Langmuir probe Takumi Abe and Koh-ichiro Oyama

An Introduction to Space Instrumentation,
Edited by K. Oyama and C. Z. Cheng, 63–75.
Langmuir probe
Takumi Abe1 and Koh-ichiro Oyama2
1 Institute
of Space and Astronautical Science, Japan Aerospace Exploration Agency,
3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan
2 Plasma and Space Science Center, National Cheng Kung University, No. 1, Ta-Hsue Road, Tainan 70101, Taiwan
Langmuir probes have been installed on satellites and sounding rockets to observe the general characteristics
of thermal plasma in the ionosphere for more than five decades. Because of its simplicity and convenience, the
Langmuir probe is one of the most frequently installed scientific instruments on spacecraft. While the algorithm
to estimate the temperature and number density of thermal electrons from Langmuir probe measurements is
relatively simple, a number of factors, such as the position of probe installation, probe surface contamination,
and electronic circuit design, have to be considered for accurate measurements. In fact, the accuracy is primarily
influenced by improving implementation errors rather than the validity of the Langmuir probe approximation for
the observed current versus voltage characteristics for the temperature and density estimates. In this paper, we
present an example of an actual specification for a Langmuir probe and its electronics along with data gathered on
a sounding rocket and a satellite in the ionosphere. Several new applications of Langmuir probes are introduced.
Key words: Electron temperature, electron density, thermal plasma, cylindrical probe.
1.
Introduction
bare metal collectors to which a DC bias is applied.
There is no general theory of Langmuir probes which
is applicable to all measurement conditions, because it depends on the probe size and geometry, plasma density and
temperature, platform velocity, and other factors. The actual design of the probe is usually determined by considering the relationship between the probe dimensions and the
Debye length of the plasma. In general, two approximations
are used to express the current on the probe in the plasma:
1) orbital motion limited (OML) and 2) sheath area limited
(SAL) (Langmuir and Mott-Smith, 1924). OML theory can
be adopted when the probe radius is smaller than the thickness of the sheath surrounding the probe, while it must be
equal to or larger than the sheath thickness in the case of
SAL theory.
We consider the collection of electrons by a probe in
plasma. The number of electrons which are incident perpendicular to a given plane per unit time due to thermal
motion is given by
An electrostatic probe was first used to measure the potential distribution in gas discharges on the ground by J.
J. Thomson. The theory was later developed by Langmuir
and his collaborators (Langmuir, 1923; Langmuir and MottSmith, 1924; Mott-Smith and Langmuir, 1926). The technique, with further developments, has been extensively applied to the study of gas discharges and also to the study of
the ionosphere. A Langmuir probe refers to an electrode immersed in charged particle plasma, whose current-voltage
(I–V) characteristics can be measured. From the I–V characteristics, one can estimate the temperature and number
density of thermal electrons as bulk parameters. The technique has been used to measure thermal plasma populations
on spacecraft in the ionosphere, although the conditions are
more complex on a fast moving platform. The first insitu measurement of electron temperature in the ionosphere
was made by Langmuir probe in 1947 (Reifman and Dow,
1949).
The Langmuir probe is a simple and conventional instrument for determining the basic characteristics of thermal plasma in the ionosphere, and has been frequently installed on sounding rockets and satellites for more than five
decades. It is possible to estimate not only the number density and temperature of electrons but also the energy distribution function and ion density of the ionospheric plasma.
In the lower ionosphere, because thermal population is the
most important constituent as plasma, the temperature and
density of the plasma are important parameters for understanding the general characteristics of the ionosphere, and
have been extensively measured since the early stages of
satellite observations. The Langmuir probe technique involves measuring the I–V characteristics of one or more
∞
N=
vx dn e (vx )
(1)
0
where x is taken in the direction perpendicular to the plane
and dn e (vx ) is the number of electrons whose velocity is
between vx and vx + dvx .
If the velocity of the electrons obeys a Maxwellian distribution, dn e (vx ) is expressed by
dn e (vx ) = Ne
me
2π kTe
1/2
e
−
m e vx2
2kTe
dvx
(2)
where Ne and Te are the electron number density and electron temperature, respectively, m e is the electron mass, and
k is the Boltzmann constant. Then, Eq. (1) can be written
c TERRAPUB, 2013.
Copyright 63
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T. ABE AND K. OYAMA: LANGMUIR PROBE
as
N = Ne
me
2π kTe
1/2 ∞
m e vx2
vx e− 2kTe dvx = Ne
0
kTe
2π m e
1/2
.
(3)
The electron current incident on the probe at zero potential
with respect to the surrounding plasma is called the random
probe current and is expressed by
Ie =
1
8kTe 1/2
S
Ne e
4
πm e
(4)
where S is the surface area of the probe.
Langmuir probes may have different electrode shapes,
such as cylindrical, spherical, and planar probes. The first
cylindrical Langmuir probe to be used in space was long
thin wires that were added to some of the dumbbell double probe experiments for sounding rocket measurements
over Fort Churchill, Canada on November 1958 (Boggess et
al., 1959). Cylindrical and hemispherical Langmuir probes
were employed for electron temperature and density measurements on a series of “Thermosphere probes” experiments (Spencer et al., 1965). Long-wire probes have been
installed on many satellites such as Explorers 17, 22, 23,
and 31, ISIS-1, and ISIS-2. Subsequently, shorter but larger
diameter probes have flown on several satellites such as the
Atmosphere Explorers-C, D, and E (Brace et al., 1973), Pioneer Venus Orbiter (Krehbiel et al., 1980), and Dynamics
Explorer-2 (Krehbiel et al., 1981).
Measurements of the ionospheric bulk parameters have
also been made by ground-based instruments. The incoherent radar backscatter technique was used to measure electron temperature and density in the late 1950’s, and subsequently reliable data of these parameters became available in the early 1960’s (e.g., Evans, 1962). However, there
has been significant controversy in the comparison between
in-situ probe and radar backscatter techniques for electron
temperature measurement. The comparison indicates that
in general Langmuir probe data are slightly higher (∼10–
30%) than those from the radar measurements. Schunk and
Nagy (1978) have given a detailed description of the disagreement.
There are several factors which may prevent accurate
measurement of electron temperature and density in plasmas by Langmuir probes. Among them, a contamination
of the probe surface is one of the most potential sources of
error. In particular, the electron temperature tends to be estimated to be higher than the true value when the probe has
a contaminated surface. Hysteresis in the measurement of
I–V characteristics may also be seen in such a situation. A
more detailed discussion including a simple equivalent circuit will be presented in Subsection 2.5.
2.
Instrument Description
2.1 Probe type and dimensions
Frequently used geometries of Langmuir probes are planar, spherical, and cylindrical shapes. The geometry is
chosen depending on the purpose of the measurements and
the platform configuration. We most commonly adopt the
cylindrical geometry because this allows the probe radius
to be small enough to satisfy the OML condition (see below for the detailed description) for usual ionospheric conditions, while the length can be long so that the surface area
can be increased. This enables us to collect sufficient current under the OML condition even at low electron densities. For a spherical probe, it is not easy to get the same
amount of current without breaking the OML condition for
the same ionospheric conditions, because the diameter of
the probe has to be increased. However, an advantage of
a spherical probe is that it is easy to consider the current
carried by photoelectrons emitted from the probe surface,
because its contribution is almost constant independent of
the sunlight direction. For a directional probe, it is possible for the apparent current to be affected by a variation of
photoelectron current on the spinning platform. However,
such an effect does not have to be considered for a spherical probe. It is also simple to consider the contribution of
photoelectrons to the probe current for a planar probe, because its influence can be expressed by a simple function of
the incident angle of the sunlight. If the platform is a sunoriented spinning satellite, the photoelectron contribution
can be minimized by installing the probe surface parallel to
the sunlight direction.
Figures 1a–c show examples of spherical, cylindrical,
and planar probes, respectively. We have adopted the spherical probe as in Fig. 1a for measuring small-scale electron
density perturbations in the ionospheric cusp region on the
ICI-2 sounding rocket. In this measurement, the rocket
spins with a frequency of ∼4 Hz, and the spherical shape
was chosen to minimize the probe current variation caused
by the variation of the rocket RAM direction in the spinning
coordinates. A spherical probe with a diameter of 20 mm
was put on a 65-mm length boom to avoid possible influences of the rocket sheath, and was located in the top-center
on the rocket axis.
In electron temperature measurements with a Langmuir
probe, contamination of the probe surface is a serious problem which has to be considered (Hirao and Oyama, 1972).
In order to avoid undesirable effects of a contaminated layer
on the measurement, Oyama and Hirao (1976) developed a
method to keep the probe surface clean by sealing the cylindrical electrode with a glass tube until the start of the measurement. This is called the glass-sealed cylindrical probe
(see Subsection 2.5 for the detail). Figure 1b shows an example of a cylindrical probe, whose diameter and length are
3 mm and 200 mm, respectively. The required glass processing is easy for a cylindrical electrode. We have installed
such probes many times on ionospheric sounding rockets
such as S-310-31 (Oyama et al., 2008) and S-310-35 (Abe
et al., 2006b).
The Japanese Akebono satellite has two planar probes installed as shown in Fig. 1c, which are mounted on the end
of the solar cell panels in such a way that the sensors are at
right angles to the panels (Abe et al., 1991). This probe is
a circular gold-plated plane composed of two semicircular
copper disks with a diameter of 120 mm. The probe surface is almost always parallel to the sun light because the
satellite is spin-stabilized so that the solar panels can almost
always face toward the sun. In this way, the contribution of
photoelectrons can be kept to a minimum.
T. ABE AND K. OYAMA: LANGMUIR PROBE
65
The dimensions of the probe should be determined by
considering special limiting cases such as OML collection
or SAL collection. For the former condition, the probe radius must be small compared with the sheath thickness surrounding the electrode, while for the latter, the radius must
be larger than the sheath thickness. For typical conditions
of the lower ionosphere (Te ≈ 1000–3000 K, Ne ≈ 104 –106
cm−3 ), the sheath thickness is of the order of 10-2 m, and it
is possible to make a probe meeting the SAL condition. On
the other hand, the sheath thickness becomes larger (∼10−1
m) in the topside ionosphere and the plasmasphere. Thus,
a typical probe is too small to maintain the SAL condition,
and the probe dimension should be determined on the basis
of the OML condition.
In general, Langmuir probes on a satellite for ionospheric
study are made small enough to maintain the OML condition. Cylindrical probes have been frequently used for satellites and sounding rockets because their length can be made
long enough to collect a measurable current, while their ra(a)
dius can remain small enough to meet the OML condition.
2.2 Installation
Several factors have to be considered in determining
where a Langmuir probe should be installed on a satellite.
The use of a boom is required for the probe to conduct measurements beyond the spacecraft sheath and outside the disturbed region (wake) caused by the satellite movements.
When the spacecraft is significantly charged either negatively or positively, a sheath will develop around its surface,
which can affect the probe’s measurements. If the Langmuir
probe is inside the sheath of a negatively charged spacecraft,
the probe characteristics may be modified compared to outside the sheath (e.g., Olson et al., 2010). Olsen et al. (2010)
suggested that the probe characteristics are likely to depart
from the usual OML theory, having a detrimental effect on
the process of extracting plasma parameters from measured
current-voltage (I–V) curves. Since the Debye length increases as the electron temperature increases or the electron
(b)
density decreases, care must be taken regarding the sheath
effect when using a Langmuir probe on such situation.
The shape of the satellite wake is not simple and varies
depending on the satellite’s shape and velocity, the number density and the temperature of the surrounding plasma.
To minimize the influence of the disturbed plasma, a boom
length longer than 30 cm is generally preferable for measurements in the ionosphere. If the probe is installed on a
three-axis stabilized platform, it should be in a place which
is not affected by the wake. If the platform is a spinning
satellite, the probe must be placed such that it can go outside the wake for at least some period during its spin, paying
attention to the relationship between the RAM direction and
probe surface.
The shock effect on Langmuir probe measurements
should also be considered. The spatial structure of the
(c)
spacecraft shock depends on its velocity, the number density, and the temperature of the surrounding plasma. If the
probe is placed at a distance from the satellite or sounding
Fig. 1. (a) Spherical probe installed on “ICI-2” sounding rocket. (b) rocket using a boom, the influence of the shock on the meaCylindrical probe installed on Japanese sounding rockets. (c) Planar surement will be less significant.
probe installed on Japanese Akebono satellite.
Thus, it is important to find a location where the measurement can be made outside the sheath and shock region.
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T. ABE AND K. OYAMA: LANGMUIR PROBE
Fig. 2. Deployed cylindrical probe in the payload section of “S-310-31”
sounding rocket.
Figure 2 shows a picture of a deployed cylindrical Langmuir
probe in the top part of the payload section on the Japanese
“S-310-31” sounding rocket. The probe was deployed in
a direction perpendicular to the rocket axis by the onboard
timer during the rocket flight.
2.3 Derivation of electron density and temperature
When a probe is immersed in plasmas, the probe current
generally depends on the collections of positive ions, negative ions, and electrons. We consider the electron current
on a spherical probe under the condition that the electrons
have a Maxwellian velocity distribution in a coordinate system fixed with respect to the probe. For the averaged ionospheric condition, the mean thermal velocity of electrons
exceeds the satellite velocity by an order of magnitude.
Figure 3 shows the current-voltage (I–V) characteristics
obtained by sweeping the probe voltage, V p , with respect
to the spacecraft potential, Vs , while measuring the net current, I , which consists of the ion current, Ii , and the electron current, Ie . The I–V characteristics has three different
regions; 1) ion saturation region where the electrons are repelled but ions are collected, 2) electron retarding potential
region where most of the current is due to electrons, but
the actual current is determined by the number of electrons
which can overcome a retarding potential Vr (= Vs − V p ),
and 3) electron saturation region where ions are repelled
but electrons are attracted to the probe. In the electron retarding potential region, the electron current is expressed as
follows:
−eVr
Ie = Ie0 exp
(5)
kTe
Ie0
kTe
= Ne e
2πm e
1/2
S
(6)
whereIe0 is the random electron current and e, k, Vr , Te , and
S are electron charge, Boltzmann constant, probe potential
relative to Vs , electron temperature, and surface area of
the probe, respectively. In reality, the current obtained in
the electron retarding region includes both electron and ion
currents.
For a cylindrical probe, the random electron current is
Fig. 3. Ideal I–V curve for a Langmuir probe.
expressed differently, given by the following equation:
Ie0
kTe
= Ne e
2π m e
1/2
2
√ S.
π
(7)
In general, the electron current is calculated by subtracting the ion current from the probe current, where the ion
current is estimated by extrapolation from the ion saturation current. The electron temperature is estimated from the
gradient, which is proportional to 1/Te , in a plot of log(Ie ).
The random electron current is a function of the electron
temperature and density. Therefore, once the random electron current and the electron temperature are known, the
number density of electrons can be calculated. The space
potential may be taken as the inflection point between the
electron retarding and electron saturation regions, both of
which change almost linearly in a plot of log(Ie ).
2.4 Electronics
The electronics for a Langmuir probe measurement include an electrometer and circuitry that controls the rate and
amplitude of a triangular sweep and the current gain. The
current incident on the electrode is detected by a DC amplifier, and the electrometer output is digitized and transferred
to a telemetry system for transmission to the ground.
The electron density may change in the order of 103
cm−3 to 105 cm−3 according to various dynamical and photochemical processes occurring in the ionosphere. When
an electrometer is designed to cover the maximum electron
density with one telemetry channel, a 12-bit analog to digital converter (ADC) may not have enough resolution in the
current measurement. In this case, it is recommended to
prepare two or three different current gains for the measurement so that it can measure with sufficient accuracy for
large changes in the current.
The Langmuir probes on the Atmospheric Explorer
(Brace et al., 1973) and Pioneer Venus Orbiter (Krehbiel
et al., 1980) use an advanced method to improve current
T. ABE AND K. OYAMA: LANGMUIR PROBE
67
Fig. 4.
Block diagram of Langmuir probe electronics installed on
“S-310-35” sounding rocket.
measurement, employing adaptive circuitry which automatically sets the current gain so as to focus on parts of the I–V
characteristics used for Te and Ne estimations. The adaptive
circuitry adjusts the electrometer gain using the ion current
level observed at the beginning of each voltage sweep. This
assures that the ion saturation region is ideally resolved.
In general, the raw data in Langmuir probe measurements contain noise that may be intrinsically generated
from the data acquisition system and/or interactions between the probe and plasma. The plasma potential is determined by finding the inflection point of the electron current
data, which indicates the peak of the first-order differentiation. Since current noise tends to increase when it is differentiated, it becomes more difficult to find the plasma potential in the differentiated current. In this case, a pre-amplifier
may be used between the electrode and main electronics. A
numerical algorithm may also be applied to reduce the noise
level of the probe current.
Figure 4 shows a block diagram of the Langmuir probe
electronics which was installed on the Japanese sounding
rocket “S-310-35” (Abe et al., 2006a). Detailed information on this Langmuir probe has been given by Abe et al.
(2006b). Three channels were prepared to cover currents
up to 4.0 µA (Gain-L), 0.2 µA (Gain-M), and 0.01 µA
(Gain-H), respectively. The electronics may have a calibration mode to confirm the health of the instrument even when
it is not immersed in plasma. The leftmost part of Fig. 4 was
used to generate the calibration signal; a half current level
to the full scale is detected in the Gain-M channel when the
instrument is operated in the calibration mode by switching
the input from the probe to resistance inside the electronics.
2.5 Measurement accuracy
In Langmuir probe measurements, the accuracy depends
primarily on minimizing implementation errors rather than
the validity of the Langmuir probe approximation to the observed I–V characteristics for the temperature and density
estimates (Brace, 1998). For accurate measurements, it is
necessary to remove the sources of implementation error
as well as to overcome shortcomings in the design. Brace
(1998) has discussed the theory of the method, the main
sources of error, and some approaches that have been used
to reduce the errors.
Measurement error may arise from the following factors:
1) Contamination of the probe surface.
2) Inadequate positioning of the probe in the spacecraft
or rocket body .
3) Insufficiently uniform collector surface material.
4) Electronics not satisfactorily resolving the I–V char-
Fig. 5. I–V characteristics when an electrode (3 mm in diameter, 20 cm
in length) is contaminated. The sweep frequency is changed from 0.1
Hz (top), 0.4 Hz (middle), and 1 Hz (bottom). The probe voltage is a
triangular signal of 0–3 V. The direction of the voltage sweep is denoted
by arrow. The electron temperature and density, when are calculated
when the hysteresis vanishes, are 1400 K and 2×104 cm−3 , respectively.
acteristics.
5) The spacecraft/rocket failing to serve as a stable potential reference.
6) Non-uniformity of the work function on the probe
surface.
7) Magnetically induced potential gradient due to movements of the spacecraft.
It is well-known that a contaminated Langmuir probe includes erroneous information in space plasma as well as
in laboratory plasma. As shown in Fig. 5, when a bias
to the contaminated probe is swept from negative to positive and from positive to negative, the I–V curve exhibits
hysteresis, i.e., it follows a different path in the two di-
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T. ABE AND K. OYAMA: LANGMUIR PROBE
Fig. 6. Equivalent circuit to express the effect of electrode contamination.
Cc and Rc are the capacitor and resister of which the contamination
layer might consist.
rections. It is generally accepted that hysteresis is caused
by surface contamination. For example, Hirao and Oyama
(1972) showed that the estimated electron temperature is
higher than the true value when the probe has a contaminated surface, and indicated that the measured high temperature in the ionospheric E region might be due to a contaminated Langmuir probe. The hysteresis decreases as the
frequency of the sweep voltage increases, and finally disappears. In ionosphere plasma, the hysteresis diminishes at
about 10 Hz with a sweep voltage of 3 V. The hysteresis also
decreases when the electron density reduces. These two
features, which are associated with the electrode contamination, are well explained by an equivalent circuit model,
which is shown in Fig. 6.
Among the factors which are influential in the measurement of the ionospheric plasma, contamination on the electrode surface is one of the most serious issues, and therefore we pay special attention to the cleanness of the surface. In order to perform a Langmuir probe measurement
with a clean electrode on a sounding rocket, we prepare a
glass-sealed cylindrical probe by following the procedure
developed by Oyama and Hirao (1976). The procedure we
are using for the sounding rocket is as follows:
1) A cylindrical stainless probe with a diameter of 3 mm
is covered by a glass tube with a diameter of 10 mm.
2) This glass tube with the probe is connected to a vacuum chamber evacuated by a pumping system.
3) To outgas from a contaminated layer on the probe
surface, the cylindrical probe sealed in the glass tube is
baked at a high temperature of 200◦ C in low pressure for
more than 24 hours.
4) After confirming that the gas pressure has reached a
low enough level (<10−7 torr), the glass tube is sealed.
5) The probe is installed on the sounding rocket and the
glass is broken by a spring-actuated sharp edge during its
flight.
6) One second later, the probe is deployed in the direction vertical to the rocket spin axis.
7) The glass is removed by a centrifugal force due to the
rocket spin and the uncontaminated probe is exposed to the
plasma outside of the rocket sheath.
In this way, the possible influence on the ionospheric
plasma measurement can be avoided. As hysteresis in the I–
Fig. 7. Vacuum pumping of a glass-sealed Langmuir probe.
V characteristics is observed in most cases when the probe
surface is contaminated, it is possible to ascertain the degree
of probe contamination by comparing the I–V characteristics between the upward and downward voltage sweeps.
Figure 7 shows a picture of a glass-sealed cylindrical
probe evacuated by a pumping system. Such a glass-sealed
probe may not always be applicable for measurements on a
spacecraft. For a spherical probe or a planar probe, it is not
easy to seal the probe with glass or remove the glass during
the spacecraft flight.
Amatucci et al. (2001) presented another technique to remove surface contaminants on a sounding rocket spherical
Langmuir probe. They showed that the contamination can
affect not only the parameters derived from the probe’s I–
V characteristic, but also “single-point” measurements such
as floating potential or ion/electron saturation current. They
also suggested that adsorbed neutral particles can be removed from the probe surface by heating the probe from
the interior using a small halogen lamp, which results in accurate plasma parameter measurements. This suggests the
possibility that contamination can affect density estimates
as well as electric field measurements. They concluded
that the errors due to surface contaminants are more important for measurement accuracy than that introduced by
work function variations within the surface.
Piel et al. (2001) also discussed the influence of the geomagnetic field effects and probe contamination by analyzing a nonlinear equivalent circuit of the contamination layer.
The resulting error caused by the distortion of the I–V char-
T. ABE AND K. OYAMA: LANGMUIR PROBE
69
Table 1. Specification of Langmuir probe for sounding rocket “S-310-35”.
Sampling
Sweep period
Sweep voltage
Current gain
Output offset
Weight
Size
Power
1.25 msec (800 Hz)
250 msec (sweep up 125 msec, down 125 msec)
Triangular, 3 V p− p (with respect to the rocket)
Gain high mode
Gain low mode
Low gain
×1.0
×0.5
Middle gain
×20.0
×10.0
High gain
×400.0
×200.0
+1 V
Probe: 1.5 kg (incl. deployment and glass cutter mechanism)
Electronics: 1.5 kg
Pre-amplifier: 0.25 kg
Probe: 255 × 65 × 92.2H mm
Electronics: 211 × 100 × 60H mm
Pre-amplifier: 126 × 29 × 83H mm
250 mA (+18 V)
150 mA (−18 V)
acteristic for decreasing and increasing probe voltages is determined for a range of capacitance (C) and resistance (R)
values of the contamination layer. They described a method
to determine the parameters R and C from the flight data.
As described in Subsection 2.3, the electron current (Ie )
on a logarithmic scale is expressed by a linear expression
whose gradient is a function of Te when the electron energy distribution function is considered to be Maxwellian.
This condition is generally satisfied in the low altitude ionosphere where no energization process is functioning. Therefore, we are able to determine that measurements can be
considered valid by evaluating whether the electron current
exponentially varies with the probe bias in the retarding portion. In a particular situation, such as in the presence of auroral particles or a strong electric field, the measured I–V
characteristics may not be approximated by an exponential.
This implies the possible existence of non-thermal components, a bi-Maxwellian distribution, or a high-energy tail in
the distribution function. The I–V characteristics include
various information on plasma properties existing in the
ionospheric plasma. Thus, it is possible to assess the measurement accuracy by examining the consistency between
the Langmuir probe theory and the obtained I–V characteristics.
Photoelectron emission from the probe surface, which
appears as a positive incident current, may also introduce
errors in the accurate estimation of Te and Ne in Langmuir
probe measurements particularly for low plasma density.
The apparent ion current would be larger than the actual
current. In this case, a floating potential tends to be shifted
toward a space potential, and the Ne estimated from the random electron current may be smaller than the ion density
based on the ion current. The actual degree of the influence on the I–V characteristics depends on the background
electron temperature and emission rate of secondary electrons from the probe. Thus, careful consideration of the
I–V characteristics should be made. Electromagnetic interference from other instruments or equipment can also possibly affect probe measurements, and these effects would
appear as distortions of the I–V characteristics. The cause
of any interference should be determined for accurate mea-
surements. The source of the interference may be difficult
to identify because the interference may have various values of amplitude or frequency or methods of propagation
(radiative or inductive). However, decreasing the interference level should make for a better measurement.
It is also important to determine the appropriate specifications of the electronics for the probe measurement, such
as adequate range and resolution for the applied voltage and
the current. First, it is necessary to know what range of Te
and Ne is likely to be encountered in the measurement. Second, the range of the probe current is determined by considering the maximum of the electron saturation current.
The amplitude of the triangular sweep voltage is decided by
referring to the expected potential of the spacecraft or the
rocket. In order to make accurate measurements of Te and
Ne , one should obtain the I–V characteristics in fine voltage steps so that the rising portion of the electron current
can be accurately reproduced, which is particularly important for the exact measurement of Te . However, the choice
of the voltage step is constrained by the rate of data transfer
between the spacecraft and the ground. The voltage sweep
rate has to be determined by considering the spacecraft velocity, spin rate, and available rate for sending current data.
3.
Actual Specification and Data
3.1 Example of specification
As an example of an actual specification, detailed information of the Langmuir probe on the sounding rocket “S310-35” is presented. For this rocket, a cylindrical stainless
probe with a length of 140 mm and a diameter of 3 mm was
installed on the payload zone (Abe et al., 2006b). The probe
was deployed in the direction vertical to the rocket axis during its flight. The detailed specifications of the probe are
given in Table 1. The probe is directly biased by a triangular voltage with amplitude of 3 V with respect to the rocket
potential and a period of 250 msec in order to provide the
incident I–V relationship. The current incident on the probe
was sampled with a rate of 800 Hz, and amplified by three
different gains (low, middle, and high). In order to measure
the ion current as well as the electron current, the amplifier has an offset voltage of +1 V; a positive (>1 V) volt-
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T. ABE AND K. OYAMA: LANGMUIR PROBE
(a)
Fig. 9. I–V characteristics obtained at (a) 00:36:13 UT and (b) 00:37:51
UT on December 13, 2004, by the Langmuir probe on the S-310-35
sounding rocket.
(b)
Fig. 8. (a) Stowed appearance of a glass-sealed cylindrical Langmuir
probe. (b) Appearance of cylindrical Langmuir probe extending from
a window on the rocket wall.
age indicates an electron current while a negative voltage
indicates an ion current. The electronics were designed to
obtain a calibration signal by switching the input from the
probe to the resistance once every 30 seconds.
3.2 Data examples from Langmuir probe measurement
In December 2004, the Institute of Space and Astronautical Science (ISAS) of the Japan Aerospace Exploration
Agency (JAXA) launched the sounding rocket “S-310-35”
from Andøya Rocket Range in Norway during the Dynamics and Energetics of the Lower Thermosphere in Aurora
(DELTA) campaign (Abe et al., 2006a). The main objective
of this rocket experiment was to study the lower thermospheric dynamics and energetics caused by auroral energy
input. A glass-sealed Langmuir probe was installed on this
rocket to investigate the thermal structure and energy balance of the plasma by measuring the electron temperature
in the polar lower ionosphere (Abe et al., 2006b). Figure 8a
shows a picture of the actual installation of the glass-sealed
Langmuir probe inside the instrument box, while Fig. 8b
shows the appearance after breaking the glass tube and extending the probe from the outside wall of the rocket.
During the rocket flight, the cylindrical probe began to be
extended at 66 sec after the rocket launch (hereafter called
X + 66) and was completely exposed to the plasma outside
the rocket sheath about 17 sec later (X + 83) at an altitude
of 92.7 km. The left-side panel and right-side panel of
Figs. 9a and b show the I–V characteristics and the electron
current on a logarithmic scale, respectively, as a function
of the probe voltage. The linear fitting to the ion current is
represented by a thin line in the left panel. Shown at the
top of the right panels are the electron temperatures (in K)
calculated from the linear fitting to the electron current in
a logarithmic scale and the number density of electrons (in
cm−3 ) estimated from the random electron current at the
space potential. The I–V characteristics shown in Figs. 9a
and b were obtained at X + 193.52 sec and X + 291.54
sec, when the rocket altitude was 139.6 km and 85.5 km,
respectively. Note that the gradient of the probe current
with respect to the probe bias tends to decrease in the range
from 1.4 to 2.3 V, but becomes slightly steeper above 2.3 V,
which seems unusual behavior for the I–V characteristics.
This may be related to a local variation of the background
electron density during the sweep period of the probe bias.
Figure 10 represents the altitude profile of the electron
temperatures for the rocket descent. Each temperature point
is given by taking a running mean of seven data points obtained by the procedure described above. The temperature
T. ABE AND K. OYAMA: LANGMUIR PROBE
71
Fig. 11. Block diagram of the instrument to pick up the second harmonic
component from the distorted probe current.
Fig. 10. Altitude profile of the electron temperature observed by the
Langmuir probe on the S-310-35 sounding rocket during its downleg.
profile during the descent has a relatively monotonic trend,
in which no obvious increases of the electron temperature
are observed between 105 and 140 km. However, a small
increase (∼100–200 K) of the electron temperature against
the background temperature was observed between 114 and
119 km altitude. It seems that the temperature peak is not
single, but that there are multiple peaks, with local maxima
at 118.4, 117.6, and 116.0 km. These local increases may
be caused by electron heating mechanisms occurring in the
polar ionosphere.
4.
(a)
Applications and Improvement
4.1 Measurement of electron energy distribution
The energy distribution function, f (E), where E is the
electron energy in eV, of thermal electrons can be estimated by adopting the well-known Druyvesteyn’s method
(Druyvesteyn, 1930). In this section, a way to derive f (E)
with a Langmuir probe is described.
As already introduced, Langmuir I–V characteristics are
obtained by applying a triangular DC sweep voltage and
(b)
measuring the probe current. When an AC voltage with
small amplitude is superimposed on the DC sweep voltage, a relationship between the second derivative of the I–
V characteristic curve with respect to the probe voltage, Fig. 12. (a) Semi-logarithmic plot of the second harmonic component
as a function of the probe potential. These data were measured on
I (V ), and the second harmonic component of the probe
the sounding rocket K-9M-81. (b) Example of the second harmonic
current, I2w , can be given as follows (Boyd and Twiddy,
component on a semi-logarithmic scale. The curve is not linear with
1959):
respect to the probe potential, which shows that the energy distribution
of thermal electrons is not Maxwellian. The result was obtained by the
a 2 sounding rocket K-9M-62.
I2w ≈
I (V )
(8)
4
where a denotes the voltage amplitude of the small AC sig-
72
T. ABE AND K. OYAMA: LANGMUIR PROBE
Fig. 13. Example of the second harmonic current profile as a function of
the probe potential from TED observation on Akebono satellite. The
solid line represents the gradient of the second harmonic current in this
format, from which the electron temperature can be estimated.
nal superposed on the DC voltage. Usually, I2w is electronically obtained by the second harmonic method (Boyd and
Twiddy, 1959) and detected by a narrow band lock-in amplifier.
The energy distribution function, f (E), is expressed using I (V ) as follows (Druyvesteyn, 1930):
4 Vs − V p (9)
f (E) =
I (V )
2e 2
Ne
e S
me
where Vs , V p , and S denote the space potential, probe potential, and collecting probe surface area, respectively, and
Ne , me, and e are the electron number density, electron
mass, and electron charge, respectively. Using (8) and (9),
f (E) can be derived by measuring the second harmonic
component of the probe current.
When thermal electrons in the plasma obey a Maxwellian
distribution, Im (V ) is expressed as follows:
kTe
e 2
eV
Im (V ) = S Ne e
. (10)
exp −
2πm e kTe
kTe
It is understood that the second derivative, Im (V ), in a
logarithmic scale is expressed by a linear function of V ,
and the gradient is a function of Te . In other words, the
second derivative linearly changes in a log plot of Im (V )
when the thermal electrons obey a Maxwellian distribution.
If the energy distribution is considered to be Maxwellian,
the electron temperature and density can be calculated by
applying the standard formula (Druyvesteyn, 1930).
An example of a block diagram to pick up the second
harmonic component of the probe current is shown in Fig.
11 (Oyama and Hirao, 1985). A sweep voltage is superposed on a sinusoidal signal of 1 kHz with an amplitude of
70 mV and applied to the electrode. In this block diagram,
Fig. 14. (a) Measured and modeled profiles of electron temperature during
daytime and nighttime at equatorial latitudes, (b) for low latitudes,
and (c) for mid-latitudes. Adapted from Balan et al. (1996b) with
permission.
the probe current is measured as a voltage drop through a
resister, and only a component with a frequency of 2 kHz
is picked up by using a band-pass filter from the probe current, which is distorted due to the non-linearity of the I–V
characteristic curve. The envelope of the filtered signal is
amplified by four linear amplifiers of different gain, to get
the information in all height regions. The preamplifier was
prepared as a current amplifier, and the four DC amplifiers
T. ABE AND K. OYAMA: LANGMUIR PROBE
73
Table 2. Detailed specification of the energy distribution mode of the TED measurement on the Akebono satellite.
Sweep voltage
Density range
Frequency of AC signal
Amplitude of AC signal
Data acquisition rate
Voltage sweep rate
Read rate
Type of measurement
Weight of electronics box
Weight of sensors
0–2.5 eV or 0–5.0 eV
102 –106 cm−3
6 kHz
100 mV or 200 mV (peak to peak)
Data sampling rate of 1024 Hz
0.5 s or 1.0 s
4 s (1024W) or 8 s (2048 W) at high bit rate
16 s (1024W) or 32 s (2048 W) at medium bit rate
Two planar probes in the shape of two semi-circular disks
mounted on the tip of the solar cell paddle
1.76 kg
0.08 kg × 2
were changed to a logarithmic amplifier. If the energy distribution of the electrons is considered to be Maxwellian,
the output signal shows a linear line versus probe voltage.
Two examples of the measurement are shown in Figs. 12a
and b. Figure 12a shows that the observed energy distribution is Maxwellian, while the latter shows the case when the
energy distribution has a high energy tail.
An instrument to measure the electron energy distribution based on such a principle was also installed as a thermal electron energy distribution (TED) instrument on the
Japanese Akebono (EXOS-D) satellite. Figure 13 shows an
example of raw output from the energy distribution mode
of the TED measurement (Abe et al., 1990). The scale of
the abscissa denotes the probe voltage relative to the space
potential, and the ordinate shows the second harmonic component of the probe current. The different symbols (triangle
and cross) used in Fig. 13 represent the second harmonic
component corresponding to the ascending and descending
phases of the triangular-sweep voltage, respectively. It is
ascertained from the data that the consistency of the probe
currents between these two phases suggests an isotropic
energy distribution at least in a plane perpendicular to the
satellite spin axis. When the electrons are isotropic in the
velocity space, we can estimate the energy distribution in
the direction perpendicular to the probe surface from the
second derivative.
The instrumental parameters of the energy distribution
mode of the TED measurement are summarized in Table 2.
In this mode, the sweep voltage range and the voltage sweep
rate can be changed according to scientific interest. The
amplitude of the superimposed AC voltage can be chosen
to be either 100 mV or 200 mV (peak to peak), and the gain
of the amplifier is also changeable by ground commands.
Both the probe bias and the gain of the amplifier in the
energy distribution mode can be modified through the system operation so that an appropriate I–V curve can be observed. Two levels of voltage sweep rate (0.5 and 1.0 s) and
two levels of the AC signal amplitude (100 and 200 mV)
can be selected. In the standard operation, 256 words (current data) per probe are sampled linearly in the range from
0 to 5 V during the time interval of 0.5 s. In the following
0.5 s time interval, 256 words are again sampled with the
voltage scanning sequence in the opposite direction. Since
eight words are assigned to each odd number frame, a total
of 32 frames are necessary to reproduce one data set (256
words).
Data obtained by TED measurements were used to investigate various subjects of the ionospheric and plasmaspheric
electron temperatures. Abe et al. (1993a) showed that variations in electron temperature at altitudes from 300 to 2300
km are closely related to field-aligned structures in the auroral region. At higher altitudes, the electron temperature
increases in the upward field-aligned current region while
it decreases in the downward current region. Electron temperature data from TED measurements in the polar wind
region were used to investigate the relationship between the
local magnitude of ion acceleration and the ambipolar electric field, which is known to be directly dependent on the
electron temperature. A comparison between electron temperature and drift velocity of thermal ions indicated that at
a given altitude, the polar wind velocity increases linearly
with electron temperature (Abe et al., 1993b), which is direct in-situ evidence of ion acceleration due to the ambipolar electric field.
Balan et al. (1996a) studied electron temperature distributions in the plasmasphere using TED data, particularly
to investigate the local time, geomagnetic latitude, and altitude variations. The observed plasmaspheric electron temperature is almost constant during both day and night and is
found to have large day-to-night differences that vary with
altitude and latitude. Subsequently, Balan et al. (1996b) focused on the altitude (1000–8000 km) profiles of the electron temperature for magnetic latitudes 0◦ –40◦ at different
times of the day, and compared the profiles with those computed by the Sheffield University plasmasphere-ionosphere
model, modified to include nonlocal heating due to trapped
photoelectrons and an equatorial high-altitude heat source.
Their results show that a photoelectron trapping of up to
100% is required to raise the modeled electron temperatures to the mean measured values. Figures 14a–c show the
measured and modeled electron temperature profiles during daytime and nighttime at equatorial latitudes, for low
latitudes, and for mid-latitudes, respectively. The modeled
profiles shown in this figure also reproduce the observed
features at ionospheric altitudes (Balan et al., 1996b).
Kutiev et al. (2002) attempted to reveal the average thermal structure of the plasmasphere at altitudes between 1000
and 10,000 km based on TED data set. In their analysis, the
74
T. ABE AND K. OYAMA: LANGMUIR PROBE
Fig. 15. Statistically averaged electron temperature distribution at altitudes from 1000 to 10000 km in the plasmasphere based on Akebono observation
data. Left half shows the altitude-latitude distribution in the noon (MLT 1200) meridian, while right half shows the midnight (MLT 0000) meridian.
analytical expressions are fitted to the measured electron
temperature values in each altitude/local time zone, and a
large scatter of fitting coefficients was found. They also
studied the solar activity dependence on electron temperature at altitudes between 2500 and 3500 km.
Figure 15 shows one example of the plasmaspheric electron temperature distribution, which was obtained by statistical analysis of the TED observations on the Akebono
satellite (Abe et al., 1991) at altitudes from 1000 to 10,000
km in the noon (left-side) and the midnight (right-side)
meridian planes. The broken lines represent the geomagnetic field lines from 30◦ to 80◦ separated by 10◦ . Note
that no electron temperature is shown in the region above
4000 km altitude and 60◦ invariant latitude, because the low
electron density prevents accurate estimation of the electron
temperature. The electron temperatures were found to be almost constant along the magnetic field lines above 2000 km
altitude. The daytime electron temperature is higher than
the nighttime temperature by 2000–3000 K.
4.2 Other applications of Langmuir probe
Holback et al. (2001) presentesd a double Langmuir
probe instrument called LINDA (Langmuir interferometer and density instrument for the Swedish micro-satellite
Astrid-2). LINDA consists of two lightweight deployable
boom systems, each carrying a small spherical probe. The
use of two probes and a high sampling rate enables the discrimination of temporal structures from the spatial structures of plasma density and temperature. This instrument
can be operated in a constant bias voltage operation for the
study of slow and fast variations of plasma density as well
as in sweeping operations of probe bias for obtaining I–V
characteristics. By using the two probes, it is possible to
determine correlation functions and discriminate stationary
structures from plasma waves.
Lebreton (2002) proposed the segmented Langmuir
probe (SLP) to derive the bulk velocity of plasmas, in addition to the electron density and temperature that are routinely provided by standard procedure of Langmuir probe
measurements. The basic concept of this probe is to mea-
T. ABE AND K. OYAMA: LANGMUIR PROBE
sure the current distribution over the surface using independent collectors under the form of small spherical caps and
to use the angular anisotropy of these currents to obtain the
plasma bulk velocity in the probe reference frame. To ascertain the capabilities of this instrument, Séran et al. (2005)
developed a numerical particles in cell (PIC) model to compute the distribution of the current collected by a spherical
probe. According to their model calculation, it is clear that
the ion velocity measurement accuracy is not as good as
that provided by the ion analyzer technique, at least at the
present stage of the instrument development. Nevertheless,
the SLP has interesting advantages, e.g., it only requires
modest spacecraft resources. From the SLP measurements
they estimated that a plasma velocity of about 150 m s−1
and 250 m s−1 perpendicular to the satellite orbital velocity
can be resolved for O+ and H+ plasmas, respectively.
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T. Abe (e-mail: [email protected]) and K. Oyama