advancement of space plasma measurements with novel
TRANSCRIPT
Advancement of Space Plasma Measurements with Novel
Langmuir Probe Technologies.
by
Joseph Isaac Samaniego
B.A., Boston University, 2013
M.S., University of Colorado, 2018
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
Department of Physics
2020
This thesis entitled:Advancement of Space Plasma Measurements with Novel Langmuir Probe Technologies.
written by Joseph Isaac Samaniegohas been approved for the Department of Physics
Prof. Mihaly Horanyi
Prof. Xu Wang
Prof. Tobin Munsat
Prof. Thomas Degrand
Prof. David Malaspina
Date
The final copy of this thesis has been examined by the signatories, and we find that boththe content and the form meet acceptable presentation standards of scholarly work in the
above mentioned discipline.
iii
Samaniego, Joseph Isaac (Ph.D., Physics)
Advancement of Space Plasma Measurements with Novel Langmuir Probe Technologies.
Thesis directed by Prof. Mihaly Horanyi
Langmuir probes have been flown on spacecraft missions for in-situ measurements of
the local plasma environment from sounding rocket missions to flagship missions like Cassini
or Rosetta over the past 50 years. Langmuir probes are conductors of simple geometries
(spheres, disks, cylinders, etc.) inserted into a plasma. By sweeping a voltage on the probe
and measuring the current collected or emitted, a current-voltage (I-V) relationship can
be found and interpreted to derive the density, temperature, and potential of the ambi-
ent plasma. However, even after decades of use, there are still challenges in the analysis
and interpretation of Langmuir probe measurements due to non-ideal plasma environments
encountered by or created by the spacecraft.
In the upper atmospheres of planets atomic oxygen is present in high densities capable
of degrading the probe surface, warping the I-V curve of a Langmuir probe or otherwise caus-
ing a the probe to incorrectly measure the plasma. Due to plasma interactions with the probe
itself and spacecraft there is often an anisotropic or inhomogeneous plasma environments.
The following dissertation summarizes the research to find probe coatings whose measure-
ments are least affected by atomic oxygen as well as the construction of a double hemisphere
Langmuir probe (DHP) to improve space plasma measurements in: i) Low-density plas-
mas where the Debye sheath from the SC will interfere with probe measurements; ii) flowing
plasmas where asymmetric current collection causes characterization of the density; iii) high-
surface-emission environments where photoemission from the probe or SC will pollute the
measurements of the ambient plasma.
Dedication
This work is dedicated to my mother, my brothers, and my big Mexican family. My
mother is the greatest teacher I have had, and without her lessons I would not have made it
to where I have. My brothers have been my comrades and my family has been my tribe.
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Acknowledgements
I would like to acknowledge my PI, Professor Mihaly Horanyi who has been patient and
supportive during though out my PhD, allowing me flexibility and freedom to pursue many
profession interest while keeping me focused. Additionally, I express great appreciation for
Dr. Xu Wang who has been instrumental in my PHD. Dr. Wang has been a constant source
of knowledge and counsel both professionally and personally, and I consider him to be a
good friend.
A special thanks to Drs. Bob Ergun, Laila Andersson, and David Malaspina for their
collaboration on the oxidation of Langmuir and electric field probe coatings, as well as Dr.
Wojciech Miloch for the opportunity to work on their ionospheric experiment in Oslo Norway.
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Contents
Chapter
1 Introduction 1
2 How Langmuir Probes Work 7
2.1 Electron Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 The Debye Sheath . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 Sheath Expansion and OML Theory . . . . . . . . . . . . . . . . . . 12
2.2 Ion Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1 Bohm Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.2 Presheath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Special Langmuir Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 Emissive Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.2 Electric Field Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Interpretation of Langmuir Probe Measurements 30
3.1 Plasma Potential and the ‘Knee’ of the I-V Curve . . . . . . . . . . . . . . . 30
3.2 Electron Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Electron Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 Ion Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
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4 Issues of Probe Surface Oxidation 36
4.1 Oxidation on Langmuir Probe Measurements . . . . . . . . . . . . . . . . . . 36
4.1.1 Experimental Setup and Method . . . . . . . . . . . . . . . . . . . . 38
4.1.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.1.3 Comparison with MAVEN LPW . . . . . . . . . . . . . . . . . . . . . 54
4.1.4 Discussion: Implications for different Langmuir probe coatings . . . . 56
4.2 Oxidation Effect on Photoemission and Electric Field Probes . . . . . . . . . 57
4.2.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.2 Results and Comparison Between Different Materials . . . . . . . . . 62
4.2.3 Exposure to Larger Ion Fluence . . . . . . . . . . . . . . . . . . . . . 65
4.2.4 Discussion: Implications for electric field probe coatings . . . . . . . . 67
4.3 Suggested Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5 A Novel Langmuir Probe Technology - Double Hemispherical Probe (DHP) 69
5.1 Current In-Situ Langmuir Probe Issues . . . . . . . . . . . . . . . . . . . . . 70
5.2 Concept of the DHP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6 Probe in Sheath 76
6.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.2 Characterization of I-V curves taken in the SC sheath . . . . . . . . . . . . 80
6.3 Methods to retrieve true ambient plasma characteristics using DHP . . . . . 85
6.3.1 Retrieving Spacecraft Potential . . . . . . . . . . . . . . . . . . . . . 87
6.3.2 Retrieving Electron Temperature . . . . . . . . . . . . . . . . . . . . 88
6.3.3 Retrieving Electron Density . . . . . . . . . . . . . . . . . . . . . . . 89
6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
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7 Probe Under Photoemission 94
7.1 Photoemission on Langmuir probe measurements . . . . . . . . . . . . . . . 95
7.2 DHP to Minimize the Probe Photoemission Effect . . . . . . . . . . . . . . . 96
7.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.4 Conclusion and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
8 Probe in Flowing Plasmas 101
8.1 Theories of Probe Current Collection in Flowing Plasmas . . . . . . . . . . . 102
8.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
8.3.1 Probe Self-Wake Effects on Measurements . . . . . . . . . . . . . . . 108
8.3.2 Utilization of DHP to minimize self-wake effects . . . . . . . . . . . . 111
8.3.3 Conclusion and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 113
9 DHP Flight Prototype 115
10 Conclusion 121
Bibliography 125
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Tables
Table
4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
x
Figures
Figure
1.1 Previously Flown Langmuir Probes . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Ideal I-V Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Ideal Sheaths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 OML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Sheath Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Lab Sheath Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6 Emissive Probe Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.7 Emissive Probe Schematic from SERT II . . . . . . . . . . . . . . . . . . . . 22
2.8 Emissive Probe I-V Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.9 Electric Field Probes on THEMIS . . . . . . . . . . . . . . . . . . . . . . . . 26
2.10 Electric Field Probe Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.11 Electric Field Probe Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1 An I-V Curve and its Derivative . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Electron Temperature and Saturation Currents . . . . . . . . . . . . . . . . 34
3.3 Ion Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1 RGA Analysis of Oxidation Environment . . . . . . . . . . . . . . . . . . . . 41
4.2 Oxidation Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 Effect of Systematic Contamination . . . . . . . . . . . . . . . . . . . . . . . 43
xi
4.4 Oxidation Distortion on Known Oxidizers . . . . . . . . . . . . . . . . . . . 44
4.5 Oxidation Distortion on Current Probe Materials . . . . . . . . . . . . . . . 45
4.6 Oxidation Distortion on New Probe Materials . . . . . . . . . . . . . . . . . 46
4.7 Oxidation Effect on Vp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.8 Oxidation Effect on Te . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.9 Oxidation Effect on ne . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.10 Effect of Atomic Oxygen Impact Energy . . . . . . . . . . . . . . . . . . . . 53
4.11 O2 vs O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.12 MAVEN LPW Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.13 Oxidation Effect on Photoemission Set-up . . . . . . . . . . . . . . . . . . . 59
4.14 Photoemission Flux Comparisons . . . . . . . . . . . . . . . . . . . . . . . . 62
4.15 Percent Changes in Photoemission . . . . . . . . . . . . . . . . . . . . . . . 63
4.16 Photoemission Yield after High Fluence Exposure . . . . . . . . . . . . . . . 65
4.17 Photoemission Yield after High Fluence and Recleaning . . . . . . . . . . . 66
5.1 DHP Flight Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2 DHP Preliminary Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.1 Ideal I-V curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.2 DHP in SC Sheath Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.3 Effects of the SC sheath on Langmuir Probe Measurements . . . . . . . . . . 84
6.4 Potential Profile Around Probe in Sheath . . . . . . . . . . . . . . . . . . . . 85
6.5 Ratios of Saturation Current in Sheath . . . . . . . . . . . . . . . . . . . . . 86
6.6 VSC vs Sheath Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.7 Te vs Sheath Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.8 Local Potential and ne . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.9 DHP vs Single Langmuir Probe . . . . . . . . . . . . . . . . . . . . . . . . . 92
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7.1 Photoemission I-V Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.2 DHP Under Photoemission Set-up . . . . . . . . . . . . . . . . . . . . . . . . 98
7.3 DHP Photoemission Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
8.1 Ion Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
8.2 Ambipolar Feilds of a Plasma Wake . . . . . . . . . . . . . . . . . . . . . . . 106
8.3 CSWE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
8.4 DHP I-V Curves in Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
8.5 Current and Density Errors due to Flow . . . . . . . . . . . . . . . . . . . . 113
9.1 DHP Flight Ready Prototype . . . . . . . . . . . . . . . . . . . . . . . . . . 117
9.2 DHP Pre–amp Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
9.3 DHP Vibration Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
9.4 DHP Flight Prototype and Testing Chamber . . . . . . . . . . . . . . . . . . 120
Chapter 1
Introduction
This dissertation focuses on the development of a new technology of Langmuir probes
to increase their utility and robustness over a wide range of space plasma environments.
Langmuir probes were first developed in the 1920’s to measure laboratory plasmas
[Mott-Smith and Langmuir (1926)]. Langmuir probes are conductors of simple geometries
(spheres, wires, or discs) placed in a plasma to measure its characteristics. They work by
sweeping a bias voltage on the conductor to collect the current, resulting in a current-voltage
(I-V) curve. Analysis of the I-V curve determines the three basic characteristics of a plasma:
density, temperature, and electric potential. Due to their simplicity to construct, Langmuir
probes are one of the most-used diagnostics in laboratory plasmas including both industrial
and fusion plasmas [Chen (2009), Loewenhardt (1999)]. Over the past 50 years, Langmuir
probes have been widely used in various space plasma measurements from sounding rockets
to deep space missions.
In space, plasma is the most abundant matter and is the medium with which things
interact. It therefore plays a vital role in the interplanetary environment of the solar sys-
tem and its interactions with planets. The interactions of the solar wind and UV radia-
tion with bodies in the solar system create: 1) magnetospheres around the planets with
global magnetic fields [Blanc et al. (2005)]; 2) ionospheres of the planets with significant
atmospheres [Jakosky. (2005)]; and 3) charged surfaces and plasma wakes of airless bodies
[Wang et al. (2016), Wurz et al. (2007), Lin et al. (1998)]. All of these processes play a
2
critical role in determining how the solar system works and evolves. Therefore, these pro-
cesses are of fundamental interest in heliophysics and planetary science. Langmuir probes
are most useful in characterizing low-energy thermal plasmas in these processes.
A Langmuir probe is usually mounted on the end of a boom attached to the body of
a spacecraft (SC) in order to minimize the effect due to the spacecraft being charged on
probe measurements. Because Langmuir probes are directly exposed to the ambient plasma,
they can measure the SC potential with respect to the ambient plasma, which is a critical
parameter for SC safe operations and correct interpretations of measurements by many other
plasma instruments. When two Langmuir probes are used together, the electric field can
be determined from the potential difference measured between the two probes, hence these
probes as a pair become an electric field probe [Eriksson et al. (2007), Mozer (2016)].
3
Figure 1.1: Previously Flown Langmuir Probes
a) The Cassini Langmuir probe as part of the Radio and Plasma Wave Science(RPWS) instrument [Gurnett et al. (2004)]. b) One of the Langmuir probes onRosetta [Eriksson et al. (2007)]. c) Segmented Langmuir probe flown on DEMETER[Lebreton et al. (2006)]. d) One of the Langmuir probes of the Langmuir Probe and Waves(LPW) instrument on MAVEN [Andersson et al. (2015)].
Figure 1.1 shows examples of space-borne Langmuir probes on various missions. Lang-
muir probes were used on the Mars Atmospheres and Volitional Evolution (MAVEN) mission
to measure the Martian ionosphere to understand how Mars lost its atmosphere over time
[Andersson et al. (2015)]. Langmuir probes on the Rosetta mission studied the out-gassing,
ionization, and subsequent plasma processes due to the solar wind interaction with comet
4
67P [Eriksson et al. (2007)]. The Cassini Langmuir probe, as part of the Radio and Plasma
Wave Science (RPWS) instrument suite, measured plasma environments not just of Saturn’s
upper atmosphere, but also Saturn’s magnetosphere, rings, and moons, contributing to paint
a never before seen picture of the Saturnian system [Gurnett et al. (2004), Jacobsen. (2009),
Garnier et al. (2012)]. Closer to home, missions like Detection of electro-magnetic Emissions
Transmitted from Earthquake Regions (DEMETER) used plasma measurements assisted by
a Langmuir probe [Lebreton et al. (2006), Imtiaz et al. (2013)]to determine seismic and vol-
canic activity on Earth.
Though Langmuir probes have been widely used in space missions, a number of chal-
lenges remain and mainly come from interactions of the space plasma and radiation environ-
ment with the SC and probes themselves. One situation is the probe surface oxidation. In
the upper atmospheres of many planets, oxygen is present in many forms (e.g., O, O2, O+
and O+2 ) and in relatively high densities [Osepian et al. (2008), Zhang et al. (1993)]. When
the probes are taking measurements in or traveling through such environments, the surfaces
of the probes have a high risk of being oxidized. The oxidized forms of most probe materials
have reduced conductivity of the surface layers, causing a reduction in the current collected
at a given voltage during the probe sweep. The I-V curves are therefore changed, resulting
in errors in the derived plasma parameters [Ergun et al. (2015)].
The interactions of the SC and probes themselves with the ambient plasma often
create a local plasma environment around the probes, which is different from the true am-
bient plasma to be measured. As a result, significant errors may be introduced in the
derived plasma parameters. Specifically, due to SC charging, in low-density or high tem-
perature plasmas a potential barrier is formed around the SC that can engulf a Lang-
muir probe at the end of a fixed boom with a finite length. This barrier restricts some
charged particles that enter into the region in the vicinity of the SC and therefore changes
the current collected by the probe, causing mischaracterization of the ambient plasma
[Wang et al. (2015), Olson et al. (2010), Odelstad et al. (2015)]. In environments with solar
5
UV illumination, photoelectrons will be emitted from the surfaces of the SC and the probe it-
self, causing the I-V curve to be altered by a superposition of additional electron populations
that are not from the ambient plasma [Garnier et al. (2012), Eriksson et al. (2007)]. This
probe current ‘contamination’ is more severe when the SC is close to the Sun (e.g., missions
to Mercury or Venus, and orbiting the Sun like the Parker Solar Probe mission). Due to fast
SC motion relative to the ambient plasma, an ion wake is created on the back side of the
probe. This ion wake may not only affect the ion collection by the probe [Hutchinson (2003)]
but also the electron collection, depending on the probe size compared to the Debye length.
Such effects has been indicated from the split probe measurements in Earth’s ionosphere
[Bering et al. (1973b)]. Lastly, in dust-rich plasma environments (e.g. in the environment
around Jupiter and Saturn’s moons), impacts from dust particles on the probe can create
a local plasma cloud that will interfere with the probe current collection, as indicated from
the Cassini Langmuir probe measurements [Morooka et al. (2011)].
This dissertation characterizes the hindering effects of these non–ideal plasma condi-
tions on our ability to correctly interpret Langmuir probe measurements, and proposes solu-
tions to these issues by developing novel technologies — new surface coatings for Langmuir
probes in oxygen-rich environments and a Double Hemispherical Langmuir Probe (DHP).
Specifically, this work: 1) characterizes the effect of surface oxidation of Langmuir probes
on I-V curve measurements, and tests new coating materials whose properties are unaffected
by oxidation; and 2) introduces the DHP to improve probe measurements in the following
scenarios: i) low density plasmas; ii) high surface-emission (especially photoemission) envi-
ronments; iii) flowing plasmas; and iv) dust-rich plasmas. However, while DHP is expected
to improve space plasma measurements in dusty plasmas this dissertation will not discuss
the characterization of the DHP under dust impacts.
This dissertation is outlined as follows. Chapters 2 and 3 describe the theories of
Langmuir probe operations as well as the techniques used to interpret I-V curves. Chapter
4 studies the effects of oxidation on Langmuir probe measurements and solutions with new
6
surface coating materials. Chapter 5 introduces the concept of the DHP. Chapter 6 studies
the SC sheath effect on probe measurements and the ability of the DHP to retrieve the true
plasma characteristics. Chapter 7 investigates the DHP under the photoemission contami-
nation. Chapter 8 studies the probe self-wake effect and how to use the DHP to minimize
such effect on probe measurements. Chapter 9 reports the design and fabrication of the
DHP flight prototype. Lastly, chapter 10 concludes the overall findings and implications for
future work of this dissertation.
Chapter 2
How Langmuir Probes Work
This chapter focuses on basic theories of Langmuir probes. Though this dissertation
is focused on space plasma measurements and space–borne Langmuir probes, much of the
data presented in the following chapters comes from laboratory experiments simulating space
plasma environments. For this reason, the context of this chapter is kept general.
First, this chapter considers situations where the plasma is weakly collisional, where
electron and ion populations are in thermal equilibrium with themselves (i.e., Maxwellian
distributions) but where the electron temperature (Te) is greater than the ion temperature
(Ti). Additionally, the plasmas are considered to be quasineutral, implying the densities of
the ion and electron populations are approximately equal (ni ≈ ne).
To understand how a Langmuir probe collects current at different voltages, it is first
necessary to make the distinction between the plasma potential (Vp) and the floating potential
(Vf ) of the probe, as shown in Fig. 2.1. Potential is a relative value. In the lab, a plasma is
bounded by a vacuum chamber. Due to higher mobility of electrons than ions, the plasma will
stay at a positive potential relative to the chamber wall grounded to Earth, which balances
electrons and ions flowing out of the plasma. In space, the ambient plasma is assumed to
be a reference potential (i.e., 0V ). When a Langmuir probe, or any solid surface inserted
in a plasma without an external bias, it will be charged to a potential that equilibrates the
electron and ion fluxes to the probe, This potential is called the floating potential where
the net current is zero. In general, the floating potential is more negative than the plasma
8
potential because of the higher mobility of electrons than ions.
Figure 2.1: Ideal I-V Curve
A schematic of I-V curves for a Langmuir probe of different geometries with the floating(Vf ) and plasma (Vp) potentials marked. The V = 0 line is arbitrary and holds no relevanceto Vf or Vp. The electron saturation region is the region when the probe bias Vb is morepositive than Vp and collects the electrons of all the energies. The electron retarding region isa region where only the electrons of sufficient energy are able to overcome the potential barrierbetween the probe and ambient plasma to be collected by the probe. The ion saturationregion is described by the region where the ions of all the energies are collected by the probe.[Hershkowitz (1989)]
The I-V curve is a superposition of electron and ion currents. Fig. 2.1 shows I-V curves
of a Langmuir probe of different geometries. Here ions are assumed to be much colder than
electrons. In this case, the I-V curve can be divided into three regions: electron saturation,
electron retarding, and ion saturation regions. Theories and interpretation of I-V curves have
been developed and described by [Mott-Smith and Langmuir (1926), Hershkowitz (1989)].
When Vb � Vp, all the electrons are repelled and only the ions are collected. This region is
the ion saturation region. As Vb is more positive, only the electrons with kinetic energies large
9
enough to overcome the potential barrier between the probe bias and plasma potential (i.e..,
Vp− Vb) are collected by the probe, this is the electron retarding region. When Vb ≥ Vp, the
electrons with all the energies are collected by the probe, reaching the electron saturation
regions. The lack of an ion retarding region in Fig. 2.1 is because of the assumption of
cold ions, and this will be discussed in Section 2.2. In the electron saturation region, the
electron current is governed by the Orbital Motion Limited (OML) theory that depends on
the probe geometry [Mott-Smith and Langmuir (1926), Allen(1992)]. Further discussions
of these three regions are described in Sections 2.1 and 2.2. Section 2.3 discusses special
Langmuir probes that will be referenced in this work: emissive probes and electric field
probes.
2.1 Electron Current
This section focuses on probe collection of the electron population only. As described
above, the current collection can be divided into two regions: the electron retarding and
saturation regions. In the retarding region, the electron current collected by the probe is
shown below [Hershkowitz (1989)].
Ie = Je A = e ne ve A = eA
∫ ∞vmin
f(v) v dv; vmin =√
2 e (Vp − Vb)/me (2.1)
where Ie is the electron current collected by the probe, Je is the current density, A is the
surface area of the probe, e is the elementary charge, ne is the electron density of the plasma,
ve is the velocity of the electrons in the plasma, and me is the electron mass. vmin is the
minimum velocity of the electrons that can overcome the potential barrier (i.e., Vp − Vb)
to reach the probe, where Vp and Vb are the plasma potential and the probe bias voltage,
respectively. Once Vb reaches Vp, the probe no longer repels any electrons and all electrons
are able to make it to the probe surface, reaching the saturation current.
10
Assuming a Maxwellian velocity distribution:
f(v) = ne
(m
2 π Te
)1/2
exp(−m v2/2 Te), (2.2)
where Te is the electron temperature measured in units of energy, Eq. 2.1 becomes
Ie =
Isat∗e exp
[−e (Vp−Vb)
Te
], for Vb ≤ Vp
Isat∗e , for Vb ≥ Vp
(2.3)
where Isat∗e = Anee/√Te/(2πme) is the electron saturation current at the plasma potential,
which is derived from Eq. 2.1 for vmin = 0. The first line of Eq. 2.3 shows the retarded
electron current when Vb < Vp. Once Vb ≥ Vp, the current saturates. In situations where
the probe is treated as a simple plane, Ie = Isate a constant for Vb ≥ Vp. However, when
the probe has a more complex geometry than a planar probe (such as sphere or cylinder),
the saturation current (Isate , Ie at Vb > Vp) increases as the probe bias increases due to a
phenomenon called sheath expansion (described in section 2.1.2), and it takes a more general
form as follows:
Isate =
Isat∗e , for Vb ≤ Vp
Isat∗e
[1 + Vb−Vp
V0
]β; for Vb ≥ Vp
(2.4)
where V0 = 12mv20 and is further defined in Eq. 2.9, and β is determined by the probe
geometry. β = 0, corresponds to a plane probe and yields the aforementioned constant
saturation current. β = 0.5 and β = 1, corresponds to cylindrical and spherical probes,
respectively. The rigorous definition of the probe geometry is determined by the probe size
relative to the Debye length and the saturation current as a function of the probe geometry
is governed by the OML theory. These subjects are described in detail in subsections 2.1.1
and 2.1.2.
11
2.1.1 The Debye Sheath
When a charged probe (or any object) is inserted in a plasma, it will attract particles
with an opposite charge that form a cloud around the probe, which shields the surrounding
electric field of the probe from interfering with the ambient plasma. This is called the Debye
shielding or sheath. The thickness of the sheath is scaled by a characteristic length called
the Debye length. Figure 2.2a, shows the sheath around a positive point charge in a plasma,
with the potential of the charge above the ambient plasma (φ = 0V ) [Chen et al. (2016)].
The sheath around a positive point charge is derived below as an example.
Figure 2.2: Ideal Sheaths
a) A sketch of the potential profile of an ideal sheath caused by a positive charge corre-sponding to a potential φ0 above the plasma potential. b) A sketch of the potential profileof a negatively charged surface w.r.t. the ambient plasma potential. For both figures theambient plasma potential is taken to be φ = 0V [Chen et al. (2016)]
According to Poisson’s equation,
ε0∇2φ = −e (ni − ne), (2.5)
12
where ∇2 is the Laplacian, φ is the electric potential, and ni,e are the ion and electron
densities, respectively. Ion and electron densities are assumed to follow the Boltzmann
distributions:
ni = n0 exp
(−eφTi
)and ne = n0 exp
(eφ
Te
), (2.6)
Simplifying Poisson’s equation by assuming that the potential of the shielding region
varies slowly and is small relative to the plasma temperature, eφ/Te � 1 and eφ/Ti � 1,
ε0∇2φ =1
r2d
dr
(r2dφ
dr
)= n0 e
2
(1
Te− 1
Ti
)φ = λ−2D φ, (2.7)
where λ−2D = λ−2e + λ−2i and λe,i = (ε0Te,i/n0e2)1/2 in MKS or in CGS units λe,i =
(Te,i/4πn0e2)1/2.
λD is the Debye length. Because Te � Ti, λD ≈ λe. The eφ/Te,i � 1 limit is not
true close to the charge source where the potential changes rapidly; however, the ’thickness’
of the sheath is dominated by the slow potential change near the plasma-sheath boundary,
where the eφ/Te,i � 1 limit is valid.
The Debye length is an important parameter when rigorously defining the probe geom-
etry in addition to the physical geometry. When the Debye length is much smaller than the
probe radius, a probe is treated as a planar probe, regardless of if its shape is disc, cylinder
or sphere. When the Debye length is much larger than the probe size (the size here is the
length for a cylinder as an example), a probe is treated as a spherical probe. For a cylinder
to be treated as a cylindrical probe, it requires the radius of the cylinder to be smaller than
the Debye length and the length of the cylinder to be longer than the Debye length.
2.1.2 Sheath Expansion and OML Theory
When the probe bias is more positive than the plasma potential, the probe will not
only attract electrons that would have directly collided with the probe but also attract flyby
13
electrons, bend their trajectories and in some cases capture them, causing the collection of
an additional current [Allen(1992)]. This results in an effective surface area to be larger than
the physical surface area of the probe. As the probe bias increases, the effective surface area
increases, causing an increased probe current. This is called the ’sheath expansion’ effect.
Figure 2.3 shows the trajectory of an electron diverted by a positive bias on the probe.
The additional current collected by the probe at biases higher than the plasma potential is
described by the Orbital Motion Limited (OML) theory [Mott-Smith and Langmuir (1926)].
Figure 2.3: OML
A schematic of the trajectory of a charged particle being altered by a biased Langmuir probeof circular cross-section with with probe radius of rp, an impact parameter of h, radius ofclosest approach p. [Allen(1992)]
According to the conservation of energy and momentum for a particle with velocity v0,
a distance h from the center of the probe as shown in Fig. 2.3 is
1
2m v20 =
1
2m v2c − e (Vc − Vp)
mv0 h = m rc vc
(2.8)
where Vc is the potential at closest approach, Vp is the plasma potential at a point far from
14
the probe, vc is the speed at the closest approach, h is the impact parameter, v0 is the initial
velocity of an electron starting at infinity from the probe, and rc is the radial distance from
the center of the probe at closest approach – all variables coincide with Fig. 2.3. Combining
Eqs. 2.8 in terms of the impact parameter, it gives
h = rc
(1 +
(Vc − Vb)V0
)1/2
, (2.9)
where eV0 = 12mv20. Assuming the closest approach is the probe radius, rc → rp and Vc →
Vb. Therefore, if monoenergetic electrons come from infinity in all directions, a cylinder
or sphere’s effective radius increases as the bias on the probe is increased [Allen(1992),
Hershkowitz (1989)]. Using the impact parameter h as the effective radius of the probe,
Isate = Jsate A becomes Eq. 2.4 for Vb > Vp with β = 0.5 for a cylindrical probe, as shown
here. The β value therefore comes from the impact factor h that varies between the cylinder
and sphere. As λD becomes large with respect to rp, the sheath around a probe of finite size
begins to change the cross-section of the OML collection to exhibit a different β closer to a
sphere [Hoang et al. (2018)].
2.2 Ion Current
In cases of Ti ≈ Te, the ion current can be interpreted in an exactly same way as
for the electron current described above. However, in cases of Ti � Te such as in our
lab experiments, ions will be accelerated by the presheath to the ion sound velocity (i.e.,
the Bohm velocity) before entering the probe’s sheath. This Bohm velocity can be larger
than the ion thermal velocity and determines the ion collection by the probe. Fig. 2.4
illustrates a whole picture of the sheath, presheath, and its effects on the electron and ion
species for a general case of thermal plasmas. The ions and electron densities are the same
(i.e., quasineutral) up until the sheath boundary. In the sheath, the quasineutrality breaks,
forming a potential barrier that balances the fluxes of electrons and ions to the surface.
15
Figure 2.4: Sheath Profile
a) A schematic of the electron and ion densities, ne and ni respectively, as a function of loca-tion from a negatively charged surface with the ambient plasma, presheath and sheath regionsmarked. The electron density decreases as expected by the Boltzmann relationship and theion density decreases in accordance with Eq. 2.13. The electron and ion densities are equalin situations in the presheath and the ambient plasma. [Lieberman & Lichtenberg (2005)]b) A schematic of the potential profile. The presheath is defined as the boundary wherethe potential drops 0.5Te from the ambient plasma potential for a collisionless case. us andu(x) are the ion velocities at the sheath boundary (Bohm velocity) and within the sheath,respectively. [Lieberman & Lichtenberg (2005)]
16
Figure 2.5: Lab Sheath Profile
The sheath potential profile measured in the lab as a function of distance from a negativelycharged plate in a plasma. Data is measured using an emissive probe discussed further insection 2.3.1..
2.2.1 Bohm Velocity
Fig. 2.4 shows the sheath density and potential profiles away from a negatively charged
solid surface. The potential barrier between the surface and plasm returns lower energy
electrons and attracts the ions to the surface. At equilibrium, the fluxes of the electrons
and ions are balanced at the surface. For the case of Ti � Te, the ion thermal speeds are
negligible and the ion population cannot be represented by the Boltzmann relationship (Eq.
2.6). Instead, the ion population in the sheath is treated as a flow. It is shown that the
ions need to satisfy a Bohm sheath criterion when they enter the sheath, which is derived
as follows.
According to conservation of energy,
1
2mi u
2i =
1
2mi u
20 − eφ (2.10)
17
ui =
(u20 −
2 e φ
mi
)1/2
(2.11)
where mi is the mass of the ion, ui is the ion velocity in the sheath, u0 is the ion drift velocity
at the sheath edge, φ is the potential difference from the sheath edge and at a position in
the sheath, and e is the elementary charge. Using Eq. 2.11 in the continuity equation,
n0 u0 = ni ui (2.12)
we have
ni = n0
(1− 2 e φ
mi u0
)−1/2. (2.13)
Inserting this into Poisson’s equation gives,
ε0∇2φ = ε0d2φ
dx2= −e (ni − ne) = e n0
[exp
(eφ
Te
)−(
1− 2eφ
miu0
)1/2]
(2.14)
Making the following substitutions,
χ ≡ −eφTe
ξ ≡ x
λD= x
(n0e
2
ε0Te
)1/2
M ≡ u0(Te/mi)1/2
(2.15)
Eq. 2.14 becomes
d2χ
dξ2=
(1 +
2χ
M2
)1/2
− exp(χ). (2.16)
Multiplying both sides by dχdξ
and integrating them from the ambient plasma (φ = 0→ ξ = 0)
to a position in the sheath (ξ), we obtain:
1/2
(dχdξ
)2
−(dχ
dξ
)2∣∣∣∣∣ξ=0
= M2
[(1 +
2χ
M2
)1/2
− 1
]+ exp(χ)− 1. (2.17)
18
It is shown that dχdξ
∣∣∣∣∣ξ=0
= 0 because the electric field in the plasma is zero. The L.H.S. of
Eq. 2.17 and thus the R.H.S must be positive. Expanding the R.H.S for χ � 1 in Taylor
series to the first order,
1
2χ2
(1− 1
M2
)> 0 (2.18)
or that v0 >√Te/mi, which is called the Bohm velocity (vB). Interestingly, this is also the
sound velocity of ion acoustic waves in the Ti � Te limit:
vs =
√Te + Timi
≈√Te/mi (2.19)
The question then of how cold ions are accelerated to this Bohm velocity to enter the sheath
led to the discovery of the ’presheath.’
2.2.2 Presheath
While Eq. 2.18 references an inequality; physically, the ions are assumed to enter the
sheath with a velocity equal to the Bohm velocity. While rigorous proofs are needed, the
basic principle is that a stable solution requires the minimum energy in the system to reach
the equilibrium. Additionally, if the flux is known when the ions reach vB, then the flux at
any other point in the sheath, including at the probe surface, is the same and can be used
for current calculations.
As shown in Fig. 2.4, the presheath is a region between the sheath and plasma, where
cold ions from the plasma are accelerated to the Bohm velocity to enter the sheath. Assuming
a collisionless presheath, conservation of energy gives
1
2mi u
20 =
1
2mi v
2B − e φ =
Te2− e φ = e (φPS − φ) (2.20)
where mi is the ion mass, u0 is the ion drift velocity in the plasma, and φ is the potential
drop across the presheath (i.e., between the plasma and sheath edge). φPS is the potential
19
at which the ions are accelerated to the Bohm velocity and defines the boundary of the
presheath.
φPS = 0.5Te (2.21)
The ion current density can be now derived as follows:
Jsati = JBohm ≈ 0.6e n0
√Te/mi, (2.22)
where Te is measured in units of Joules and the factor of 0.6 comes from the Boltzmann
factor, i.e. exp(−0.5) ≈ 0.61.
Lastly, while we have focused on the Ti � Te limit because of our laboratory
set ups it is important to note that this is common in space plasmas as well. In the
ionosphere of planets the thermal temperature of the ions (Ti) can equal the thermal
temperature of the electrons (Te) [Kohnlein (1986)], especially at lower altitudes where
collisions are more frequent, but at higher altitudes and especially during intense diur-
nal processes associated with solar illumination Te > Ti [Liu. (1969), Willmore (1970),
Lieberman & Lichtenberg (2005), Moore & Khazanov (2010), Hsu & Heelis (2017)]. In the
solar wind, the ratio of electron to ion temperature is dependent on solar wind flux and
energy output but the electron temperature is usually at least several times that of the ions
[Montgomery (1972), Feldman et al. (1975), Newbery et al. (1998), Laming (2004)].
Additionally, the Ti � Te in our lab implies an overall low ion current that makes
the ion populations difficult to analyze. Because of this, this dissertation focuses only on
retrieving information on the electron population and electron plasma parameters (Te and
ne) and from now on, unless otherwise stated, all parameters are referencing the electron
population.
This concludes the discussion of how Langmuir probes collect electron and ion currents.
20
2.3 Special Langmuir Probes
In addition to conventional Langmuir probes described in the previous sections, we
briefly introduce two special Langmuir probes that are relevant to this thesis work: Emis-
sive probe and Electric field probe. Both probes measure local plasma potentials based on
electron emission from the probe itself. Emissive and electric field probes are mainly used
in lab and space plasma measurements, respectively.
2.3.1 Emissive Probes
Figure 2.6a shows a schematic of an emissive probe, where a tungsten wire is exposed
to a plasma. The tungsten wire is heated till glowing so that electrons gain enough energy
to overcome the surface work function to be freed, which are then accelerated by a negative
bias voltage applied to the wire relative to the plasma potential, Fig, 2.6b. Figure 2.7 shows
the schematic of the emissive probe used on Space Electrical Rocket Test (SERT II) mission,
testing at the time novel electrostatic ion thrusts [Vernon and Daley (1970)]
21
Figure 2.6: Emissive Probe Schematic
a) A lab design of an emissive probe, where two electrodes are connected by a thoriatedtungsten wire. The electrodes are isolated from the plasma with ceramic paint such thatonly the tungsten wire is exposed to the plasma. b) Electrical schematic of an emissive probe.The tungsten wire is heated by a closed-loop heating current and thermionic electrons areemitted by applying the negative bias on the wire.
22
Figure 2.7: Emissive Probe Schematic from SERT II
[Vernon and Daley (1970)].
An emissive probe works as a ‘hot’ Langmuir probe in contrast to ‘cold’ Langmuir
probes described in the previous sections. Because the exposed wire is a conductor in a
plasma being swept by a voltage, the emissive probe would collect current identical to that
of a ‘cold’ Langmuir probe, as shown in Fig. 2.8a. In addition to the collection current,
there is an emission current of thermionic electrons. The overall I-V curve of the emissive
probe is then the superposition of the collection and emission currents. When the probe bias
is lower than the plasma potential, the probe emits the electrons; and when the probe bias
is higher than the plasma potential, the emitted electrons are returned to the probe. This
transition region gives where the plasma potential is. The emission current is expressed in
the following equation:
23
Figure 2.8: Emissive Probe I-V Curves
a) Schematic of the I-V curve of an emissive probe showing the overall current being asuperposition of the collection current, identical to a Langmuir probe of similar geometry,and an emission current, caused by the wire being heated. I∗e marks the beginning of theelectron saturation current of a Langmuir probe, given by Eq. 2.3. Ie0 marks the temperaturelimited emission current, given by Eq. 2.24. b) Data showing the overall I-V curve as thetemperature of the wire is increased by increasing the heating current through the wire. Twis the temperature of the wire. The discontinuity in the overall current (blue dotted line),dominated by the emission current at high Tw, marks the local ambient plasma potential Vp.[Sheehan & Hershkowitz (2011)]
Ie =
Ie0, for Vb ≤ Vp
Ie0 exp[−e (Vp−Vb)
Tw
]g(Vb − Vp), for Vb ≥ Vp
(2.23)
where Tw is the temperature of the probe in eV, g(Vb − Vp) is a geometrical factor similar
to Eq. 2.4, and Vb and Vp are the probe bias and plasma potential, respectively. Ie0 is the
temperature limited emission current given by the Richardson-Dushman equation:
Ie0 = R T 2w A exp
(eφwTw
), (2.24)
where R is the Richardson constant, A is the surface area of the wire, φw is the work func-
tion of the probe [Sheehan & Hershkowitz (2011), Ibach & Luth (2011)]. It shows that the
emission is only a function of the probe bias relative to the plasma potential and the tem-
24
perature of the wire, and not dependent on other plasma conditions such as electron/ion
velocity distributions, plasma drifting and/or inhomogeneous/anisotropic plasma environ-
ments. Figure 2.8b shows the emissive probes ability to mark the local potential increases
as Tw increase. This means that emissive probes can measure the plasma potential more
accurately than ‘cold’ Langmuir probes that only have the collection current. Additionally,
this means that emissive probes can be even used in vacuum (i.e., in the absence of plasma)
[Hershkowitz (1989)].
Several methods are available to interpret the plasma potential with the emissive probe,
including the floating potential [Sheehan et al. (2011)], the inflection point at zero-emission
[Smith (1995)], and the current-bias [Pedersen et al. (1978a), Diebold et al. (1988)] meth-
ods. The method used in this work is the current-bias method, which was first used in space
plasma measurements [Pedersen et al. (1978b)] and adopted for lab plasma measurements
[Diebold et al. (1988)].
The current-bias method works as follows. When the emissive probe bias is equal
to the plasma potential, the probe emits a saturation current, Ip. The probe is forced to
emit a current Ib that is close or equal to Ip, the bias voltage at this emission current gives
the plasma potential. The biggest advantage of the current-biased method is that it does
not require to sweep the bias voltage to obtain the full I-V curve to determine the plasma
potential so it allows for fast measurement rates.
Lastly, emissive probes are mostly used in the lab, such as in this thesis work. In
space, emissive probes are not often used because the probe needs to be constantly heated,
causing limited lifetime and requiring more power. Instead, probes taking advantage of
photoemission over thermionic emission are used in space for local potential measurements.
Electric field probes work exactly in this way.
25
2.3.2 Electric Field Probes
Electric field probes make use of the difference in local potential measurements made
by two identical probes mounted on a SC anti-parallel to each other to determine the electric
field. Usually, there are 3 orthogonal pairs to fully characterize the electric field around a
SC. Figure 2.9 shows an example of how electric field probe are usually oriented. Each of
the two probes in measuring the local potential has a same working principle as an emissive
probe discussed above, where instead of using a hot, biased filament to emit thermionic
electrons from the probe, an electric field probe makes use of photoemission to create an
emission current. Photoemission is the process of electrons being released from the probe
surface by absorbing the energy of photons according to the photoelectric effect. Similar to
the ones shown in Fig. 2.8a, Figure 2.10 shows a breakdown of the emission and collection
currents from photoemission and the ambient thermal plasma, respectively, with emission
current being positive here.
26
Figure 2.9: Electric Field Probes on THEMIS
Schematic of the orientation of electric field probes on board the THEMIS SC. Numbers 1–6indicate the location of the electric field probes. [Bonell et al. (2008)]
27
Figure 2.10: Electric Field Probe Theory
a) A simplified schematic of the I-V curve of an electric field probe taking into accountphotoemission and the thermal electron collection. At high altitudes the plasma density islow so the I-V curve is dominated by photoemission. b) A simplified schematic of the I-Vcurve of an electric field curve with photoemission, thermal electron collection, and a biascurrent imposed by the circuit to measure the floating potential. In both figures emissioncurrent is considered to be positive. [Mozer (2016)]
Similarly, to measure the ambient potential, a bias current is introduced. This current
serves to cancel out the thermal electrons collected at positive bias and attempt to bring the
floating potential to the plasma potential. Figure 2.11 shows data from the Time History of
Events and Macroscale Interactions during Substorms (THEMIS) mission, where an identical
bias current is swept across two anti-parallel probes and the corresponding measure of the
floating potentials is used to calculate the electric field.
28
Figure 2.11: Electric Field Probe Data
a) Data from one of the THEMIS missions (THEMIS A) showing the bias current beingswept on the top and the corresponding measurement of the electric field in the bottom.V 12 represents potential data taken from probes 1 and 2 that are anti-parallel. b) Isolationof a single bias current sweep and its corresponding electric field measurement correspondingto the red box of figure a. Notice the region of accurate local potential measurement shownin between the red dotted lines and therefore the region where the electric field measurementis trusted. [Mozer (2016)]
Figure 2.11 shows that as bias currents cause the floating potential to become closer
to the ambient plasma potential a consistent measure of the electric field is made. This is
because like an emissive probe, when the floating potential in the vicinity of the plasma
potential, the potential measurements are largely unaffected by changes in the bias current.
Measurement of the electric field can therefore be trusted in the regions shown in Fig. 2.11b
between the red dotted lines, where the measure is consistent and mostly unchanging as a
function of bias current.
The more intense the photoemission and the lower the density of the ambient plasma,
the more accurate the electric field measurement is. However, it is also highly important
that the bias currents and voltage measurements between the two probes are identical since
any asymmetry will cause an incorrect measure of the electric field. Because of this electric
field probes are highly susceptible to oxidation as it will change the work function and lower
the photoemission, as well as introduce asymmetries in the surface properties the system of
29
probes, discussed further in section 4.2.
Chapter 3
Interpretation of Langmuir Probe Measurements
The plasma characteristics, including density, temperature and plasma potential (or
SC potential relative to the ambient plasma in space), are derived by fitting an entire I-
V curve with the addition of the ion and electron currents in both retarding and satura-
tion regions. This method is more accurate and appropriate for more complicated plasma
conditions, and is usually used in interpreting probe measurements in the space plasma
environment[Hoang et al. (2018), Ergun et al. (2015), Olson et al. (2010)].
In most lab plasmas, including the ones in this dissertation, where ions are cold (i.e.,
Ti � Te) and electrons have an approximately Maxwellian distribution [Hershkowitz (1989)],
and a simplified analysis method can be used, which focuses on interpreting the electron char-
acteristics. For this reason, the development of the DHP in this thesis work was studied and
tested in terms of the electron density, the electron temperature, and the plasma potential.
This simplified method is described in detail in the following subsections.
3.1 Plasma Potential and the ‘Knee’ of the I-V Curve
The plasma potential divides the I-V curve between the electron retarding and satu-
ration regions. When the probe bias is more negative than the plasma potential, electrons
with the energy lower than the potential difference between the probe and plasma will be
returned to the plasma. As the probe bias is swept from negative to positive getting closer
to the plasma potential, more electrons are able to reach the probe to be collected. Once the
31
probe is at the same potential as the surrounding plasma, the probe collects all the electrons
in its vicinity, reaching the current saturation region. The plasma potential is labeled from
now on as Vp.
The point at which the probe current reaches saturation from the retarding region
creates a discontinuity in the I-V curve called the ’knee,’ Vk, as shown in Fig. 2.1. In
most plasmas, the knee indicates the plasma potential (i.e., Vk = Vp). However, as will be
discussed in further chapters, this is not always the case.
For a planar probe, Vk is easily determined when the current goes from the exponential
retarding region to flat saturation region, as shown in Fig. 2.1. However, as discussed in
section 2.1.1, even planar probes with a finite size can be warped due to sheath expansion.
Additionally, cylindrical and spherical probes have a less obvious ‘knee’ shown on a linear
scale. It has been shown that the first derivative of the I-V curve gives a better solution
to identify the ‘knee’ [Hershkowitz (1989)]. Figure 3.1 shows the I-V curve of a cylindrical
probe in a linear scale and the first derivative of the I-V curve. A peak is clearly shown in
the first derivative, which is correlated with the slope change from the exponential retarding
region to the saturation region in the I-V curve. The ‘knee’ and thus the plasma potential
is defined as the probe bias at the peak in the first derivative of the I-V curve.
32
Figure 3.1: An I-V Curve and its Derivative
Data of an I-V curve of a cylindrical probe (left y-axis) and the first derivative (right y-axis).The ’kink’ in the linear scale called the ’knee’ shows where the I-V curve transitions fromthe electron retarding region to the electron saturation region. The location of the ‘knee’ iseasily identified from the peak in the first derivative, marking the plasma potential.
Some methods instead will use zero-crossing in the second derivative of the I-V curve
to define the plasma potential. However, the biggest disadvantage is largely amplified noise
due to twice differentiations of a measured I-V curve. For this reason, the first derivative is
mostly often used to determine the plasma potential.
In all the lab experiments performed in this thesis work, the potential is defined with
respect to the chamber wall that is connected to Earth ground. Fig. 3.1 shows that Vp is
slightly more positive than ground. Due to higher mobility of electrons than ions, a sheath
33
higher than ground is created around the chamber wall to return some of the electrons to
the plasma to balance the ion flux at the wall, causing the plasma potential to be higher
than ground. Similarly, the probe needs to be biased more negatively relative to ground in
order to balance the electron and ion fluxes to have a zero net current, causing the floating
potential to be negative, as shown in Fig. 3.1.
However, in the case of space plasma measurements, there is no well-defined ground.
Rather, the ambient plasma is considered to be ’ground,’ making Vp = 0, and the measured
Vk of the ’knee’ in the I-V curve gives the SC potential (i.e., VSC = -Vk) with respect to the
ambient plasma. This will become relevant in chapter 7, but for the following sections unless
otherwise stated, the measurements of Vp refer to the lab experiments and with respect to
Earth ground.
3.2 Electron Temperature
In the retarding region, as described in previous sections, only electrons with energy
high enough to overcome the potential barrier Vp−Vb can be collected by the probe. There-
fore, the electron energy distribution can be derived from the current changes as a function
of the probe bias within the retarding region. While thermal electrons in the space envi-
ronment can sometimes be better fit with a Kappa energy distributions (Maxwellian with a
power-law tail [Livadiotis et al. (2018)]), most thermal plasmas, including lab plasmas, are
approximated with a Maxwellian distribution [Kim et al. (2014)]. An advantage of using
a Maxwellian distribution is that the population can be defined in terms of temperature.
Taking natural log on both sides of Eq. 2.3 gives
ln(Ie) =e
Te(Vb − Vp) + ln(Isat∗e ) (3.1)
It shows that Te (in electron-volts) is 1/slope of the I-V curve in the retarding region with
the current in natural-log scale, as shown in Fig. 3.2a. Unless otherwise stated, the electron
34
temperature will be quoted in electron-volts (eV).
Figure 3.2: Electron Temperature and Saturation Currents
a) Absolute value of data in semi-natural log scale of an I-V curve showing a linear slopeof the retarding region. The inverse of this slope is equal to the electron temperature. b)Data in linear scale of an I-V curve with the plasma potential, Vp, marking the saturationcurrent, Isate , that is used to determine the electron density.
3.3 Electron Density
Once Te and Vp are determined, the electron density, ne, can be calculated by assum-
ing that the probe collects the electrons with all energies when the probe bias reaches Vp.
Therefore, Eq. 2.1 can be inverted to solve for ne,
ne = Isat∗e /(Ae√Te/2πme) (3.2)
where, Isat is the measured current at the plasma potential, Vp, and Te is the measured
electron temperature [Hershkowitz (1989)].
35
3.4 Ion Subtraction
As described above, this work focuses on interpreting the electron characteristics. In
order to analyze the electron current, the ion current needs to be subtracted first. In lab
plasmas, because of Ti � Te, the ion current is a beam-like current with a Bohm velocity
(Section 2.2.1), meaning that retarding region is replaced by a shelf. Because sheath expan-
sion will also cause the ion current to increases as the probe bias becomes more negative
but because the ion current is still much smaller than the electron current, the ion current
is simply fit with a line in the negative bias region beyond the electron retarding region,
extended to the plasma potential, and subtracted from the I-V curve so that only the elec-
tron current remains. Figure 3.3 shows an schematic of the superposition of the electron and
ion currents, representing how the need of ion subtraction in order to recreate the correct
electron retarding region.
Figure 3.3: Ion Subtraction
a) Simplified sketch of the superposition of the electron and ion currents and how they affectthe retarding region for a planar probe. Ion current exaggerated for visual ease. b) Data ofa spherical probe zoomed in on the ion saturation and electron retarding region as an examleof ion subtraction.
Chapter 4
Issues of Probe Surface Oxidation
The information presented in this chapter has been published in the following papers:
[Samaniego et al. (2018)] and [Samaniego et al. (2019)].
In atmospheres and ionospheres of planets, oxygen in many forms (e.g., O, O2, O+ and
O+2 ) is present in relatively high densities [Osepian et al. (2008), Zhang et al. (1993)]. When
the probes are taking measurements in such environments, the surfaces of the probes have
the high risk of being oxidized because of the relatively high energy (1 – 6 eV depending on
the SC speed) of oxygen impinging on the probes. Section 4.1 discusses the oxidation effects
on Langmuir probe measurements (plasma density, temperature, and potential). Section
4.2 specifically reports the oxidation effect on photoemission and how it pertains to electric
field probes. Section 4.3 suggests new surface coatings for Langmuir probes in oxygen-rich
environments.
4.1 Oxidation on Langmuir Probe Measurements
The oxidized forms of most materials have reduced surface conductivity, causing
a reduction in the current collected at a given voltage during the probe sweep. The
I-V curves are therefore changed, resulting in errors in the derived plasma parame-
ters [Ergun et al. (2015)]. Currently, the most common coatings for Langmuir probes
are DAG (a resin based graphite dispersion)[Lundin et al. (1995), Wygant et al. (2013),
Lindqvist et al. (2016)], Gold [Tejumola et al. (2016), Kai et al. (2012)], and TiN (Tita-
37
nium Nitride) [Wahlstrom et al. (1992), Eriksson et al. (2007), Andersson et al. (2015)].
DAG and Gold have long history of use in oxygen-rich environments but both have
shortcomings. Some forms of DAG coatings (AquaDAG) are known to erode over time in
the presence of oxygen and therefore have the risk of exposing the naked probe surface
[Visentine (1983), Visentine et al. (1985)]. Additionally, currently used DAG 213, while
being an improvement over previous forms of AquaDAG, are still known to have the surface
affected by atomic oxygen exposure as observed by Time History of Events and Macroscale
Interactions during Substorms (THEMIS) and Van Allen Probes (VAP) [Mozer (2016)].
Gold, on the other hand, while being inert at room temperature, has been shown to oxidize
when bombarded by high energy oxygen ions [Gottfried et al. (2013)]. Additionally, due
to the softness of both DAG and Gold, the coating layers can be damaged or eroded by
interplanetary dust, for example. Their softness may also pose an issue during pre-flight
handling and ground work that can damage the probe.
TiN coating was developed for its high corrosion resistance and high hardness, as
well as highly uniform surface conductivity and work function in contrast to DAG and
Gold. TiN was first used on the Cassini Langmuir probe and performed in Saturn’s
dust-rich environment [Wahlstrom et al. (1992)], and has since been used on several other
missions, such as Rosetta and MAVEN [Eriksson et al. (2007), Andersson et al. (2015)].
However, the Langmuir probe measurements from the recent MAVEN mission showed
anomalies in their I-V curves after the SC dipped into the Martian ionosphere in which
the density of atomic oxygen (O) is high [Ergun et al. (2015), Andersson et al. (2017),
Benna et al. (2015), Mahaffy et al. (2015)]. These I-V curve anomalies were likely to be
caused by the reduced surface conductivity due to the oxidation of TiN coating. With a
SC speed of approximately 4-5 km/s, the O impinged the probe surface with a correspond-
ing energy of 1.3 –2 eV. This energy corresponds to temperature of 15,000-24,000 K, high
enough to cause TiN to be oxidized [Yin et al. (2007), Desmaison et al. (1979)].
In contrast to DAG, Gold, and TiN, Iridium shows promise as new Langmuir probe
38
coating candidate because: 1) It is difficult to oxidize[Chalamala et al. (1999)]; 2) The oxi-
dized forms remain highly conductive [Chalamala et al. (1999)]; and 3) It has high corrosion
resistance and high hardness[Toenshoff et al. (2000), Zhu et al. (2011)]. Additionally, Rhe-
nium was also tested due to its similar properties to Iridium and having been flown as a
Langmuir probe on the Pioneer Venus Orbiter [Brace et al. (1988)].
The following section characterizes the effect of O on Langmuir probe measurements
of plasma density, temperature, spacecraft potential as a function of probe material. We
compared them to current probe coating materials (DAG, TiN, Gold) and metals easily
oxidized (Copper and Nickel) as controls. Sections 4.1.1 and 4.1.2 discusses the experimental
apparatus and setup, the procedure of the oxidation process and the I-V curve comparison.
Section 4.1.3 shows the results and discussion. Section 4.1.4 compares the laboratory data
with the MAVEN data. Section 4.1.5 discusses the implications of various coating choices.
4.1.1 Experimental Setup and Method
All tested Langmuir probes were metal wires 2 cm long and 0.5 mm in diameter.
Copper, Nickel, Gold, Iridium, and Rhenium probes were solid wires of high purity. The
DAG probe was a wire of 303 stainless steel coated with AeroDAG-G (a type of AquaDAG).
The TiN probe was a Titanium wire with nitride coating via Physical Vapor Deposition.
The I-V curves were swept for each probe in an argon plasma before and after exposing it
to an oxygen plasma to determine the oxidation effect on the probe measurements.
In upper atmospheres of planets, oxygen is usually present in the form of O
while molecular oxygen (O2) dominates in the lower atmospheres [Osepian et al. (2008),
Mahaffy et al. (2015)]. The oxidation process can be caused by neutral O and O2 bombard-
ing the probe surface with energies up to a few eV depending on SC speeds. Oxidation can
also be caused by oxygen ions (O+, O+2 ) bombarding the probe surface with the energies due
to the acceleration by the potential difference between the probe and ambient plasma. In
the laboratory, it is difficult to achieve the energy of a few eV for neutral particles. Instead,
39
we exposed the sample probes to an oxygen plasma. The probes were electrically floated to
-10 V or biased to -1.5 V with respect to the plasma potential. Consequently, the oxygen
ions were accelerated to the energies of 10 eV or 1.5 eV to bombard the probe surfaces for
the oxidation process.
Because O is less stable than O2 and is therefore a good oxidant, we used an ultraviolet
(UV) lamp to photo-dissociate a fraction of the O2 into O. The Residual Gas Analyzer (RGA)
measurements showed that both O and O2 exist with the partial pressure of roughly 20% O
and 80% O2 (Fig. 4.1). Therefore, both O+ and O+2 were created in the oxygen chamber.
The probes were exposed for 20 minutes at a total ion flux of 1018m−2s−1. Taking into
account that only 20% of ions are O in our experiment, this is equivalent to approximately a
few hours to a few months in the ionosphere of Earth, depending on O densities at different
altitudes. The estimate assumes that the density of O is ∼ 106cm−3 at ∼ 700 km and
∼ 104cm−3 at ∼ 1000 km [Silverman (1995), Banks et al. (2004)].
4.1.2 Procedure
Because introduction of oxygen plasma also oxidizes the chamber walls and thus
changes the plasma environment, two vacuum chambers were used: One chamber was des-
ignated as the argon chamber in which the I-V curves would be taken in an argon plasma;
and a second chamber was designated as the oxygen chamber in which an oxygen plasma
would be created for the oxidation process. Figure 4.2 shows the schematics of both cham-
bers. Both argon and oxygen plasmas were created by a negatively biased hot filament that
emitted energetic electrons to impact and ionize neutral particles.
To best test the oxidation effect on the probe measurements, the probe surface needs
to be as clean as possible. The probes were first cleaned with solvents and an ultrasonic
cleaner. They were also cleaned in situ in the argon plasma by applying a large positive
potential to the probes to draw a large electron current to heat their surfaces.
The following outlines the procedure of the oxidation process and I-V curve comparison:
40
(1) Clean the probe with solvents and the ultrasonic cleaner.
(2) Insert the probe in the argon chamber, perform in situ plasma cleaning for the probe
and sweep it for an I-V curve before the oxidation process. Probes are swept from
-30 V to +10 V with a step size of 0.1V, with each step averaging 5000 data points
for a total sweep time of 10 seconds.
(3) Transfer the probe to the oxygen chamber. First, feed the argon gas and create an
argon plasma for in situ cleaning of the probe. Then, switch to the oxygen gas and
turn on the UV lamp to dissociate O2 to O. Finally, create the oxygen plasma for the
oxidation process for 20 minutes. The probe was electrically floated to a potential
approximately 10 V more negative than the plasma potential, i.e., the O+ and O+2
bombarding the probe surface with an energy approximately 10 eV.
(4) Transfer the probe back to the argon chamber after the oxidation process and sweep
it again for an I-V curve in the same argon plasma.
(5) Reclean the probe with the same in situ argon plasma cleaning method to see if
the oxidation layer would be removed. This process may also provide a method for
in situ cleaning of the probes once they become oxidized in space. This step also
ensures that the argon plasma is the same before and after the oxidation process.
The recleaning proccess consisted of running a heating current of 3 mA through
the probe by applying +350 V on the probe in the argon plasma. Each probe was
cleaned for 30 seconds. If the I-V curves didn’t return to the control sweep after
the first exposure, then they were cleaned again or at higher current (only relavent
for Gold and TiN). In all cases with the exception of TiN the recleaned I-V curve
overlaps with the control curve, proving the effectiveness of the cleaning method and
the reproducibility of the plasma.
(6) Compare the I-V curves before and after the oxidation process as well as after re-
41
cleaning.
Figure 4.1: RGA Analysis of Oxidation Environment
Log plot of the partial pressures of O and O2 as a function of time measured by the RGA.Column A, shows the partial pressures at vacuum. Column B, shows the partial pressuresafter oxygen is introduced into the chamber. The increase of O in column B is caused by theoperation of the RGA dissociating a fraction of O2 into O. Column C, shows a jump in O(Mass 16), and a dip in O2 (Mass 32) from column B to C due to photodissociation after theUV lamp is turned on. Column D, shows the partial pressures after the filament is turnedon to create plasma. With the UV radiation, O and O2 are about 20% and 80% of the totalpressure, respectively.
42
Figure 4.2: Oxidation Set-up
a) Oxygen plasma chamber for the probe oxidation process. A UV lamp is used to dissociate
a fraction of the O2 to O. b) Argon plasma chamber used for comparing the I-V curves of the
probe before and after the oxidation process. Plasmas in both chambers are created using a
negatively biased hot filament.
4.1.2.1 Effect of Contaminants
The probe surface was mostly contaminated from two sources: deposition of vacuum
pump oil, and moisture from the air when transferring the probe from the oxygen chamber
to the argon chamber. To minimize these two effects we did the following: the probes were
cleaned in situ using argon plasma before the oxidation process as described in the previous
section, and the vacuum chambers were brought to atmosphere with nitrogen gas instead of
the air to minimize the amount of moisture introduced into the system. Even with these
countermeasures minimal contamination was still present. The effect of contamination was
characterized by running each probe through the procedure described in section 2.1 without
the presence of the oxygen gas. Figure 4.3 shows an example of the contamination effect
43
Figure 4.3: Effect of Systematic Contamination
Effect of contamination on the Iridium probe’s I-V curve measurements after going throughthe oxidation process procedure in the absence of oxygen gas. This curve, and others like itfor different probe materials, was used to correct for the contamination effect on each probe’sI-V curve measurements.
44
on the Copper probe measurements after going through the oxidation process procedure
without oxygen gas. This curve, and others like it for different materials, was used to correct
for the contamination effect on each probe’s I-V curve to yield the true effect of oxidation.
Figure 4.4: Oxidation Distortion on Known Oxidizers
I-V curves, semi-log plot, and derivatives of the Copper and Nickel probes before and afterthe oxidation process as well as recleaned using the in situ plasma cleaning method. These
graphs show an example of oxidation effects on the I-V curves of Langmuir probesincluding a more positive plasma potential with a more rounded ’knee,’ hotter electron
temperature, and lower plasma current.
45
Figure 4.5: Oxidation Distortion on Current Probe Materials
I-V curves, semi-log plot, and derivatives of the TiN, Gold, and DAG probes before andafter the oxidation process as well as recleaned using the in situ plasma cleaning method.
46
Figure 4.6: Oxidation Distortion on New Probe Materials
I-V curves, semi-log plot, and derivatives of the Rhenium and Iridium probes before andafter the oxidation process as well as recleaned using the in situ plasma cleaning method
Figures 4.4–4.6 show the linear I-V curves, semi-log I-V curves, and first derivatives
of all the testing probes probes before and after the oxidation as well as after the recleaning
processes. Table 4.1 shows the measured plasma potential, temperature, and density by
the probes before and after oxidation. Figures 4.7– 6.8 show the percentage changes in the
measured plasma parameters after oxidation.
Oxidation effects on the I-V curves of a Langmuir probe are found to have the following
general features and are best represented in the Copper probe measurements (Fig. 4.4):
(1) Reduced current at a given probe potential. This is because the oxidation forms a thin
insulating layer on the probe surface, which causes a potential drop on the oxidation
layer exposed to plasma and consequently a lower current.
(2) The derived plasma potential becomes more positive.This is because the probe poten-
tial exposed to the plasma is lower than the given bias potential due to the oxidized
47
insulating layer, causing the probe bias potential to be more positive than the true
plasma potential to reach the electron saturation current. In addition, the ‘knee’
in the derivative of the I-V curve becomes more rounded, making it more difficult
to accurately determine the plasma potential. The exact origin of the rounding of
the ‘knee’ is unclear, but may be caused non-uniform oxidation of the surface. This
implies that not all regions of the probe surface experience the same voltage shift
and the superposition of these voltage shifts affects the ability to accurately resolve
the plasma potential.
(3) The derived electron density decreases. This corresponds to the decrease in the probe
current as described above.
(4) The derived electron temperature becomes hotter. Similar to the rounding of the
knee, if the probe did experience non-uniform oxidation on its surface then the
superposition of the voltage shifts will also cause the retarding region to be ’stretched’
and consequently a hotter electron temperature.
48
Figure 4.7: Oxidation Effect on Vp
Percentage change of the measured plasma potential (Vp) normalized by the true electrontemperature (Te) after oxidation. General trends suggest that an oxidized probe measures amore positive plasma potential than the true one. Percent errors shown in Figures 4.7, 6.7,and 6.8 are derived from largest of the either the resolution of the probe sweeps or standarddeviation in measured plasma parameters.
49
Figure 4.8: Oxidation Effect on Te
Percentage changes of the measured electron temperature (Te) after oxidation. Generaltrends suggest that an oxidized probe measures a higher electron temperature than the trueone.
50
Figure 4.9: Oxidation Effect on ne
Percentage change of the measured electron density (Ne) after oxidation. General trendssuggest that an oxidized probe measures a lower electron density than the true one.
51
Vp/Te[1/e] Te[eV ] Ne [cm−3]
Before After Before After Before After
Cu 0.4±0.1 1.9±0.3 1.6±0.2 2.0±0.4 1.8×106 ± 2× 105 1.1×106 ± 3× 105
Ni 0.4±0.1 0.4±0.3 1.7±0.1 1.6±0.3 1.8×106 ± 5× 105 1.2×106 ± 1× 105
TiN 0.8±0.1 0.9±0.3 1.8±0.2 1.7±0.2 6.6×106 ± 5× 105 3.3×106 ± 1× 105
Au 0.9±0.1 1.0±0.2 1.9±0.2 2.2±0.4 5.6×106 ± 4× 105 4.0×106 ± 6× 105
DAG 0.4±0.1 0.7±0.1 1.5±0.1 1.7±0.1 1.8×106 ± 2× 105 1.6×106 ± 2× 105
Rh 0.3±0.1 0.5±0.1 1.7±0.3 1.6±0.2 1.5×106 ± 1× 105 1.3×106 ± 3× 105
Ir 0.3±0.1 0.4±0.1 1.6±0.1 1.6±0.2 1.5×106 ± 1× 105 1.5×106 ± 2× 105
Table 4.1:
Derived plasma parameters measured by the Langmuir probes before and after the oxidation
process. Metals are organized top to bottom from worst to best. Errors shown are the largest
of the either the resolution of the probe sweeps or standard deviation in measured plasma
parameters.
Both control materials (Copper and Nickel) showed oxidation effects on the probe
measurements while the effect on the Copper probe is much more pronounced with the
features described above (Fig. 4.4). The oxidation process caused the moderately reduced
current of the Nickel probe and the ‘knee’ in the derivative of its I-V curve to be more rounded
but without a significant shift. However, the decrease in the electron density derived from
the Nickel probe’s I-V curve after the oxidation process is larger than that from the Copper
probe measurement. This is because the derived more positive plasma potential in the
Copper probe measurements compensates the reduced current at a given bias potential.
The TiN probe measurements showed the significant changes in both the I-V curves
(Fig. 4.5) and derived parameters (Table 1). Unlike all other testing probes, the TiN probe’s
I-V curve did not return to the control after the probe was recleaned, even after several
minutes at maximum output (7mA), implying that once it is oxidized in space, it is very
52
difficult to be cleaned in situ. This effect corroborates what was measured by the TiN coated
Langmuir probes on the MAVEN mission[Ergun et al. (2015), Andersson et al. (2017)].
Gold showed moderate oxidation effects on the probe measurements (Fig. 4.5). At
room temperature, Gold is highly resistant to oxidation. However, in our tests, the Gold
probe was bombarded by O+ and O+2 with the energy of 10 eV that is much higher
than the room temperature (i.e., 0.025 eV). This result is in agreement with other stud-
ies that have shown Gold can be oxidized when exposed to oxygen at higher energies
[Gottfried et al. (2013)]. Also, Gold required a much larger electron current (almost 6mA
for 1 minute) to remove the oxidized layer during the recleaning phase described in section
2.1, suggesting extreme difficulty for in situ cleaning of the probe in space.
DAG showed a noticeable but overall small oxidation effect on the probe measurements
(Fig. 4.5). The deviation between the I-V curves before and after oxygen exposure is approx-
imately 30% in plasma potential potential and 10% change in the density and temperature.
We believe the oxygen reacting with the carbon produces gaseous compounds that do not
stay on the surface. However, if this is true, it is likely that this will cause a certain degree
of erosion depending on the type of DAG used.
Of the new coating candidates, Rhenium showed a similar oxidation effect on the
measured plasma parameters to DAG. Among all the testing materials, Iridium showed the
least oxidation effect on the probe measurements (Fig. 4.6). After the oxidation process, the
Iridium I-V curve remained almost unchanged and the derived plasma parameters changed
less than 10%. Considering the 1.5 to 10 eV bombardment energy and the high likelihood
of oxidation at those temperatures, the good performance of Iridium is likely attributed
to the high conductivity of its oxide form [Chalamala et al. (1999)]. In addition, Iridium’s
extremely high hardness makes it more suitable and robust than both DAG and Gold for
Langmuir probes used in space environments where impacts on the probe are likely from
dust [Toenshoff et al. (2000), Zhu et al. (2011)].
53
Figure 4.10: Effect of Atomic Oxygen Impact Energy
Measurements of the Copper (left) and Gold (right) probes exposed to 10 eV and 1.5 eVoxygen ions. Oxidation effects are shown with both ion energies.
Figure 4.11: O2 vs O
Difference in oxidation effect on the Copper with and without the UV irradiation. It showsthat O (only 20% of the total oxygen) contributes more to the oxidation process then O2.
The probes were exposed to oxygen ions with bombarding energy of 1.5 eV to simulate
slower SC moving at a few km/s, for example MAVEN at 4km/s. Figure 4.10 compares the
effect of oxidation on the Copper and Gold probes at both 1.5 and 10 eV. The 10 eV ions only
54
show slightly higher oxidation effect than the 1.5 eV ions, suggesting that the effects that
we report are above the energy threshold for oxidation, and that these effects are expected
for probes at realistic SC speeds.
The significance of O+ compared to O+2 on the oxidation process was tested with and
without UV illumination that photo-dissociates a fraction of O2 to O. Figure 4.11 shows
that the Copper probe had a more than twice reduced current at a given bias voltage with
UV than without UV illumination. As shown in Fig. 4.1, the partial pressure of O is only
20%, meaning that O+ has much higher oxidation reaction rate than O+2 .
4.1.3 Comparison with MAVEN LPW
The possible oxidation effect on the MAVEN’s Langmuir Probe and Waves (LPW)
measurements has been indicated as a deviation of the measured I-V characteristics from
the expected ones [Ergun et al. (2015)]. Similar to our lab results, the potential with re-
spect to the SC becomes more positive and the ‘knee’ becomes more rounded. In addition,
multiple peaks shown on the derivative of the I-V curves (Fig. 4.12) at low altitudes sug-
gest that the effects of probe degradation are amplified when the plasma density is high
[Andersson et al. (2017)]. The multiples peaks were only experienced by one of the two
booms (Fig 4.12b), suggesting that one probe had degraded more than the other. The mul-
tiple peaks are suggested to be caused by the non-uniform oxidation effect due to the change
in the SC ramming direction.
55
Figure 4.12: MAVEN LPW Data
a) Normalized first derivatives of I-V curves of MAVEN LPW Boom 1 as the SC dips into theMartian atmosphere stacked as a function of time and corresponding altitude. The red andblue lines call out I-V curves that are in the high density and low density regions respectively.b) Selected first derivative traces of Boom 1 and Boom 2 in the low and high density regions.Red and blue lines on figure ‘a’ corresponds to red and blue traces on figure ‘b.’ Noticethat at low altitude where the density is highest (red line and red traces) the Boom 1 showsmultiple peaks where Boom 2 does not.
As indicated from the data taken by Neutral Gas and Ion Mass Spectrometer (NGIMS)
on board MAVEN from a variety of dips a during February and May of 2015, the average
density of O was 1.7 × 108cm−3. Given an average SC speed of 4km/s, the average flux of
O was approximately 7× 1017m−2s−1. Comparing to the flux of O+ in our experiments, 20
min exposure in our chamber corresponds to a almost 10 minutes of MAVEN exposure, or a
fraction of a dip into the Martian atmosphere. This implies that MAVEN’s LPW instrument
would experience degradation due to oxidation shortly after first being exposed. Because
MAVEN’s LPW instrument was not turned on until it had made many dips into the Martian
atmosphere, it is likely that the instrument was already affected by oxidation before the first
measurements were carried out.
Additionally, after MAVEN made several deep dips (below 500km) into the Martian at-
56
mosphere the electrostatic analyzer, Suprathermal and Thermal Ion Composition (STATIC),
experienced similar oxidation effects on the surface potential of the curved plates, resulting
in errors of the ion energy measurements [Andersson et al. (2017)]. This indicates oxidation
will not only affect Langmuir probes, but also any instruments sensitive to potential control.
4.1.4 Discussion: Implications for different Langmuir probe coatings
We have tested a variety of samples in a laboratory oxygen plasma to find a new coating
material for improving in situ Langmuir probe’s I-V curve measurements in an oxygen-rich
plasma environment, such as planetary atmospheres and ionospheres. The oxidation species
in the laboratory were mainly O+2 and O+ while in space it can be both neutral and ionized
oxygen atoms and/or molecules. The energies of oxygen ions were 1.5 – 10 eV to mimic
the energies of oxygen particles bombarding the probe due to high–speed SC and/or probe
sweeping voltages. Overall, the oxidation effect on the probe surface led to measuring a more
positive plasma potential, hotter electron temperature, and lower plasma density. We found
that of the three most commonly used coatings (TiN, DAG and Gold), TiN showed the most
significant changes in the I-V curve and derived plasma characteristics, and these changes
are irreversible after the cleaning process attempt. Gold showed a moderate oxidation effect
on the probe measurements, and was found to be difficult to be recleaned. DAG showed
small but noticeable oxidation effects on the probe measurements. In the new coating candi-
dates, Rhenium showed a similar oxidation effect to DAG. Among all the testing materials,
Iridium showed the least effect due to oxygen exposure on the probe measurements, which
is likely attributable to the high conductivity of its oxide form [Chalamala et al. (1999)].
Additionally, Iridium has extremely high hardness compared to Gold and DAG, making it
more suitable and robust than current coatings for Langmuir probes to be used in dusty
space environments.
These results are also important for other plasma instruments that are sensitive to the
potential variation of their electrode surfaces, such as Retarding Potential Analyzers (RPAs),
57
electrostatic analyzers, and electric field probes. When these instruments are exposed to an
oxygen-rich environment, their electrode surfaces may become oxidized, causing measure-
ment errors. However, electric field probes work are also highly sensitive to changes in there
photoemission properties. Therefore, the effectiveness of Iridium, and the other materials, as
a coating on electric field probes (e.g., Langmuir probes doubling as an electric field probe)
needs further understanding of the photoemission characteristics to fully characterize.
4.2 Oxidation Effect on Photoemission and Electric Field Probes
As alluded to in the previous section, O can degrade the surface conductivity and
can negatively affect instrument’s sensitivity to potential variations on the probe surfaces.
Additionally, it has been observed that oxidized layer of most materials will reduce the
photoemission yield, causing the change of the probe’s current-voltage (I-V) curves and
subsequent derived plasma parameters [Ergun et al. (2015)] or errors in electric field mea-
surements [Mozer (2016)].
For Langmuir probes, photoelectrons emitted from the probe surface will contaminate
the probe’s I-V curve measurements of the ambient plasma parameters. It requires these
photoelectrons to be well characterized in order to properly remove them from the I-V curve
for the interpretation. On the other hand, photoemission from the probe is essential for the
electric field probe measurements, especially in low-density plasmas. Electric field probes
rely on the photoelectron current emitted from the probe to determine the local plasma
potential of each probe based on the current-bias method [Mozer (2016)]. The potential dif-
ference between two probes separated over a certain distance gives the electric field. Ideally,
in order to accurately determine the local potential in a sparse plasma, the photoemission
current dominates over the collection current and other currents dependent on the ambient
plasma. Though electric field probes are usually used in interplanetary plasma or planetary
magnetospheres in which oxygen is absent, many probes ’dip’ or otherwise travel through the
oxygen-rich upper atmospheres of planets, depended on the SC orbits for mission require-
58
ments [Mauk et al. (2013), Burch et al. (2016)]. As presented here, the impact of oxidation
on photoelectron production is important for both Langmuir probes and electric field probes.
Advancement in the understanding of photoemission from different probe coatings will im-
prove the interpretation of Langmuir and electric field probe measurements and give future
missions insight on coating material selection.
This following section supplements the previous (section 4.1) by providing the effect
of oxidation on the photoemission of various materials, including DAG213 (a resin based
graphite coating), AquaDAG (a simple graphite coating), Au,TiN, Ir, Rh, and Copper (Cu).
Additionally, because of its use on the Parker Solar Probe mission [Bale et al. (2016)], we
tested the photoemission response of Niobium (Nb). Section 4.2.1 discusses the experimen-
tal apparatus and setup. Sections 4.2.2 and 4.2.3 present the results of oxidation on the
photoemission characteristics. Section 4.2.4 discusses implications of our findings.
4.2.1 Method
To test the photoemission characteristics of various probe materials, Langmuir probes
of each material were constructed. All probes were wires 2 cm long and 0.5 mm in diameter.
Cu, Au, Ir, Rh and Nb probes were solid wires of 99.8 % purity. The TiN probe was a
Titanium wire with nitride coating. Two DAG probes were made of a wire of 303 stain-
less steel coated with AeroDAG-G (a type of AquaDAG) and DAG213, respectively. The
photoemission current from the probe surface was measured before and after the oxidation
process as well as after recleaning in an argon plasma.
Figure 4.13 shows the setup of the vacuum chamber. The oxidation process followed
a same procedure to our previous experiment [Samaniego et al. (2018)]. Oxygen gas (O2)
was filled in the chamber with 20% of oxygen atoms (O) created due to photo-dissociation
using a UV lamp (Wavelength: 172 nm, FWHM ± 10 nm; Photon flux to the probe surface:
1016photons cm−2s−1). The neutral particles were ionized by impact of energetic electrons
emitted from a hot filament. The probes were electrically floated to -10 V with respect to
59
the plasma potential. Both O+2 and O+ were then accelerated to the probe surface with an
energy 10 eV, equivalent to a ram velocity of 8 km/s and 11 km/s for O2 and O respectively.
The probes were exposed to the oxygen ions for 20 minutes, which is equivalent to a few
hours to a few months exposure in Earth’s upper atmosphere between 700km and 1,000 km
altitude [Silverman (1995), Banks et al. (2004)].
Figure 4.13: Oxidation Effect on Photoemission Set-up
Plasma chamber for the probe oxidation process and photoemission measurements. A UVlamp is used to dissociate a fraction of the O2 to O and plasma is created using a negativelybiased hot filament. UV lamp is also used for creating photoemission from the probe.
60
To best test the oxidation effect on the probe measurements, the probe surface needs to
be as clean as possible. The probes were cleaned with solvents and an ultrasonic cleaner at
preparation. They were also cleaned in situ in an argon plasma by applying a large positive
potential to the probes to draw a large electron current to heat their surfaces.
The following outlines the procedure of the oxidation process and photoemission tests:
(1) Clean the probe with solvents and the ultrasonic cleaner.
(2) Insert the probe into the vacuum chamber, perform in situ plasma cleaning with an
argon plasma. The cleaning process is performed by running a heating current of 3
mA through the probe by applying +350 V on the probe in the argon plasma. Each
probe is cleaned for 30 seconds.
(3) Sweep the I-V curves of the probes exposed to the UV light in vacuum to obtain the
photoemission current (Before Oxidation). Probes are swept from -40 V to +40 V
with a step size of 0.1V, with each step averaging 5000 data points for a total sweep
time of 10 seconds.
(4) Introduce oxygen gas and create the oxygen plasma (with both O+ and O+2 ) for the
oxidation process. Probes are left to oxidize for 20 minutes.
(5) Turn off the oxygen plasma and bring the chamber back to vacuum, and then repeat
step 3 for the photoemission current measurement (After Oxidation).
(6) Reclean the probe in the argon plasma as described above and repeat step 3 to see
the change of the photoemission current (After Recleaning).
(7) Compare the photoemission current measurements before and after the oxidation
process, as well as after recleaning.
Because the photoemission current was on the same order of magnitude of the noise
of the electronics, the baseline noise was measured before oxidation, after oxidation, and
61
after recleaning, respectively, and then subtracted from the corresponding measurements.
Additionally, each photoemission sweep was taken multiple times, and each material was
tested with multiple samples on different days to ensure repeatability in the results and to
quantify statistical errors in the photoemission curves.
The experiment also went through the process described above but without introducing
oxygen plasma to measure any drift in the photoemission current as a function time. This
drift was taken into account and is expressed in the error bars of the figures.
62
4.2.2 Results and Comparison Between Different Materials
Figure 4.14: Photoemission Flux Comparisons
The photoemission flux of each material before oxidation, after oxidation, and after reclean-ing. AquaDAG is labeled as ’DAG’ on this figure.
63
Figure 4.15: Percent Changes in Photoemission
(Left) The percent change (with respect to the surface before oxidation) in photoemission af-ter oxidation for each material. (Right) The percent change in photoemission after recleaningfor each material. AquaDAG is labeled as ’DAG’ on this figure.
Figure 4.14 shows the photoemission flux of each material before oxidation, after ox-
idation, and after recleaning. Figure 4.15 shows the percent change in the photoemission
after oxidation and after recleaning, respectively. As a clean coating surface (i.e., before
oxidation), DAG213 and Cu had the largest photoemission flux. Ir, Au, AquaDAG, TiN
and Nb had a similar photoemission flux, about 25% lower than that of DAG213 and Cu.
Rh had the least photoemission flux, approximately half of the emission from DAG213 and
Cu.
After the oxidation process, the photoemission flux of Cu, Au and Nb dropped most
significantly by more than 75%. DAG213, TiN and Rh dropped between 50% and 70%. Ir
and AuqaDAG only dropped less than 35%. After all, Ir, DAG213 and AuqaDAG had the
larger photoemission flux than the rest of the materials.
After recleaning, the photoemission flux of Ir, Rh and Cu returned to the level before
oxidation while Au and TiN did not fully come back to the same level. These results are
consistent with previous results of the removal of the oxidation layers on these materials after
recleaning [Samaniego et al. (2018)]. Figure 4.15 shows that the photoemission remains
64
low once Nb becomes oxidized, indicating its oxidation layer is difficult to be removed.
Interestingly, both AquaDAG and DAG213 showed remarkable increases in photoemission
after the recleaning procedure. This may be because oxygen reacts with carbon and other
impurities on the surface, and the reaction products are then cleaned off during the recleaning
phase.
65
4.2.3 Exposure to Larger Ion Fluence
Figure 4.16: Photoemission Yield after High Fluence Exposure
The percent decrease in photoemission current after oxidation as the fluence of oxygen ionsis increased. Fluence is defined as the total number of oxygen ions per unit area (i.e.,time integrated flux). DAG213 photoemission remains unchanged as the oxygen ion fluenceincreases while the Ir slowly decreases.
66
Figure 4.17: Photoemission Yield after High Fluence and Recleaning
The percent decrease in photoemission current after recleaning as the fluence of oxygen ionsis increased. Ir photoemission remains unchanged as the oxygen ion fluence increases whilethe increased photoemission first seen in DAG213 decreases and degrades.
The results reported above are for the probes undergone 20 minutes exposure with the
oxygen ion flux of 1018m−2s−1. We also examined the oxidation effect on the photoemission
of both Ir and DAG213 surfaces with the larger ion fluxes at 5× 1018m−2s−1 for 30 minutes
and 1019m−2s−1 for 40 minutes, which are equivalent to several days to a week exposure at
700 km or a year to 3 years at 1000 km in Earth‘s atmosphere, respectively. Ir was chosen
because its high performance in the I-V curve measurements of the ambient plasma after
oxygen exposure, as shown from previous section 4.1. DAG213 was chosen for its wide use
67
for the coating of electric field probes.
Figure 4.16 shows that the photoemission of Ir decreased as the oxygen ion fluence
(fluence is defined as the time integrated flux, i.e. total number of oxygen ions per unit area)
was increased, while DAG213 showed little change when the ion fluence was larger than
1.2 × 1021m−2 . This suggests that the oxidation effect on the photoemission of DAG213
happens quickly while Ir is affected over a much longer time. Additionally, after recleaning
the probe, Figure 4.17 shows Ir constantly returning to its previous photoemission char-
acteristics. Conversely, the enhancement of photoemission of DAG213 after the recleaning
process decreased as the fluence of oxygen exposure increased. This may be because at high
fluence a portion of the carbon has been eroded, exposing the resin to the plasma.
4.2.4 Discussion: Implications for electric field probe coatings
For electric field probes, the probe photoemission is necessary for measurements.
AquaDAG performed the best with the least drop in the photoemission current after the
oxidation process; however, as discussed in previous section (4.1) AquaDAG is known to
erode over time [Visentine (1983), Visentine et al. (1985)]. DAG213, TiN and Nb showed
the significant reductions, making them undesirable for missions that are expected to spend
significant time in the presence of oxygen. Unlike TiN and Nb, DAG213 after recleaning
showed a significant increase in the photoemission current. This result suggests that DAG213
may self-clean itself once the probe is removed from the oxygen rich environment, making
DAG213 desirable for missions where the threat of oxidation is minimal or infrequent. Ir
showed a relatively small drop in photoemission after oxidation among all the tested materi-
als. The large fluence exposure test showed that though the photoemission decreases as the
oxygen fluence increases, the photoemission current approaches that of DAG213 under the
ion fluence of 1022m−2 that is equivalent to 3 years exposure in Earth‘s upper atmosphere
(1000km). This suggests Ir to be the most resilient to SC missions expecting long term ex-
posures to oxygen. Additionally, Ir returned to original photoemission characteristics after
68
recleaning, suggesting that the surface may be cleaned in-situ. Overall, our results suggest
that Ir is a coating material appropriate for both electric field probes and Langmuir probes.
4.3 Suggested Coatings
For Langmuir probes, Ir is a promising new coating material in an oxygen-rich plasma
environment because of the high-conductivity of its oxidized form. Rh was a close second
and AquaDAG showed promise but degrades over time. For electric field probes, AquaDAG
showed the least change after oxidation and DAG213 off gasses its contamination, making
them both good candidates for electric fields probes when erosion over long mission times is
not a significant worry. Additionally, while the photoemission of Ir did decrease, it did not
show the properties of degradation that the DAG probes did, suggesting that an Ir probe
may be oxidized before hand to minimize the change in the photoemission over time.
Depending on the probe, photoemission can be a contamination or a necessity for the
probe measurements, depending on the probes intended use and environment. For Langmuir
probes, photoelectrons emitted from the probe are considered a contamination to the collec-
tion of ambient plasma electrons and ions. All tested materials show reduced photoemission
due to oxidation. The previous section 4.1, showed that Ir is a promising new coating ma-
terial in an oxygen-rich plasma environment because of the high-conductivity of its oxidized
form. Combining these two results, it is suggested that the Ir probe surface might be oxi-
dized before flight in order to minimize the photoemission effect on the measurements while
possessing the high surface conductivity for the collection of ambient electrons and ions.
Chapter 5
A Novel Langmuir Probe Technology - Double Hemispherical Probe (DHP)
Even after decades of use, there are still challenges in the analysis and interpretation
of Langmuir probe measurements. Specifically, due to ambient plasma interactions with the
SC and probes themselves, a local plasma environment is often created around the probes
that is different from the true ambient plasma. This local plasma is often inhomogeneous
or anisotropic, making it difficult for traditional Langmuir probes to identify and remove
its effects on the probe measurements. As a result, this may introduce large errors in the
derived plasma parameters, such as the plasma density, temperature, and potential.
Directional probes have been developed for characterizing anisotropic plasma fea-
tures in space but were only limited to plasma flow measurements. In the 1970’s, a
two sided planar probe was used to measure the current density and plasma flow in
space on board several sounding rocket missions [Bering et al. (1973b), Bering et al. (1975),
Bering et al. (1982)]. Later, the Segmented Langmuir Probe (SLP), onboard the French
DEMETER [Lebreton et al. (2006), Imtiaz et al. (2013)] and the ESA’s PROBA2 missions
[Santandrea et al. (2013)], was designed to measure the ion flow velocity in Earth’s iono-
sphere. However, 1) the SLP has disadvantages in the probe design: a) the probe sen-
sor consists of 7 segments, making both the mechanics and electronics complicated; b)
the sensor’s signal-to-noise ratio is largely reduced due to the reduced surface area of
each segment comparing to the total; 2) the split planar probes, like the ones used
in [Bering et al. (1973b), Bering et al. (1975), Bering et al. (1982)], only work in high-
70
density/low-temperature plasmas, in which the plasma Debye length is smaller than the
radii of the probes.
The traditional double and triple Langmuir probes [Sung el al. (2002),
Eckman et al. (2001), Naz et al. (2011)], are designed for the situations of no well-
defined ground (double probes) or transient plasmas (triple probes). These probes are not
able to characterize anisotropic or inhomogeneous plasma conditions and are unrelated to
our motivation.
5.1 Current In-Situ Langmuir Probe Issues
Specifically, traditional Langmuir probes have difficulties in the following scenarios: I)
low-density plasmas; II) high surface-emission environments; III) flowing plasmas; and IV)
dust-rich environments.
I. Low-density plasmas create large Debye sheaths around the SC that may engulf the
Langmuir probe mounted at the end of a boom. The potential barrier in the sheath can
change the characteristics of charged particles being collected by the probe, causing mischar-
acterization of the ambient plasma. As of now, there is no way to correlate probe measure-
ments in the sheath to the ambient plasma, or to get accurate measurements of the sheath
itself using a single Langmuir probe. This issue has been recently recognized for Langmuir
probes on the Cassini and Rosetta missions [Wang et al. (2015), Odelstad et al. (2015)].
II. High surface-emission environments are either due to energetic plasmas that cause
secondary electron emission, or due to intense UV radiation generating photoemission from
the SC or probe itself. In environments with directional solar UV illumination and/or in
the presence of energetic electrons, electrons will be emitted from the surfaces of the SC
and/or the probe that will contaminate the probe current collection. The SC and probe
emission issue will be more severe for in-situ measurements close to the Sun (e.g., missions
to Mercury or Venus, and the Parker Solar Probe orbiting the Sun), as well as when the SC
enters planetary magnetospheres in which energetic electrons (> 100 eV) often exist.
71
III. Flowing plasmas are by definition anisotropic and therefore cause fundamental
issues in interpreting the I-V curves. Ions in space are generally far from isotropic w.r.t the
SC and thus the probe. Examples of this case include the solar wind flow in interplanetary
space, a corotational plasma-flow within planetary magnetospheres or the SC moving with
a high-speed relative to thermal ions at rest, for example, in planetary ionospheres.
IV. Dust-rich plasma environments will cause dust particles to impact on the probe and
SC as the SC travels through them. At speeds > 1 km/s, these impacts can generate inter-
mittent localized plasma clouds that cause interference with the probe measurements. Dust
impacts causing spikes in the I-V curves have been detected by the Cassini Langmuir probe at
Enceladus’ plume and during the crossings of Saturn’s diffuse E Ring [Morooka et al. (2011)].
5.2 Concept of the DHP
In order to improve space plasma measurements in difficult scenarios described above,
we developed a Double Hemispherical Probe (DHP) [Wang et al., 2018]. The DHP keeps
the simplicity of the double planar probe flown in the 1970’s [Bering et al. (1973b)], but
with the geometry of a sphere to allow the probe to work in lower density and/or higher
temperature plasmas. More importantly, we advance the prior directional probe technology
from the measurements of flowing plasma to much broader applications. The main objective
of the DHP development is to remove or minimize the anisotropic or inhomogeneous local
plasma effects, due to the interactions of the ambient space environment with the SC and/or
the probe itself, on the probe measurements.
The concept of a DHP, is a Single Spherical Probe (SSP) that is split into two elec-
trically isolated hemispheres that are swept simultaneously with the same potential biases,
resulting in two separate I-V curves. The differences in the I-V curves between the two
hemispheres identify anisotropies and inhomogeneities of the local plasma around the probe,
which can be removed or minimized from the probe measurements. In situations of isotropic
and/or homogeneous plasmas, the currents from the two hemispheres are identical and the
72
total current from both hemispheres can be analyzed as a traditional SSP. The following dis-
cusses how, with calibration, a DHP will improve our ability to extract true characteristics
of the ambient plasma when a SC is in the environments discussed above.
To test the DHP in various lab plasmas a lab model of the DHP was constructed to
test the various cases discussed above. A lab model consists of two halves of a 4 mm steel
ball bearing isolated from each other with a Kapton spacer (Fig. 5.1a), was used to test
cases I and III. A conceptual design of a space-borne model is shown in Fig. 5.1b–d. A
second lab prototype similar to the conceptual model of Fig. 5.1b was used to test case II.
Figure 5.1: DHP Flight Concept
a) The laboratory model of the DHP. b) The conceptual model of a space-borne DHP witha boom. c) An exploded view of the DHP probe sensor. d) The cross-section of the DHPprobe sensor.
I. When the probe is in the Debye sheath of the SC, the two hemispheres will collect
73
different currents. Figure 5.2a shows test results with the DHP lab model at different lo-
cations in a sheath above a plate electrically floated to a negative potential relative to the
ambient plasma. This simulates a general case of a sheath around a negatively charged SC.
In this test, both the DHP and SSP were used. Firstly, it shows that the addition of the
currents from the DHP hemispheres is always consistent with the SSP current, as expected.
The measurements from the SSP did not identify if the probe was situated in the sheath.
On the other hand, the measurements of the DHP showed a difference in the current be-
tween the two hemispheres. The hemisphere facing the plasma collects more current than
the one facing the SC because the electrons and ions come from the plasma toward the SC
surface. As the probe moves deeper in the sheath, this current difference increases. This
monotonic increase in the current difference will be used to inform how ‘deep’ the probe
is in the sheath and determine the true ambient plasma parameters. Detailed studies are
reported in Chapter 6.
II. If the probe is subject to photoemission or secondary electron emission, the hemi-
sphere facing the Sun or energetic electrons will emit photoelectrons or secondary electrons
while the hemisphere in the shadow will, at most, collect photoelectrons or secondary elec-
trons emitted from the SC surface. Figure 5.2b demonstrates I-V curves measured with
probes situated in a 100 eV electron beam. It shows that the beam-facing hemisphere and
the SSP show an opposite slope in the negative bias region to the hemisphere in the shadow,
indicating the secondary electron emission from the probes [Garnier et al. (2013)]. For probe
photoemission, the lit hemisphere current will show a constant offset compared to the current
of the dark side hemisphere in the retarding region (probe bias less than plasma potential)
of the I-V curve. The difference in the two I-V curves then yields the photoemission currents
that can be characterized and then removed for data interpretation. Contamination due to
secondary electron emission is difficult to characterize since the direction of the incoming en-
ergetic electrons is not easy to know. In this situation, a data survey with the probe pointing
in different directions can be conducted to better determine the direction of electron flux.
74
Detailed studies are reported in Chapter 7.
III. In the case of plasmas flowing relative to the SC and thus the probe, the hemisphere
in the ram direction will detect more ions than the hemisphere in the ion wake. The ion
current ratio can be used to derive the ion flow speed [Chung et al. (2004)]. Electrons
entering the ion wake region are determined by the ambipolar electric field created due to
charge separation at the wake boundary. This ambipolar field depends on the ratio of the
probe radius to the Debye length. Detailed studies are reported in Chapter 8.
IV. Though not addressed in this work, when the SC travels in a dust-rich environment,
the effects of the dust impacts can be analyzed when the probe is pointed in the travel
direction of the SC. The impact-generated plasma from the SC surface is expected to have
a minimal effect on the probe measurement because its density is largely dispersed at the
probe location. The un-impacted hemisphere can be then used for characterizing the ambient
plasma while the difference between the I-V curves of two hemispheres gives the knowledge
of impacting dust characteristics.
75
Figure 5.2: DHP Preliminary Tests
a) I-V curves of the DHP and SSP at different locations in the sheath and the bulk plasma.
b) Semi-logarithmic of I-V curves of the DHP and SSP in an electron beam. Positive
slopes on the ion current side indicate secondary electron (SE) emission from the probes.
[Wang et al. (2018)]
Chapters 6–8 experimentally characterize the effect of the phenomena discussed above
(with the exception of dusty plasmas) on Langmuir probe measurements, as well as showing
the DHP’s ability to mitigate them.
Chapter 6
Probe in Sheath
The information presented in this chapter has been published in the following paper:
[Samaniego and Wang. (2019)].
Due to SC charging and the Debye shielding effect discussed in Chapter 2, a sheath will
be formed around the SC. The conditions of the local plasmas around the probe are therefore
different from the true ambient plasma to be measured. I-V curves of the probe taken in
the SC sheath can be distorted, causing errors in derived plasma parameters depending on
how ‘deep’ the probe is in the sheath [Olson et al. (2010), Wang et al. (2018)]. Figure 6.1
shows an ideal I-V curve for a spherical probe in linear and semi-log scale, as well as the
first derivative of the I-V curve for comparison throughout this chapter.
77
Figure 6.1: Ideal I-V curves
Schematic of an ideal I-V curve labeling the ion saturation region, electron retarding region,and electron saturation region of a spherical Langmuir probe. a) Linear scale. b) Firstderivative. The plasma potential is indicated at the ’knee.’ c) Semi-log scale after the ioncurrent has been subtracted.
In space, both plasma density and temperature vary across wide ranges. Consequently,
the plasma Debye length varies between centimeters (e.g., in planetary ionospheres) and
meters (e.g., in solar wind plasma or planetary magnetospheres). Due to a finite length
of a probe’s boom, probes may have a risk of being situated in the SC sheath in plasma
78
environments in which the Debye length is significant compared to the boom length. This
issue has been recognized for Langmuir probe measurements on both Cassini and Rosetta
missions [Wang et al. (2015), Olson et al. (2010), Odelstad et al. (2015)].
Traditional Langmuir probes with a single sensor have difficulties to identify whether
the probe is engulfed by the SC sheath and to correct errors resulted from measurements
taken in the sheath. The DHP is intended to address this problem.
The chapter is outlined as follows. Section 6.1 explains the experimental set up and
procedure. Section 6.2 discusses how I-V curves change when a probe is in the SC sheath
compared to in the ambient plasma. Section 6.3 shows the methods for retrieving the true
ambient plasma parameters using the DHP. Section 6.4 concludes our findings.
6.1 Experimental Setup
To test the efficacy of the DHP presented in chapter 5, a laboratory DHP model 2 mm
in radius is used for testing probe measurements in the sheath and bulk plasma. The DHP
is made of two halves of ball bearings: one hemisphere (HS1) facing the bulk plasma and the
other (HS2)facing the plate (SC), as shown in Fig. 6.2a. Figure 6.2b shows the schematic of
an experimental setup for testing probe measurements in the SC sheath, neglecting the effect
of the boom. A conducting plate 56 cm in diameter representing the SC surface is electrically
floated in a thermal plasma in a vacuum chamber 1 m tall and 60 cm in diameter. The plasma
is created using a negatively biased, hot filament that emits energetic primary electrons to
impact and ionize neutral Argon atoms. A stopper above the filament prevents primary
electrons from entering the bulk plasma above the plate. A sheath is formed above the plate
that charges to a floating potential. No photoemission or secondary electron emission is
created from the plate, simulating the scenario in which currents to and from the SC surface
are dominated by charged particles from the ambient plasma.
79
Figure 6.2: DHP in SC Sheath Set-up
a) Schematic of the lab DHP model. Two hemispheres HS1 and HS2 are electrically insulatedfrom each other and biased through two separate wires. b) Schematic of the experimentalsetup for testing the DHP in the sheath of the SC. An electrically floated conducting platesimulates the SC surface. Plasma is created by a hot filament below the plate. A stopperprevents primary electrons from entering the bulk plasma above the plate. The DHP movesvertically in the sheath above the plate. HS1 faces the bulk (ambient) plasma and HS2 facesthe plate (SC).
The sheath potential profile is characterized using an emissive probe that emits
thermionic electrons from a heated, thin filament 3mm long and 0.025mm thick
[Hershkowitz (1989)]. Using a current-bias method, the local plasma potential is determined
by the probe bias voltage for a properly chosen emitting current[Pedersen et al. (1978a),
Diebold et al. (1988)]. Plasmas with various densities (1.6× 105 − 1.5× 107cm−3) and tem-
80
peratures (0.4 – 0.8 eV) are created. The Debye lengths (0.2 – 1.1 cm) are comparable to
or larger than the radius of the probe. The corresponding sheath thickness ranges from 3
to 8 cm, about 10 Debye lengths. The electron-electron and electron-ion mean-free-paths
are meters to tens of centimeters, respectively, much larger than the sheath thickness. The
sheaths above the plate are therefore collisionless, simulating typical space situations. The
larger than expected sheath thickness is caused by leaked energetic primary electrons from
the source that make it to the plate that charges the plate more negatively than expected
with the electron temperature smaller than 1 eV [Godyak et al. (1995)]. However, we expect
this to have minimal effects on our experimental results because all the parameters of inter-
est are normalized by the characteristics of the cold plasma electrons dominating the total
electron population.
6.2 Characterization of I-V curves taken in the SC sheath
For the rest of this chapter it is convenient to define our symbols in one place for
reference:
φlocal: Local potential at the DHP’s location.
φSC : SC potential.
VSC Meas: SC potential derived directly from the probe’s I-V curve.
Vk: The plasma potential measured by the knee in the first
derivative of the I-V curve
Vb: Probe bias voltage
Te Meas, ne Meas: Electron temperature and density derived directly from the
probe’s I-V curve.
Te True, ne True: True electron temperature and density in the bulk plasma.
VSC rt, Te rt and ne rt: SC potential, electron temperature and density retrieved using
the DHP technique.
λD: Debye length.
81
*All the potentials are with respect to the bulk (ambient) plasma potential. φ rep-
resents true potentials measured independently by an emissive probe while V represents
potential measured by the I-V curves of the DHP.
Below discusses how the I-V curve changes when a probe is moved from the bulk
(ambient) plasma to the sheath.
Figure 6.3a shows an example of the sheath potential profile above the plate floated at
-22V. Figures 6.3b,c show an example of I-V curves taken by the DHP in the bulk plasma
and sheath, respectively. Because this work focuses on the electron characterization, the
ion current was subtracted from the I-V curves with a linear fit in the ion saturation region
for analysis [Hershkowitz (1989)]. I1 and I2 are the currents collected by HS1 and HS2,
respectively. Note that here we only consider characterizing electrons with current is much
larger than the ion current. Prior to probe measurements in the sheath, the DHP was
verified with a traditional Single Spherical Probe (SSP) with the same radius. Figure 6.3b
shows that the sum of the I-V curves from two hemispheres of the DHP is identical to
the one taken by the SSP in the bulk plasma, in agreement with the results shown by
[Wang et al. (2018)]. Here we therefore use the term ‘whole’ I-V curve to indicate the sum
of the two I-V curves of the DHP. As also shown by [Wang et al. (2018)], two other features
about DHP measurements are shown in Figs. 6.3b,c as follows: 1) When the DHP is in the
bulk plasma, the I-V curves from two hemispheres are identical; and 2) When the DHP is
in the sheath, the two I-V curves diverge and the whole I-V curve deviates from the one
measured in the bulk plasma.
The changes in the I-V curves are actually caused by the changes in the potential
structure around the probe when the probe is in the bulk plasma compared to in the sheath.
Figure 6.4 shows the spatial potential profiles around the DHP biased at various voltages in
the bulk plasma and sheath, measured via an emissive probe. The DHP remains at a certain
location. When the emissive probe is moved vertically from the plate (i.e., SC) surface to
the bulk plasma, it passes the DHP closely (∼1 mm offset) to measure the potential profile
82
in proximity of the DHP with a fixed bias voltage. Potential structures around the probe in
the bulk plasma and sheath are described below.
1) Probe in the bulk plasma. As shown in Fig. 6.4a, potential structures around a DHP
biased at different voltages Vb are monotonic and isotropic. When Vb ≥ 0, the probe collects
the electrons with all energies (i.e., the electron saturation region in the I-V curve); when
Vb < 0, the probe collects the electrons with retarded energies (i.e., the electron retarding
region in the I-V curve). A ’knee’ point between the two regions Vk equals to 0 V (Fig. 6.3e).
2) Probe in the sheath. As shown in Fig. 6.4b, potential structures around the probe
become complicated by an asymmetric potential profile between the plasma-facing side and
plate-facing (i.e. HS1 and HS2 of the DHP respectively). Additionally, a nonmonotonic
potential profile with a potential dip is formed between HS1 and the bulk plasma when
the Vb is more positive than φlocal and the dip disappear as Vb becomes more positive. On
the plasma-facing side (HS1), as described in [Olson et al. (2010)], the I-V curve is divided
into three regions: i) Vb ≤ φlocal, HS1 collects the electrons overcoming the sheath potential
barrier between the probe and bulk plasma. ii) φlocal < Vb < Vk, The potential profile
becomes nonmonotonic with a potential minimum Vm between the probe and bulk plasma.
As Vb increases, Vm increases and HS1 collects more electrons until Vm disappears, Vb also
reaches Vk. This region is called the transition region. iii) Vb ≥ Vk, HS1 collects the electrons
with all energies, entering the saturation region. On the SC-facing side (HS2), HS2 collects
the reflected electrons from the surface. When Vb ≥ φlocal, the monotonic sheath around
HS2 expands towards the lower potential (i.e., the deeper sheath) where the electron density
is lower, causing I1 > I2 (Fig. 6.3c). The whole I-V curve of the DHP is therefore distorted
to be different from the one measured in the bulk (Fig. 6.3b,c).
In space plasma measurements, the probe is biased with respect to the SC poten-
tial. Using the parameters defined in our laboratory tests, the SC potential is expressed as
VSC Meas = φsc−Vk. As seen by the knee in Fig. 6.3e, Vk increases as the probe in the deeper
sheath, causing VSC Meas is more negative than φSC . Te Meas derived from the I-V curves
83
taken in the sheath is hotter than Te True because of the ‘stretched’ transition region (Fig.
6.3d). The data shown in Fig. 6.3d,e is in agreement with the theoretical expectations.
It has been shown by [Wang et al. (2018)] that the current difference between the two
hemispheres increases with the probe in the ’deeper’ sheath. As described above, the current
difference is determined by the changes in the potential structure around the probe, which
relates to the potential gradient in the sheath. Although there are currently no theories to
analytically define the I-V curves of a probe in the sheath, we will show in the following
section that the relations between plasma parameters measured in the sheath and in the
bulk are correlated with the current ratio. Such relationships can be used to retrieve true
plasma parameters.
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Figure 6.3: Effects of the SC sheath on Langmuir Probe Measurements
a) Potential profile above the plate measured by an emissive probe. X is the distance fromthe plate. The arrows indicate the locations for Langmuir probe measurements. b) I-Vcurves taken by the DHP and Single Spherical Probe (SSP) in the bulk plasma. The sum ofthe I-V curves of the two DHP hemispheres yields the same I-V curve as the SSP of the samediameter. c) I-V curves of the DHP in the sheath above the plate (SC). The currents of thetwo hemispheres separate. d) Semi-Log plot of the I-V curves taken at different locations(indicated in a) by the arrows in both the bulk and sheath). The dashed lines show the slopein the electron retarding region, which equals 1/Te. e) First derivative of the I-V curves atdifferent locations. Three arrows show the shifting of the ‘knee’ used to characterize theplasma potential.
85
Figure 6.4: Potential Profile Around Probe in Sheath
Potential profiles around the DHP biased at different voltages as measured by an emissiveprobe. X-axis shows the distance from the plate (SC). Vertical lines indicate the DHPlocation. a) DHP in the bulk plasma. The potential profiles are monotonic and symmetricaround the probe when it is in the bulk plasma. b) DHP in the sheath. The potentialprofiles are asymmetric when the probe is in the sheath and a nonmonotonic potential dip isformed on the plasma facing side of the probe at a probe bias higher than the local potential.
6.3 Methods to retrieve true ambient plasma characteristics using DHP
Figure 6.5a shows the current ratio I1/I2 in the electron saturation region of the DHP at
various locations in the sheath. It is shown that the current ratio is constant and increases
monotonically from 1 when the probe is in the bulk to larger than 1 as the probe is in
the deeper sheath. Followed by the speculation made in section 6.2, the current ratio as
a function of the potential gradient in the sheath (defined as φlocal/λD) is plotted in Fig.
6.5b. The potential gradient indicates the sheath depth (the larger potential gradient the
deeper sheath). It indeed shows an intrinsic relationship in which the current ratio increases
linearly with the potential gradient. In the following sections, we will show that ratios of the
measured parameters to the true parameters show intrinsic relationships with the potential
gradient as well. This allows us to directly establish relationships between the measured, the
true plasma parameters and the current ratio, which can be used to retrieve the true plasma
86
parameters from probe measurements in the SC sheath.
The measured plasma parameters of the DHP (VSC Meas, Te Meas, ne Meas) were derived
via interpretation of I-V curves as described in chapter 3, regardless if the DHP was in
the bulk plasma or sheath of the SC. Errors in defining the plasma potential (Vk) due to
rounding of the knee propagate to error measurements of VSC Meas. Errors in the electron
temperature come from the uncertainly in the fit of the slope of the electron retarding
region. Errors in the electron density and other derived quantities (e.g. the Debye length)
are calculated by propagating the uncertainty in the measurements of the saturation current,
the plasma potential, and the electron temperature. It was found that the uncertainty in
our measurements increased as the probe was moved deeper into the SC sheath.
Figure 6.5: Ratios of Saturation Current in Sheath
a) Sample graph of the ratio of the electron currents of the two hemispheres of the DHP atdifferent locations in the sheath and bulk plasma, showing that the ratio is approximatelyconstant in the saturation region. b) Ratio of the electron saturation current of HS1 (I1) toHS2 (I2) as a function of the potential gradient (defined as the sheath potential divided bythe Debye length) across a wide range of plasma conditions. Error bars show the measure-ment uncertainty of the saturation current ratio as well as the error propagated from themeasurement of the local potential measured by the emissive probe and the calculation ofthe Debye length.
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6.3.1 Retrieving Spacecraft Potential
Figure 6.6a shows the ratio of the measured to true SC potential (VSC Meas/φsc) as a
function of the potential gradient. It shows that VSC Meas/φsc increases linearly with the
increase in the potential gradient (i.e., the deeper in the sheath), as described in Section
6.2. Combining the two linear fits in Figs. 6.5b and 6.6a, a linear relationship between
VSC Meas/φsc and I1/I2 is shown in Fig. 5b.
The retrieved SC potential VSC rt can be calculated by using the fitted line from Fig.
5b as,
VSC rt =VSC Meas
9.98(I1/I2)− 8.61(6.1)
where VSC Meas and I1/I2 are derived from probe’s I-V curves taken in the SC sheath.
Figure 6.6: VSC vs Sheath Depth
a) Ratio of the measured to true SC potential as a function of the potential gradient, showinga linear relationship. b) Linear relationship between the ratio of the measured to true SCpotential and the current ratio, obtained by combining linear relationships shown in Fig.6.5b and Fig. 6.6a. Error bars indicate the error in the retrieved the SC potential using thislinear fit.
88
6.3.2 Retrieving Electron Temperature
Similar to that is shown for the SC potential, the ratio of the measured to true electron
temperature (Te Meas/Te True) shows a linear increase with the increase in the potential gra-
dient (Fig. 6.7a). Combining the two linear fits in Figs. 6.5b and6.7a, a linear relationship
between Te Meas/Te True and I1/I2 is shown in Fig. 6b.
The retrieved electron temperature Te rt can be calculated by using the fitted line form
Fig. 6b as,
Te rt =Te Meas
16.1(I1/I2)− 15.1(6.2)
where Te Meas and I1/I2 are derived from probe’s I-V curves taken in the SC sheath.
Figure 6.7: Te vs Sheath Depth
a) Ratio of the measured to true electron temperature as a function of the potential gradient,showing a linear relationship. b) Linear relationship between the ratio of the measured totrue electron temperature and the current ratio, obtained by combining linear relationshipsshown in Fig. 6.5b and Fig. 6.7a.
89
6.3.3 Retrieving Electron Density
Unlike what is shown for the SC potential and electron temperature, there was no
trend found in the ratio of the measured to true electron density (ne Meas/ne True) against
the potential gradient. This is likely due to the electron density being a function of both the
electron temperature and the electron saturation current at the plasma potential measured
from the I-V curves, which both vary with the potential gradient in the sheath.
A different approach is carried out to retrieve the electron density as follows:
(1) Assume that the SC is charged negatively with a monotonic sheath formed around
it. According to the Boltzmann relation,
ne bulk = ne local ∗ exp(−φlocal/Te True) (6.3)
where ne bulk and ne local are the electron density in the bulk plasma and the sheath,
respectively.
(2) Find φlocal and derive ne local from I-V curves taken in the sheath. Based on the
probe-in-sheath theory by [Olson et al. (2010)], as described in section 6.2, the probe
current collection for Vb ≤ φlocal is not affected due to the probe sitting in the
sheath. The I-V curve in this region can be used to derive ne local. As described in
Section 6.3, once φlocal is determined, ne local can be calculated from Isat at φlocal.
φlocal is measured by the emissive probe in this experiment to find the relationship
between φlocal/VSC Meas and the current ratio, as shown in Fig. 6.8a. It shows that
φlocal/VSc Meas is a constant value of ∼0.11 that is independent of the current ratio.
Therefore, φlocal can be readily determined based on VSC Meas retrieved using the
method described in section 3.1.
(3) Calculate ne bulk using the Boltzmann relation in Eq. 6.3. This ne bulk is the retrieved
true electron density in the ambient plasma (i.e., ne rt defined in section 6.2).
90
Figure 6.8b shows that the retrieved electron density normalized by the true electron
density (ne rt/ne True) is around 1 for the probe in various sheath depths. The normalized
electron densities derived directly from the I-V curves taken in the sheath are plotted over
in Fig. 6.8b. Interestingly, it shows relatively good agreement between the measured and
true density as well. This is actually caused by a coincident ‘canceling’ effect in finding the
probe saturation current. On the one hand, the probe current decreases as the probe is in
the deeper sheath; on the other hand, Isat at the measured plasma potential Vk increases as
a result of the increase in Vk when the probe is in the deeper sheath, as shown in Fig. 6.3e.
These two factors cancel in the probe current, resulting in Isat in the sheath similar to Isat in
the bulk plasma. Subsequently, similar electron densities are derived from I-V curves taken
in the sheath and bulk.
Figure 6.8: Local Potential and ne
a) Ratio of the local potential measured by the emissive probe to the SC potential measuredby the DHP as a function of the current ratio. It shows a constant value ∼ 0.11 that isindependent of the current ratio. b) Derived electron density normalized by the true bulkelectron density as a function of the distance of the probe from the SC surface normalizedby the Debye length. The electron density derived using the conventional SP technique andthe DHP technique are compared.
91
6.4 Results
Figure 6.9 shows the retrieved SC potential and electron temperature normalized by
their true parameters as a function of distance of the probe from the SC surface normalized
by the Debye length. Both the parameters directly derived from the I-V curves are plotted
over in Fig. 6.9. It is shown that the retrieved parameters using the DHP technique show
good agreement with the true parameters when the probe is in the sheath compared to the
results directly derived from measurements using the conventional SP technique. Figure 6.9
indicates a relatively long minimum boom length ( ∼ 20 λD) for a conventional probe to be
out of the SC sheath. This is because the sheath in our experiment is larger than expected
due to the more negatively charged plate (SC) surface by energetic primary electrons, as
described in section 6.2. It is shown that the DHP is able to recover the true ambient plasma
parameters with the probe 4 times closer to the SC surface than the SP. However, use of
the DHP should not encourage shorter SC booms. The DHP increases the measurement
dynamic range in which investigated plasma environments vary across a large Debye length
range (e.g., from planetary ionospheres to magnetospheres).
The DHP technique is limited by the ability to resolve the I-V curve characteristic
features as defined in section 6.2. Once the probe is in the deep sheath, where the I-V
curve is significantly distorted, the true plasma parameters can no longer be retrieved, as
indicated by the vertical lines of Figs. 6.8b and 6.9. Additionally, the methods described
above to retrieve the ambient plasma parameters are made for the case of a monotonic SC
sheath. In situations where nonmonotonic sheaths are formed, like those experienced by
[MacDonald et al. (2006)] or sheaths influenced by high photoemission from the SC such
as the Parker Solar Probe [Ergun et al. (2010), Guillemant et al. (2012)], Equations 6.1–6.3
are no longer valid and need to be re-evaluated by including self-emission from the DHP
probe.
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Figure 6.9: DHP vs Single Langmuir Probe
Derived SC potential normalized by the true SC potential (a) and derived electron temper-ature normalized by the true electron temperature (b) as a function of the distance of theprobe from the SC surface normalized by the Debye length. Both parameters derived usingthe conventional SP technique and the DHP technique are compared.
6.5 Conclusions
Langmuir probes can experience an issue of being immersed in the SC sheath when the
ambient plasma density is relatively low (i.e., the Debye length is significant compared to
the finite boom length of a probe), such as in planetary magnetospheres and the solar wind,
causing misinterpretations of probe measurements. Here we have shown that the DHP can
identify whether a probe is immersed in the SC sheath and to retrieve true ambient plasma
characteristics including the electron density and temperature as well as the SC potential.
A laboratory DHP model was tested in sheaths created above a plate electrically floated
in plasmas with various densities and temperatures. In all the tests, the Debye lengths
were larger than the probe radius and no photoemission or secondary electron emission was
created. It was shown that:
(1) The currents collected by the two hemispheres of the DHP are identical when the
93
probe is in the bulk plasma and diverge when the probe is in the sheath. The
current ratio between the two hemispheres increases linearly with the increase in
the potential gradient in the sheath (the deeper in the sheath, the larger potential
gradient).
(2) Linear relationships have been established between the current ratio and the ratio
of the measured to true parameters for both the SC potential and electron tempera-
ture. These relationships can be used to retrieve the true parameters in the ambient
plasma.
(3) Retrieval of the electron density is approached differently. The local potential at the
probe location in the SC sheath was found to ∼ 0.11 of the measured SC potential.
The density in the bulk plasma is calculated based on the Boltzmann relation using
the local density measured at the probe local potential.
The retrieved parameters using the DHP show much better agreement with true am-
bient plasma parameters than the conventional single probe when the probes are immersed
in the SC sheath, it thus significantly improves the plasma measurement accuracy across a
wide range of plasma environments.
Chapter 7
Probe Under Photoemission
In space, solar UV light can release electrons from solid surfaces per the photoelectric
effect,
Kmax = hf − E0 (7.1)
where Kmax is the maximum kinetic energy of the emitted electrons, h is Plank’s
constant, f is the frequency of the photons, and E0 is the work function of the surface
material. The photoelectron current density as a function of the photoelectron energy can
be written as [Grard(1973)],
J(E ′) = Is
∫ ∞E′
p(E)dE. (7.2)
where p(E) is the photoelectron energy distribution,
p(E) =1
Is
∫ ∞0
Φf (E)S(f)Y (f)df (7.3)
and where Is =∫∞0S(f)Y (f)df is the total flux of photoelectrons emitted by the sur-
face of a material. S(f) is the solar flux energy spectrum, Y (f) is the yield of photoelectrons
as a function of photon with frequency f , and Φf (E) is the energy spectrum [Grard(1973)].
Both Φf (E) and p(E) are defined such that,
∫ ∞0
p(E)dE = 1 and
∫ ∞0
Φ(E)dE = 1. (7.4)
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Equation 7.3 gives the photoemission saturation current when E ′ = 0. Figure 7.1
shows the ideal photoemission (ip, dashed line) from a probe as a function of the probe
bias. At the negative bias, all the photoelectrons are emitted from the probe, reaching a
saturation current. As the potential on the probe becomes more positive, the lower energy
photoelectrons are returned to the probe, causing the reduction in photoemission. This is the
photoelectron retarding region in which the photoemission current decreases exponentially
with the probe bias, assuming photoelectrons having approximately a Maxwellian energy
distribution [Grard(1973)].
As shown in Fig. 7.1, when the photoemission current is superimposed on the probe
collection current, the I-V curve is changed, especially in the electron saturation region of
the ambient plasma and the region around the ‘knee’ that becomes more rounded. In this
case, resolving the ambient plasma parameters is difficult without the additional information
of the photoelectrons being well-characterized. This photoemission current causes a contam-
ination to probe measurements of the ambient plasma. Such a contamination is particularly
severe when the SC moves in trajectories close to the Sun, such as the Parker Solar Probe
[Bale et al. (2016)].
7.1 Photoemission on Langmuir probe measurements
Figure 7.1 not only shows the ideal photoemission current discussed above but also
the ideal Langmuir probe collection currents of a planar probe. The addition of the two
currents shows the effect of photoemission contamination on the I-V curve. Specifically, Fig.
7.1 shows the case where the current due to photoemission is high w.r.t the current due to
the ambient plasma. In this case, attempting to resolve the ambient plasma parameters is
difficult without the additional information of the photoelectrons. However, even when the
photoemission current is small compared to the current of the ambient plasma, photoemission
can still cause a certain degree of stretching of the retarding region, and a shifting and
rounding of the knee that will cause errors in deriving the characteristics of the ambient
96
plasma.
Figure 7.1: Photoemission I-V Curve
Photoemission on Langmuir probes I-V curve of showing the ideal collection and emissionof current on a planar Langmuir probe in a low density thermal plasma. ip is the emissioncurrent due to photoemission (shown as a positive current here). ia shows the collectioncurrent. The solid line of ia − ip shows the superstition of the two, correcting for emissionbeing a negative current. [Grard(1973)].
7.2 DHP to Minimize the Probe Photoemission Effect
The purpose of the DHP is to allow one hemisphere to be pointed toward the photoe-
mission source (i.e., the Sun in space), while the shaded hemisphere performs measurements
of the ambient plasma. Additionally, the difference in the I-V curves between the two hemi-
spheres results in the characteristic curve of the photoelectrons emitted from the probe
97
surface.
To test the DHP under photoemission, a prototype 5 cm in diameter was placed in a
large cylindrical vacuum chamber (1 m tall and 0.6 m in diameter) with 6 UV lamps placed
symmetrically around the circumference of the top lid, as shown in Fig. 7.2. The UV lamps
were the same ones (172 nm wavelength, 7.2 eV photon energy) used in the Langmuir probe
oxidation experiments (Section 4.2.1). The chamber was pumped to a base pressure at 10−7
Torr; however, after the UV lamps were turned on, the pressure quickly equilibrated at
around 10−5 Torr due to off-gassing of the chamber walls caused by the radiation. The DHP
was placed at different vertical positions to measure the ability of one hemisphere to shield
the other. To minimize photoemission from the walls that affect the measurements, the walls
had stainless steel liners covered in colloidal graphite [Handley & Robertson(2009)].
98
Figure 7.2: DHP Under Photoemission Set-up
Schematic of the vacuum chamber to test the DHP under photoemission. 6 UV lamps areplaced symmetrically at the top of the chamber and the DHP is attached to a boom to thetop of the chamber, which is movable in the vertical direction. The usable space in thechamber is 60 cm tall with a diameter of 60cm. The dotted line shows the datum platecentered on the UV lamps where DHP position is measured. UV light is represented bypurple wave arrows and photoemission from the wall is shown in blue arrows.
7.3 Results
Figure 7.3 shows the overall I-V curves and photoemission saturation regions of either
hemisphere of the DHP as the DHP is moved further away from the UV sources. HS1
represents the lit hemisphere and HS2 represents the shaded hemisphere. Figure 7.3 shows
that HS1 emits more electrons than HS2. In an ideal case where HS2 is completely in the
shade of HS1, it should have zero emission current. The emission current from HS2 shown
in the experiment is because HS2 is partially illuminated by UV light from the UV sources
that are not directly above the DHP, and by UV light bounced off between the chamber
walls (Fig. 7.2a).
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The photoemission current of HS1 shows a constant value in the saturation region as
expected in theory. Interestingly, the photoemission current of HS2 shows an increase as
the probe bias becomes more negative. This slope in the photoemission current is likely
due to the space charging effect in which electrons emitted from HS2 are trapped or bound
close to the probe, causing a potential dip that prevents further emission of the electrons
[Grard(1973), Dove et al. (2012), Hershkowitz (1989)]. This causes the probe bias to be
more negative to emit more photoelectrons, similar to the space charging effect induced by
thermionic electrons from an emissive probe [Hershkowitz (1989)]. On the other hand, HS1
is closer to the top lid of the chamber in the cases of 10 cm and 20 cm away from the
top lid, such that the electric field between the probe and grounded top lid is large enough
to accelerate emitted photoelectrons to the lid, eliminating the space charging effect. As
the DHP is moved further down to 40 cm, both hemispheres show a sloped emission region
because of weakened electric fields around both hemispheres that result in the space charging
effect.
Figure 7.3: DHP Photoemission Data
I-V curves with the photoemission current of the lit (HS1) and shaded (HS2) hemispheres.The secondary graphs on each figure zoom in on the photoemission region of the I-V curvehighlighted in the red dotted box. The positive region of each I-V curves show where thehemispheres are collecting photoemitted electrons from the walls. a) is with the probe 10cm from the UV lamps. b) is with the probe 20 cm, and c) is with the probe 40 cm fromthe UV lamps.
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In the collection region (positive bias) of the Fig. 7.3, it shows the photoelectrons
emitted from the walls being collected by both hemispheres of the DHP [Wang et al. (2008)].
At 10 cm, the electron collection of HS1 is larger than HS2 due to its proximity to the UV
sources, while at 40 cm the electron collection of HS2 is greater. At 20 cm both hemispheres
receive equal fluxes from the chamber walls.
7.4 Conclusion and Discussion
In the lab, it has been demonstrated that the DHP is able to minimize the photoe-
mission effect on probe measurements by pointing one hemisphere to the UV source and
leaving the other hemisphere in the shade. The shaded hemisphere shows a less photoemis-
sion current than the directly illuminated hemisphere. Because of the limited configuration
of the UV lamps and vacuum chamber, it is believed that in space where a plane wave of UV
radiation fully illuminates one hemisphere while shading the other hemisphere, the shaded
hemisphere is expected to have much reduced photoemission current than shown in the lab
results.
Additionally, the lab results show that photoelectrons emitted from the surrounding
chamber walls contribute and contaminate current measurements of the probe. In space,
photoelectrons emitted from the surfaces of the SC and probe boom need to be minimized
from reaching the probe. Currently, the design of a guard separating the probe from the boom
and SC body is used on many missions, such as Cassini and Rosetta [Gurnett et al. (2004),
Eriksson et al. (2007)]. Our results reiterate that the guard needs to be properly designed
and used in order to maximize its efficacy.
Lastly, this experiment suggests that the DHP might be able to isolate other forms
of asymmetric bombardment such as secondary emission [Garnier et al. (2013)] and dust
impacts [Morooka et al. (2011)].
Chapter 8
Probe in Flowing Plasmas
The information presented in this chapter has been submitted to Journal of Geophysical
Research – Space Physics [Samaniego et al. (2020)].
In space, there is typically a relative velocity between the probe and ambient plasma,
either the probe is immersed in a flowing plasma (e.g., the solar wind) or the probe moves at
the SC speed relative to the ambient plasma at rest (e.g., planetary ionospheres). A plasma
wake will be created behind the probe itself. Theories for Langmuir probes in an isotropic,
nonflowing plasma no longer completely characterize the plasma. There are two parameters
affecting the probe wake formation and consequent probe current collection: 1) the ratio of
the ion flow speed vfi to the ion thermal speed vthi (i.e., Mach number M = vfi/vthi) and
2) the ratio of the probe radius to the electron Debye length (i.e., RD = r/λD). In general,
supersonic ions (M > 1) ram onto the probe, leaving an ion void behind it. The collection of
the downstream ions depends on the probe potential and M . Ambient electrons are generally
in the thermal state (i.e., its thermal speed is larger than the plasma flow speed). Depending
on RD, the electron density may decrease in the wake due to ambipolar electric fields formed
at the wake boundaries. The formation of ambipolar electric fields is described in section
8.2 in detail.
Traditional single Langmuir probes, which consist of a single conductor, have difficulties
identifying the self-wake effects on probe measurements, especially when it comes to the
characterization of electrons. Directional probes are able to improve such measurements. In
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this chapter, we discuss using the DHP to identify and minimize the probe self-wake effects
on flowing plasma characterization across a wide range of RD, to show the DHP’s advantage
over single Langmuir probes [Wang et al. (2018), Samaniego and Wang. (2019)]. This work
focuses on probe measurements in weak magnetic field environments in which the electron
gyroradii are much larger than the probe radius.
The outline of this chapter is as follows. Section 8.1 describes the theories about the
wake formation behind a probe and its effects on the current collection of both ions and
electrons. Section 8.2 describes the experimental setup. Section 8.3 shows the data with
discussion. Section 8.4 concludes the findings.
8.1 Theories of Probe Current Collection in Flowing Plasmas
This section summarizes theoretical work done on directional probes as it pertains the
DHP in flowing plasmas and briefly outlines the expected behavior of the DHP in flow.
The understanding of the DHP follows from heritage of other split or directional
Langmuir probes [Bering et al. (1973b)]. In a uniform plasma, each side of the Langmuir
probe acts as two independent Langmuir probes occupying the same space, and will re-
solve the same plasma parameters. However, in the case of flowing plasmas, a plasma
wake will be formed behind the probe, creating a region of non-uniform plasma around
the probe [Gurevich et al. (1969), Oya et al. (1970)]. This work shows the difference in
the current collection by the ram and wake facing sides of the DHP [Hudis et al. (1970),
Grabowski et al. (1974)] .
In our configuration we define HS1 as the upstream side hemisphere facing the plasma
flow (ram hemisphere) and HS2 as the downstream side hemisphere behind the flow (wake
hemisphere). The corresponding currents are I1 and I2 with the subscript i and e for ions
and electrons, respectively. We define Vb: the probe bias voltage; Vp: the plasma potential;
and Eb: the ion beam energy in eV. Here we consider a general case for space plasmas in
which the electron temperature Te is not significantly larger than the ion temperature Ti.
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1) Ion characteristics
As the speed of the SC increases relative to the thermal motion of the ions, fewer ions
are able to make it to the wake hemisphere of the probe, causing a difference in ion collection
current between the wake and ram hemispheres. Such a current difference can be used to
characterize the flow of the plasma [Oksuz et al. (2004), Chung et al. (2004)]. Figure 8.1
shows a diagram of ion collection by a negatively biased probe at low and high M . It was
shown by [Hutchinson (2003)], that when the M increases above 5, the wake hemisphere is
no longer able to collect ions. Here we divide the characteristics of each hemisphere of the
DHP into two M regions:
� 1 < M ≤ 5. When Vb > Eb/e, all the ions are stopped from reaching the probe, so
Ii = 0. When Eb/e > Vb > Vp, Ii2 = 0, so Ii equals to the ion ram current to HS1,
Ii1 (Ii = Ii1). When Vb ≤ Vp, the ions tend to be turned around and collected by
HS2. In this region, it is not trivial to analytically solve for Ii2. [Hutchinson (2003)]
performed simulations that relate M to the current ratio Ii1/Ii2. For single Langmuir
probes, it is difficult to separate Ii from the I-V curve to derive the ion characteristics.
For the DHP, only the currents collected by HS1 will be used for analysis. In this
case, Ii = Ii1 ≈ constant in the entire ion saturation region (i.e., Vb < Eb/e) and
can be used to derive the ion characteristics.
� M > 5. Ii2 is nearly zero across the entire Vb range [Hutchinson (2003)]. Again,
Ii = Ii1 ≈ constant in the ion saturation region, and it is straightforward to derive
the properties of the ions for both single Langmuir probes and the DHP. In space,
many probe measurements are in this high-M environment, such as in the solar wind
flow or with fast-moving SC in planetary ionospheres [Chen et al. (2016), ?].
2) Electron characteristics
Because of the high electron thermal speed relative to the flow speed, the electrons
move into the wake ahead of the ions, creating charge separation at the wake boundary.
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The ambipolar potential barrier is formed at the wake boundary, which returns lower energy
electrons back to the ambient plasma and tend to bend the ions towards the center of the
wake [Gurevich et al. (1969), Samir & Jew (1972), Ludwig et al. (2012)]. This ambipolar
potential barrier is characterized by the electron Debye length (from now on just called Debye
length) [Samir & Jew (1972), Li et al. (2005)]. Figure 8.2 illustrates a simplified description
of the ion wake behind a spherical probe. Specifically, it highlights the ambipolar field as
the Debye length changes relative to the probe radius, describing the local plasma in the
immediate vicinity of the probe. At a certain distance d from the probe, the ions from the
wake boundary merge [Ludwig et al. (2012), Birch et al. (2001)]. The merging of the ion
wake and other more complex details of the higher order characteristics of the ion wake are
not shown in Fig. 8.2 because this work focuses on plasma in the immediate vicinity of the
probe as it pertains to probe measurements.
Here we define φ as the potential barrier within the wake caused by the ambipolar field
and measured relative to the neutral plasma. When RD � 1, φ extends several Debye lengths
to reach the maximum depth to return high-energy tail electrons back to the ambient plasma,
leaving the wake close to approximately free of both electrons and ions [Birch et al. (2001)],
Fig. 8.2b. When RD � 1, the wake created is very small and the corresponding φ is therefore
too weak to restrict electrons to reach the downstream hemisphere [Lampe et al. (2005)],
Fig. 8.2b. While there are little quantitative studies of the transition region (i.e., RD ∼ 1),
continuity suggest that as RD approaches 1, φ at the wake boundary is still present but is not
able to fully extend into the wake, forming the ambipolar field with an intermediate depth.
This conceptual schematic of the transition region in RD is depicted in Fig. 8.2b. It shows
that the electrons with the energy smaller than the ambipolar field eφ are returned to the
ambient plasma while the electrons with the energy larger than eφ move across the wake,
which flux balances the flux of the electrons coming from the opposite side of the wake. An
equilibrium state is reached.
It is shown above that the wake has an effect on the electron collection by single
105
Langmuir probes when RD is near or larger than 1, causing the ambient electron electron
density to be underestimated. In an extreme case in which RD � 1, Ie2 ≈ 0 and the derived
electron density will be as low as approximately the half of the true density. With the DHP,
the true electron characteristics can be directly derived from I-V curves taken by HS1 that
collects undisturbed upstream electrons.
In the following sections, we use the DHP to characterize the probe self-wake effects
on the probe current collection, especially on the electron current. The methods using the
DHP to minimize such self-wake effects will be discussed. In this work, due to the limits of
our experimental setup, our tests were all at M > 10 that represents the high-M (M > 5)
case described above. The experiments with M < 5 will be performed in future studies with
a low-M machine.
Figure 8.1: Ion Collection
Schematics of the flow paths of ions collected by a Langmuir probe with a negative bias. a)Low M . Ions are turned around and collected on the downstream side of the probe; b) HighM . Ions pass by and are not collected on the downstream side of the probe.
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Figure 8.2: Ambipolar Feilds of a Plasma Wake
Simplified schematic of the ion wake (at high M) at the DHP and the potential structuresacross the wake (dashed lines) as λD varies. The schematic shows the wake region immedi-ately behind the downstream hemisphere of the DHP, which determines the probe currentcollection. The depth of the wake potential structure decreases as λD increases; b) Illus-trations showing the formation of the ambipolar potentials across the wake boundaries andthe fluxes of the electrons for the cases of small and large λD. Blue dashed lines show theambipolar potential from either side of the wake boundary and their interactions result inthe red dashed line. Thick arrowed lines indicate electrons moving across the wake and thickarrowed curves indicate electrons returned to the plasma flow.
8.2 Experimental Setup
To test the DHP and understand the current collection by probes in plasma flows, we
used a laboratory model 4 mm in diameter (Fig. 8.3a, [Wang et al. (2018)]) placed in the
Colorado Solar Wind Experiment device (CSWE, Fig. 8.3b, [Ulibarri et al. (2017)]). Flows
of nitrogen plasma are created using a Kaufman ion source with the ion energy 100-800 eV
and ion current 1-100 mA. Alongside the DHP, we placed an Ion Energy Analyzer (IEA)
to characterize and monitor the ion flows including their flow energy and current as well
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as their thermal temperature. The DHP and IEA are offset from the center of the beam
far enough to not interfere with each other while still centered within the uniform beam
width [Ulibarri et al. (2017)]. The electron density (ne) and temperature (Te) are 104 − 107
cm−3 and ∼ 1 eV. The Debye length (λD) is between 1 and 20 mm, which covers RD from
< 1 to > 1. The thermal temperature (Ti) of the beam ions is ∼ 1–5 eV, resulting in M
between 10 and 20. Similar to the general case for space plasmas, Te is not significantly larger
than Ti in our experiment. Additionally, thermal ions are found in the CSWE chamber due
to a finite neutral pressure (4 × 10−5 Torr) which causes a certain degree of ion-neutral
charge exchange collisions. The density ratio between the thermal ions and beam ions is
approximately 1 [Ulibarri et al. (2017)]. These thermal ions can affect the formation of φ,
which is discussed in the following section.
To minimize probe surface contamination caused measurement differences between the
two hemispheres of the DHP, the probe is cleaned by exposing it to a 400 eV and 40 mA ion
beam that sputters off a thin layer of contamination. A rotation stage is used to rotate the
probe 180 degrees to expose each of the hemispheres to the ion beam. Measurements of the
two hemispheres with each facing the plasma flow are compared to ensure consistency.
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Figure 8.3: CSWE
a) Schematic of the DHP. b) Schematic of the CSWE and setup of the DHP and IEA withinthe ion beam.
8.3 Results
8.3.1 Probe Self-Wake Effects on Measurements
1) Ion characteristics
Figure 8.4 shows the semilog plot of the I-V curves at a small (0.5) and large (1.5)
RD. In both cases, it shows the ion current collected by the upstream hemisphere Ii1 is
larger than the ion current collected by the downstream hemisphere Ii2 (i.e., Ii1 > Ii2). Ii1
is the ion ram current that remains approximately constant in the ion saturation region, as
shown in Figs. 8.4a,b. Because of our high Mach number (M > 10), the beam ions should
not be collected by the downstream hemisphere in an ideal plasma flow, as described in
section 8.2. The ions that are collected are actually the thermal ions that are created in the
CSWE chamber due to a finite pressure as described in section 8.3. It clearly shows that Ii2
increases as Vb becomes more negative due to the probe sheath expansion. The existence of
these thermal ions will reduce the ambipolar potential at the wake boundaries.
109
2) Electron characteristics
Regarding the electrons, Fig. 8.4 shows Ie2 = Ie1 when RD is small (0.5) and Ie2 < Ie1
when RD is large (1.5). These results are in agreement with the theoretical expectations.
As described in section 8.2, the electron density in the wake is determined by the ambipolar
potential that depends on RD. To quantify the RD effect on the wake electron density, the
measurements over a wide range of RD were taken and analyzed as follows.
The current ratio Ie1/Ie2 in the electron saturation region was found to be a constant
value, similar to that shown by [Samaniego and Wang. (2019)]. Ie1/Ie2 is plotted as a func-
tion of RD in Fig. 8.5a. Errors in the current ratio came from identifying the saturation
currents. In Fig. 8.5a, the current ratio increases as RD increases. When RD is less than
1, the wake effect on the probe electron collection is negligible, i.e., Ie1/Ie2 < 5%. In this
case, traditional single Langmuir probes can correctly derive the electron density. When RD
is increased to about 2, Ie2 drops about 16% compared to Ie1. A fitted curve expressed in
Eq. 8.1 shows that the current ratio is proportional to R2D with a factor γI ( γI=0.04 in
this experiment). In the space case, as described in the introduction section, ions as a whole
typically manifest as flowing ions relative to the probe, even in the case where ions are at
rest, they have a relative velocity against a fast-moving SC. Therefore, there is no additional
population of ‘thermal ions’ collected by the probe, which are present in our laboratory ex-
periments. It can be expected that γ will be bigger in the space case than measured in the
laboratory experiments.
I1I2
= γIR2D + 1, γI = 0.04 in this experiment. (8.1)
Figure 8.4 shows that Te and Vp derived from the slope of the retarding region and the
knee, respectively, of either hemisphere are approximately the same even at large RD. This
suggests that the probe’s self-wake has less effect on the characterization of Te and Vp than
on ne determined by the drop in the saturation current. It is unknown if Te and Vp may
110
experience deviation at higher RD.
To show the effect on traditional single Langmuir probe measurements on the electron
density (ne), ne was derived from two types of measurements. nBothe was derived from the
total current of the whole DHP and nFronte was derived from only the HS1 measurement which
shows the true electron density as described in section 8.2. Figure 8.5b shows the density
ratio of nBothe /nFronte as a function of RD. Error bars show the errors in the measurements
of the electron saturation current propagated to the derivation of the density. A fitted curve
(Fig. 8.5b) is expressed in Eq. 8.2 with γn ∼ 0.02. Again, as discussed above, γn is expected
to be larger without the presence of thermal ions in the probe wake in the space case. For
this reason a flight mission would be necessary to property quantify γn.
nBothe = [1− γnR2D]nFronte , γn = 0.02 in this experiment. (8.2)
Note that this equation is only valid when RD is finite. In the most extreme case
(RD � 1), where no current is collected by the downstream hemisphere, the density will be
underestimated by 50%.
Equation 8.2 and Fig. 8.5b show that the density ratio decreases with an increase inR2D,
indicating that 1) the density derived from single Langmuir probes is more underestimated
when the probe radius increases, especially when it is comparable to or larger than the Debye
length; 2) nBothe is approximately the true density (i.e., nFronte ) when RD < 1. This agrees
with the theoretical expectation described in section 8.2 due to the disappearance of the
ambipolar potential at the wake boundary; however, it differs from a previous experiment by
[Bering et al. (1975)], which show significantly reduced electron densities at small RD (≤ 1)
that were suggested to be due to the effect of the ambipolar potential.
In a short summary, the self-wake effects of a probe on electron density measurements
have been identified with the DHP in the laboratory experiments. Flight tests in which the
population of thermal ions is not present are needed for a full characterization and calibration
111
of such effects.
8.3.2 Utilization of DHP to minimize self-wake effects
As described above, the DHP can identify the wake effect on probe measurements
based on the current difference between the two hemispheres. More importantly, the DHP
provides simple methods to improve the accuracies for characterizing both ions and electrons
as follows.
1) Derive the ion and electron characteristics using measurements of the upstream
hemisphere.
2) If RD is smaller than 1 (i.e., Ie1/Ie2 ∼ 1 ), measurements of the downstream hemi-
sphere can be also used to derive the electron characteristics. This method takes an advan-
tage in cases where the upstream hemisphere is interfered by other charging sources. For
example in a dust-rich plasma environment. The probe can be pointed in the ram direc-
tion so that the downstream hemisphere is not affected by dust-impact generated plasma
clouds on the probe current collection as seen by the Cassini Langmuir probe measurements
[Morooka et al. (2011)].
112
Figure 8.4: DHP I-V Curves in Flow
Semi-log plots of the I-V curves of the DHP in ion flows. The Y axis is natural log scale ofthe absolute value of the current measured in micro-amps. The X axis is the probe sweepingvoltage. Front is ram facing (HS1), Back is wake facing (HS2). a) I-V curves of the DHPhemispheres for RD = 0.5. Notice, no deviation in the electron saturation current, andthe constant ion ram current on the front hemisphere, and the presence of a thermal ionpopulation being collected by the back hemisphere. b) I-V curves of the DHP hemispheresfor RD = 1.5. Notice, that there is significant deviation in the electron saturation current,but the trends of the ions currents remain the same to a). The slope of the retarding region(dashed blue line) and the location of the knee (blue circles) used to derive the electrontemperature and plasma potential, respectively, are unchanged.
113
Figure 8.5: Current and Density Errors due to Flow
a) Ratio of electron saturation currents between the upstream and downstream hemispheresas a function of RD and the corresponding best fit. b) Ratio of the measured electron densityby the whole DHP to the front hemisphere as a function of RD and the corresponding best fit.Error bars in both graphs come from the propagation of the saturation current measurements.
8.3.3 Conclusion and Discussion
The DHP has been tested in flowing plasmas in the CSWE chamber with high Mach
numbers (M > 10) and a wide range of the Debye ratio (RD) from < 1 to > 1. The
DHP consists of two hemispheres that were swept with a bias voltage simultaneously to
obtain two independent I-V curves. It was shown that, under such high M , the ion current
is the ram current collected by the upstream hemisphere, leaving an ion wake behind the
downstream hemisphere. The ion wake effect on the characterization of plasma electrons
has been investigated against various RD. It was found that 1) when RD is less than 1,
the electron currents collected by the two hemispheres are similar, indicating the electron
density is uniform around the probe. In this case, traditional single Langmuir probes can
correctly characterize the ambient electrons; and 2) As RD increases to be larger than 1, the
electron current collected by the downstream hemisphere becomes lower than the upstream
114
one, indicating the reduced electron density in the probe’s wake due to the formation of the
ambipolar potential at the boundary. This will lead to underestimated electron densities
derived from measurements of single Langmuir probes. With the DHP, such an effect of
the wake on the probe current collection can be identified and corrected for. The upstream
hemisphere of the DHP can be directly used to characterize both the ions and electrons.
In the case that RD is smaller than 1 (i.e., Ie1/Ie2 ∼ 1), measurements of the downstream
hemisphere can be also used to derive the electron characteristics with an advantage of
being not interfered by other charging effects on the upstream hemisphere. Specifically,
future work on the DHP will characterize the effect of dust impact generated local plasma
on DHP measurements, using the ram hemisphere as a ’shield’ and making accurate plasma
measurements with the wake hemisphere.
Chapter 9
DHP Flight Prototype
The ultimate goal of the DHP is to fly on SC missions to improve plasma measure-
ments and enhance the robustness of Langmuir probes in non-ideal environments. There-
fore, construction of a high-fidelity engineering model is necessary to develop the Technology
Readiness Level (TRL). The TRL gauges the level of maturity or fidelity of an instrument
or technology being used in relevant space environments. The TRL defined by NASA has 9
levels shown below
� TRL 1 Basic principles of the technology observed and/or reported.
� TRL 2 Technology concept and/or application formulated.
� TRL 3 Analytic and and experimental function and/or proof of concept.
� TRL 4 Components and electronics validated in laboratory environment.
� TRL 5 Components and electronics validated in relevant environment.
� TRL 6 Systems/subsystems model or prototype demonstration in relative environ-
ment. Vibration and Thermal testing of flight ready model.
� TRL 7 System prototype demonstrated in space environment.
� TRL 8 Actual system completed and ’flight qualified’ through tests and demonstra-
tion.
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� TRL 9 Actual system ’flight proven’ through successful mission operations.
The development of the DHP began at a TRL of 2. The dissertation summarizes the
lab work necessary to bring the DHP to a TRL of 6. Figure 9.1 shows the SolidWorks model
of the high-fidelity prototype of the DHP. This prototype consists of the probe sensor, stub,
and guard. The probe sensor is 5cm in diameter, the same size as the Langmuir probes on
the Cassini and Rosetta missions [Gurnett et al. (2004), Eriksson et al. (2007)]. The stub
is 10cm from the guard to the base of the sensor. To prevent the stub from interfering with
the sensor collecting charged particles from the ambient plasma, the length of the stub needs
to be longer than the radius of the spherical sensor. Considering the engineering limitations,
the length for this prototype is chosen to be 10 cm. The stub is intended on having a
variable voltage, either to be swept with the probe or floated relative to the probe sweep.
The purpose of the guard is to shield the probe from electrons emitted from the surfaces of
the boom and SC by biasing the guard to a negative potential relative to the SC.
117
Figure 9.1: DHP Flight Ready Prototype
a) Side view of the DHP, including the probe sensor, stub, guard, and boom (not includedin the TRL development). b) Cross section of the DHP with a preamp circuit board housedinside the probe sensor. c) Exploded view of the DHP sensor head, showing (left to right):stub, insulating spacer, bottom hemisphere, vented screw and washer, threaded isolatingspacer, triangle insolating spacer, pre–amp circuit, and top hemisphere.
118
Figure 9.2: DHP Pre–amp Circuit
a)Circuit diagram of the pre-amp housed inside the sensor head of the DHP. Two of thesecircuits are printed on the pre–amp board, one for each hemisphere. b) Finished printedcircuit board for the pre-amp.
The circuit diagram of the pre–amp is shown in Fig. 9.2. The circuit design is inherited
from the pre–amp used on MAVEN’s LPW [Andersson et al. (2015)]. Additionally, the pre–
amp board was designed to fit inside the sensor head, insuring minimal signal loss from the
sensor to the pre–amp. The screw shown on Fig. 9.1 is vented along its axis to allow 7 0.050
inch diameter wires to be threaded from the guard to the circuit. A total of 9 wires will
come from the boom to the guard, where two of them will terminate to allow for biasing of
the guard and stub.
Currently, the sensor head has been machined. The preamp boards have been fabri-
cated and tested. The constructions of the stub and guard are in progress. For full comple-
tion to achieve TRL 6, the prototype will undergo vibration and thermal tests. SolidWorks
vibration testing is shown in fig. 9.3
119
Figure 9.3: DHP Vibration Simulation
a)SolidWorks model of the DHP showing locations of securing durring launch and vibrationtesting b) Results of finite element analysis of vibration and load testing.
Lastly, the functionality of the DHP prototype needs to be tested before and after the
vibration and thermal tests to ensure the consistency of the DHP’s performance. A clean,
oil-free plasma chamber is under construction for this testing use, as shown in Fig. 9.4a.
Additionally, two probe sensors have been made, Fig. 9.4b. The first model is made from
aluminum coated with DAG213 for the functionality test and future dust impact experiments.
The second model is made from titanium and will be coated with iridium and will undergo
the vibration and thermal tests.
120
Figure 9.4: DHP Flight Prototype and Testing Chamber
a) New chamber being cleaned and tested for validating flight readiness. c) Fully machinedflight ready DHP prototypes to be used in flight readiness and environmental tests.
Chapter 10
Conclusion
Langmuir probes, as one of mostly used fundamental plasma diagnostics, have existed
over the past century. Over the past half century, they have been consistently used on various
SC missions to characterize magnetospheres, ionospheres, and interplanetary space filled with
plasma. While the theory of how to interpret Langmuir probe measurements has been well-
understood since their inception, Langmuir probe measurements under non-ideal plasma
environments are still facing challenges. The objective of this dissertation is to develop new
technologies to characterize and mitigate the effects of non-ideal plasma environments on
probe measurements and data interpretation. Specifically, this work focuses on: 1) studying
the effects of surface oxidation of Langmuir probes on their measurements, and validating
new coating materials to mitigate the oxidation effects; and 2) the development of the DHP,
a novel Langmuir probe, to improve plasma measurements in several non-ideal environments.
In the upper atmosphere of planets, O is one of major neutral atom and molecule
populations. It is highly reactive and has been shown to erode or degrade the Langmuir probe
coatings due to surface oxidation that causes reduced surface conductivity. To understand
the effects of oxygen exposure on probe measurements, we tested a variety of commonly
used Langmuir probe coatings against materials that are known to easily oxidized, as well
new coating materials in order to find a better material to mitigate the surface oxidation
effects on probe measurements. We found that for most materials the measurements of the
plasma parameters were affected in a way consistent with oxidation forming a resistive layer
122
on the surface of the probe. It was shown that after oxidation the Langmuir probe showed
a more positive plasma potential, hotter electron temperature, and lower plasma density.
Additionally, we found that the carbon of the DAG-coated probe reacts with the oxygen
and degas, effectively ’self-clean’ itself in the process. However, this loss of carbon from
a finite layer of graphite on a probe surface also implies the coating will eventually erode
over time. Of all the tested materials, Ir showed little to no change in its measured plasma
parameters after oxidation, likely due to the high conductivity of its oxide form, making it
a good coating material for Langmuir probes in oxygen-rich environments.
Additionally, the photoemission properties of these coating materials were investigated.
Iridium, DAG213, and AquaDAG (graphite coating) remain the largest photoemission after
oxidation, making them appropriate coating candidates for electric field probes. A long
exposure test shows that the photoemission from Iridium slowly degrades. Due to the high
surface conductivity and slow rate of oxidation of oxidized Iridium, it is suggested that
Iridium can be oxidized before flight to minimize the photoemission when being used as a
coating for Langmuir probes. Overall, Iridium is found to be a coating material appropriate
for both electric field probes and Langmuir probes.
In this dissertation, a significant work is to develop the DHP to improve plasma mea-
surements in non-ideal environments in which inhomogeneous or anisotropic local plasmas
are created around the probe due to interactions of the ambient plasma with the SC and
probe itself. The DHP consists of two identical hemispheres electrically isolated from each
other and swept with a bias voltage simultaneously. The current differences between the
two hemispheres can be used to identify and mitigate the effects of the inhomogeneous or
anisotropic local plasmas on the probe measurements. Specifically, this dissertation ad-
dressed the following non-ideal environments:
i) In low-density plasmas, due to SC charging, a large Debye sheath will be formed
around the SC and may engulf a Langmuir probe at the end of a fixed boom, causing
measured plasma characteristics to be different from the true ambient plasma far away from
123
the SC. The DHP was shown to be able to identify how deep the probe is the SC sheath
from the current ratio of the two hemispheres of the probe, and reconstruct the true ambient
plasma parameters using empirical relationships between the current ratio and the ratio of
the measured to true parameters established through the lab experiments. The DHP has
been shown to be able to correctly characterize the ambient plasma with the probe four
times ’deeper’ in the SC sheath than a conventional single Langmuir probe.
ii) Photoemission from the surfaces of a Langmuir probe itself or SC can cause con-
tamination on the probe current collection. This contamination is more severe when the
SC is close to the Sun. While there were limitations in our experiment, the DHP has been
shown to improve this situation by pointing one hemisphere at the UV light source (i.e.,
the Sun in space) while the other one is shaded. Because the shaded hemisphere does not
emit photoelectrons, the current difference between the lit and shaded hemispheres will yield
information about the photoemission from the probe itself. In our lab experiment, it shows
that photoelectrons emitted from the SC surface may also contaminate the probe current
collection, suggesting that the proper design and use of a guard that separates the probe
sensor from the probe boom and SC body is important to effectively prevent the SC-emitted
photoelectrons from reaching the probe sensor. Additionally, the experiment has implica-
tions for the effects of secondary electron emission if energetic electrons come to the SC in
a particular direction.
iii) Because of the relative motion between the fast-moving SC and ambient plasma,
an ion wake is often created behind a Langmuir probe. At the wake boundary, an ambipolar
electric field is formed due to charge separation between electrons and ions that move in the
wake at different timescales. Using the DHP, we characterized the ion wake effect on the
electron population in the wake as a function of the Debye length relative to the probe size.
This work shows that electrons are prevented from entering the wake by the ambipolar field
when the probe radius is larger than the Debye length, causing an underestimation of the
electron density measured by a single Langmuir probe. As the Debye length increases, the
124
ambipolar field weakens, and more electrons can move in the wake. When the Debye length
is much larger than the probe radius, the electrons can freely move in the wake, creating a
uniform distribution around the probe (i.e., no electron current difference between the two
hemispheres). The DHP can therefore identify the wake effect on electron measurements from
the current differences between the two hemispheres, and can then correctly characterize the
electrons using either hemisphere, depending on the Debye length relative to the probe
radius.
Lastly, a high-fidelity DHP prototype 5 cm in diameter is currently under construction.
The final prototype will be made of Titanium coated with the newly validated material
Iridium, and will undergo the vibration and thermal tests. The ultimate goal is to achieve
TRL 6, making it ready for future space demonstrations and missions.
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