot the results in fig. 5.1.

The simulation result is adjusted in the photoelectron emission dominated region by

a factor of 1.04, accounting for the unknown instantaneous Solar UV spectrum, roughly

corresponding to a 4% increase in flux at the time of the Rosetta measurement. The

Solar UV spectrum is not static, as it is in our simulation, and we find a 4% offset in

the photosaturation current to be very reasonable.

We find the overall fit and shape of the result to be largely a success, with only minor

discrepancies at certain regions. The CV sweep is dominated by the photoelectron

current, and we only find a small contribution to the current from the plasma electrons,

and a negligible contribution from the ions, as expected.

The average photoelectron temperature, Tph governs the shape of the knee in the

photoemission current by the electrons emitted by the probe, as well as the slope of

the photoelectron cloud absorption. Unfortunately, SPIS does not yet allow for setting

the average photoelectron temperature, Tph, to be a material property and thus unique

for each material. Instead it is treated as a global constant throughout all simulation

35

5. COMPARISON WITH PROBE SWEEP ON ROSETTA

Figure 5.1: Probe sweep in SPIS and on Rosetta - Current vs Voltage Langmuir

probe sweep. Rosetta RPCLAP091109015SRDS18NS LP1 sweep at 1 AU (red circles) with

unknown plasma parameters and spacecraft potential. Three SPIS simulations for each

particle contribution, plasma electron, ion and photoelectron (purple, solid blue and green

diamonds respectively) and the total current (solid black) on LP1. The total simulation

result current in the photoelectron emission dominated region (from -10 V to 0 V) is

slightly adjusted by a factor of 1.04 to account for the unknown instantaneous Solar UV

spectrum at the time of the Rosetta measurements. Simulation parameters: 4 million

particle simulations for a +8 V charged spacecraft at 1 AU, in Te=12 eV, Tion=5 eV, Tph=

1.2 eV, ne = 5 cm−3 solar wind at v = 400 km/s.

surfaces. In reality, photoelectrons emitted by the Langmuir probe coated with TiN be-

haves differently than photoelectrons emitted from materials from the spacecraft body,

booms and solar arrays, including Tph as well as emission and absorption properties[7].

A lower Tph will make the knee sharper, but will also steepen the photoelectron

cloud absorption curve, as shown by eq. (4.1). This is also visible in our results, where

the knee is not as sharp as the Rosetta result and we cannot simulate with a lower Tph

without diverging wildly in the attractive potential region. Nevertheless, the overall fit

is quite good.

Another source of error is the probe resolution, where the surface area is only 92%

36

of the Rosetta probe. The influence of this error on the result is expected to generate

a very small offset in the photosaturation current, much in the same way as of the

unknown instantaneous Solar UV flux error source, thus already accounted for in our

photosaturation current factor of 1.04.

37

5. COMPARISON WITH PROBE SWEEP ON ROSETTA

38

6

Solar aspect angle dependence

Another important aspect is to model the solar aspect angle dependence of the Lang-

muir probe sweep results. As Rosetta rotates around its axis, LP1 and LP2 will occupy

regions of different photoelectron densities and potentials, which will have a large ef-

fect on the probe measurements. As each Langmuir probe is mounted on booms of

different lengths which are connected at dissimilar angles to the spacecraft surface, we

expect the dependence to behave differently for each probe. A schematic on the probe

configuration at a selection of important solar aspect angles is shown in fig. 6.1.

6.1 Plasma potential

We analysed the dependence by making Langmuir probe sweep simulations of pho-

toelectrons of each angle for both probes, and by fitting the resulting photoelectron

current to our model according to eq. (4.1) to obtain values for nph and Vplasma. For

each fit, a worst case fit was made by eye to estimate the error margin of each parameter.

For Langmuir probes in a few selected regions close (. 30◦) to the wake, with

the boom partially or fully shadowed, Model 3 fails to give precise results, as seen in

section 4.4. Therefore, a second estimate for the potential was made, using the Gaussian

fit to the secondary derivative of the current, detailed in section 4.6. However, we still

preserve the error margins from the worst fit routine.

The Vplasma result, as seen in fig. 6.2 was compared to a previous SPIS 3.7 simulation

result from Sjogren [14] in fig. 6.3 with identical plasma parameters. In this version,

the Langmuir probe booms are cuboid and the Langmuir probe themselves are missing.

39

6. SOLAR ASPECT ANGLE DEPENDENCE

Figure 6.1: Schematic of solar wind wake for LAP - Assuming radial flow from the

Sun, for various values of the solar aspect angles. The green box is the spacecraft body,

seen here from the +y direction in the s/c coordinate system, with the +x and +z faces

marked in the top left panel. The red thin rectangle indicates the solar panels, and the

black arrows show the probe positions on the booms. The sunlight and solar wind flow

direction are shown by a yellow arrow. Nominal wake edges are indicated by the blue lines.

Image and text courtesy of A. Eriksson.

Therefore, the plasma potential is measured at some region in space corresponding to

where the Langmuir probes should be, and plotted against solar aspect angle.

40

6.1 Plasma potential

Figure 6.2: SPIS 5 LP sweep resultt, Vplasma vs SAA - Plasma potential mea-

surements from Model 3 fits to 42 Langmuir probe sweeps at different SAA, each point

representing a unique 7 million particle simulation in SPIS 5.

Figure 6.3: SPIS 3.7 Result, Vplasma vs SAA. - Result from Sjogren [14], with an

older model, lacking Langmuir probes, and older version of the Langmuir probe booms. The

measurements are taken as manual measurement in a region in space where the Langmuir

Probe center should be and plotted against SAA angle.

41

6. SOLAR ASPECT ANGLE DEPENDENCE

We find large discrepancies in both the shape and amplitude of the SAA dependency

to the plasma potential result Even though, from fig. 3.3, we found the plasma density

profiles to be in agreement.

The wake effect appears to be much more prominent in our results, and we recover

the expected potential drop of about 0.5 V behind the solar array in the LP1 measure-

ment (around 60◦). In the LP2 measurement (around -45◦), we expect a larger potential

drop in the wake behind the spacecraft of about 1.5V, but we find the actual drop to

be 2-3 V. Note however that we have large uncertainties in these measurements in the

wake from the model, and they are not normally evaluated for the Langmuir probes

on Rosetta. This wake effect in Sjogren’s results however, is barely distinguishable and

much less than we would expect.

The SPIS 3.7 simulation result has failed to predict the solar aspect angle depen-

dence in the solar wind [8]. To challenge Sjogrens result, we need to compare our result

to real world measurements, and a comparison can be seen in fig. 6.4. The Earth 2 and

Lutetita fly-by measurements were selected because Rosetta is believed to have been

in a similar tenuous plasma as in our measurements.

The results in fig. 6.4 show an overall agreement in the shape of the potentials, and

a decreasing potential difference from SAA = -10◦ reaching zero at around 40◦. This

is an improvement to previous simulation results, where the potential difference goes

from 0 V to 0.5 V from 0◦ to 40◦[14][8]. However, the VPS values seem exaggerated by

a factor of 4. This is further discussed in chapter 7.

42

6.1 Plasma potential

(a) VPS measurements (top row) from Rosetta Langmuir probes at the Earth 2 fly-by (left)

and Lutetia fly-by (right), and the corresponding difference in potential between probe(bottom

row), from Johlander (2012)[8].

(b) VPS vs SAA. Result of SPIS simulation.VPS = Vplasma - VSC . VSC =

+10 V, Tph = 2 eV in nominal solar wind.

(c) The VPS difference between probes in the Rosetta simulations for VSC

= +10 V, Tph = 2 eV in nominal solar wind.

Figure 6.4: Comparison of potential measurements on Rosetta measurements in space

(a) and simulation results (b)(c)

43

6. SOLAR ASPECT ANGLE DEPENDENCE

6.2 Density profile

Another very important parameter is the angular density profile surrounding the space-

craft for each probe, seen in fig. 6.5. The nph result is calculated from the current of

the probe sweep from the model fitting, and is also adjusted for the surface area error

from the resolution of the probe. For the Earth 2 fly-by, where Rosetta was in tenuous

plasma in Earth’s magnetosphere, the Rosetta surrounding is believed to be dominated

by photoelectrons [8], and should as such be a good comparison to our simulation result.

In fig. 6.5 we find a very good agreement for the Earth 2 fly-by, and we accurately

detect the size of the density drop to the wake (-10◦ for LP2, and 40◦ for LP1) from

SAA 0◦ to be a factor of 3 to 4. Also, we find an excellent fit to the shape of the density

profile for both Langmuir probes.

The results are again off by a factor between 3 and 5 for each density profile, and the

most probable cause of this is of course the somewhat unrealistic Tph in our simulation,

as well as the potential of the spacecraft, VSC . Even though we have adjusted the result

to account for the smaller probe we have in SPIS, due to the limited resolution of the

sphere, we cannot disregard this as another small source of error.

44

6.2 Density profile

(a) (b)

(c)

Figure 6.5: Rosetta log density measurements from Johlander 2012[8], assuming Tph =

1 eV for LP1 (a) and LP2 (b). Measured log photoelectron density vs SAA from Rosetta

simulations for VSC = +10 V, Tph = 2 eV in nominal solar wind (c). The error margins

for the simulation result is often too small to be visible.

45

6. SOLAR ASPECT ANGLE DEPENDENCE

46

7

Conclusions

7.1 Theoretical model

We find that the photoelectron current model described by (eq. (4.1)) accurately de-

scribes simulation and Rosetta results for a probe inside the electrostatic potential of a

positively charged spacecraft. In regions where the Langmuir probe normally operates

on Rosetta (not in wake, or in partial shadow of spacecraft), the confidence of the re-

sults reported are high and consistently produces good fits to simulation results. The

model is also independently confirmed by the first peak of the secondary derivative of

the current to the probe.

We find a clear preference in the simulation result to a theoretical model with radial

photoemission from a point[7]. This suggests that in plasmas such as the solar wind, the

SPIS Rosetta Langmuir probe is sufficiently small for the emission to be approximated

as from a point source. The theoretical model of isotropical photoemission from a

plane consistently fails to produce a good fit to the isotropical photoemission from the

Langmuir probe in SPIS.

When the probe and probe boom is in partial shadow of the spacecraft, applying

the model is problematic, as the flow of electrons is not fully understood. Reasonably,

this is because the geometry of the solution becomes very different from the ideal OML

case of particles originating from a zero potential at infinity being absorbed by a probe

with a monotonic repelling or attracting potential. To further the understanding of

this region, no better tool can be suggested than further modelling in software such as

SPIS 5.

47

7. CONCLUSIONS

7.2 Rosetta Langmuir probe sweep

The best SPIS simulation fit for a Rosetta LP1 sweep from 9/11 2009 was found to

be a +8 V charged spacecraft in the solar wind of ne = 5 cm−3, Tion = 5 eV, Te =

12 eV, Tph = 1.2 eV, vSW = 400 km/s at 1 AU. The fit was applied with a scaling

of the saturation current by a factor of 1.04, with overall great success. Some minor

discrepancies near the knee and at attracting potentials are thought to be chiefly due

to an erroneous mean photoelectron temperature of the photoemitted electrons from

the probe, and needs further investigation.

Because the simulations modelled the S/C surface and solar arrays as being of the

same material as the Langmuir probes, it is plausible that the photoelectrons emitted

from these surfaces are not accurately described. The photoelectrons emitted from the

surfaces, which amount to the photoelectron cloud, are actually from a wide array of

materials with different properties in photon absorption, photoelectron emission and

average photoelectron temperature. This yields large uncertainties in the tail end of the

probe sweep, as the positively charged probe is absorbing particles from the surrounding

photoelectron cloud.

7.3 SAA dependence

The SAA dependence of Vplasma in the the new simulation model and software config-

uration differs largely from previous results by Sjogren[14], but is found to be a more

accurate description of the actual Rosetta spacecraft Langmuir probe sweep results

[8]. The discrepancy to the previous simulations are both in applying a more realis-

tic model, as well as how the measurement was made. We believe that the Sjogren

simulation result should be regarded as unrealistic as it seems to exaggerate the pho-

toelectron density contribution to the plasma potential, as well as underestimating the

wake effect.

When comparing densities and potentials to measurements at the second Earth fly-

by ([8]), we find the SAA dependency to be largely a success in predicting the shape

of the profile, including excellent predictions of the photoelectron density drop in the

wake of the spacecraft. However the absolute values of the measured Langmuir probe

potential difference differs by a factor of 4. For the density, we find our results off by

a factor between 3-5 for both probes. The main source for these errors is believed to

48

7.4 Future work

be the high and unrealistic average photoelectron temperature, as well as, of course,

the choice of plasma parameters. Other sources of errors included the potential of the

spacecraft in our simulation, and to a minor extent, the probe resolution.

7.4 Future work

To achieve a closer fit to Rosetta results, we need a more realistic electron temperature

profile and suggest simulating with the correct material properties of each surface in

the model. If the average photoelectron temperature is still not a material property in

future versions of SPIS, we suggest a compromise by defining a Maxwellian photoelec-

tron distribution with two or more peaks at different temperatures. SPIS is apparently

already capable of doing this, but the author has yet to figure out exactly how that

can be implemented.

Improving accuracy and confidence in SPIS results can be done by improving the

probe resolution, and reworking the model of the Langmuir probe sphere, to achieve a

better spherical approximation. To optimize efficiency without increasing the sampling

error with an increased probe resolution of some factor, we suggest reducing the number

of particles backtracked by each surface by the same factor.

Investigation of the solar aspect angle dependence can also be improved by simu-

lating with a more realistic photoelectron temperature and material properties.

The new model for photoelectron absorption from a cloud can possibly explain

some, or all, of the so called ”leakage current” which has been under debate[8]. By

trying to reproduce a measurement where this phenomenon is present, we might find

support for this hypothesis.

We finally suggest simulating different plasma environments, possibly even the

comet coma, which would be a very useful reference for analysis during Rosetta’s ap-

proach to the comet 67P/Churyumov-Gerasimenko and subsequent orbit insertion.

49

7. CONCLUSIONS

50

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