Langmuir probe

Langmuir probe Takumi Abe1 and Koh-ichiro Oyama2 1Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1, Yoshinodai,...

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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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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.

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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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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

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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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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-

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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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(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

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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-

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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

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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

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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, S´eran 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. References Abe, T., K. I. Oyama, H. Amemiya, S. Watanabe, T. Okuzawa, and K. Schlegel, Measurement of temperature and velocity distribution of thermal electrons by the Akebono (EXOS-D) satellite, J. Geomag. Geoelectr., 42, No. 4, 537–554, 1990. Abe, T., K. I. Oyama, S. Watanabe, and H. Fukunishi, Characteristic features of electron temperature and density variations in field-aligned current regions, J. Geophys. Res., 98, A7, 11257–11266, 1993a. Abe, T., B. A. Whalen, A. W. Yau, S. Watanabe, E. Sagawa, and K. I. Oyama, Altitude profile of the polar wind velocity and its relationship to ionospheric condition, Geophys. Res. Lett., 20, No. 24, 2825–2828, 1993b. Abe, T., J. Kurihara, N. Iwagami, S. Nozawa, Y. Ogawa, R. Fujii, H. Hayakawa, and K.-I. Oyama, Dynamics and Energetics of the Lower Thermosphere in Aurora (DELTA)—Japanese sounding rocket campaign, Earth Planets Space, 58, No. 9, 1165–1171, 2006a. Abe, T., K.-I. Oyama, and A. Kadohata, Electron temperature variation associated with the auroral energy input during the DELTA campaign, Earth Planets Space, 58, No. 9, 1139–1146, 2006b. Amatucci, W. E., P. W. Schuck, D. N. Walker, P. M. Kintner, S. Powell, B. Holback, and D. Leonhardt, Contamination-free sounding rocket Langmuir probe, Rev. Sci. Instrum., 72, No. 4, 2052, 2001. Balan, N., K. I . Oyama, G. J. Bailey, and T. Abe, Plasmasphere electron temperature studies using satellite observations and a theoretical model, J. Geophys. Res., 101, A7, 15323–15330, 1996a. Balan, N., K. I. Oyama, G. J. Bailey, and T. Abe, Plasmasphere electron temperature profiles and the effects of photoelectron trapping and an equatorial high-altitude heat source, J. Geophys. Res., 101, A10, 21689– 21696, 1996b. Boggess, R. L., L. H. Brace, and M. W. Spencer, Langmuir probe measurements in the ionosphere, J. Geophys. Res., 64, 1627–1630, 1959. Boyd, R. L. F. and N. D. Twiddy, Electron energy distributions in plasmas. I, Proc. Roy. Soc. A, 250, 53–69, 1959. Brace, L. H., Langmuir probe measurements in the ionosphere, Measure-

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ment Techniques in Space Plasmas: Particles, Geophysical Monograph 102, American Geophysical Union, 23–35, 1998. Brace, L. H., R. F. Theis, and A. Dalgarno, The cylindrical electrostatic probes for Atmosphere Explorer-C, D, and E, Radio Science, 8, 341– 348, 1973. Evans, J. V., Diurnal variation of the temperature of the F region, J. Geophys. Res., 67, 4914–4920, 1962. Hirao, K. and K. Oyama, A critical study on the reliability of electron temperature measurements with a Langmuir probe, J. Geomag. Geoelectr., 24, 415–427, 1972. ˚ Jacks´en, L. Ahl´ ˚ en, S.-E. Jansson, A. I. Eriksson, J.-E. Holback, B., A. Wahlund, T. Carozzi, and J. Bergman, LINDA—the Astrid-2 Langmuir probe instrument, Ann. Geophys., 19, 601–610, 2001. Krehbiel, J. P., L. H. Brace, R. F. Theis, J. R. Cutler, W. H. Pinkus, and R. B. Kaplan, Pioneer Venus Orbiter Electron temperature probe, IEEE Trans. Geosci. Remote Sens., GE-18, No. 1, 49–54, 1980. Krehbiel, J. P., L. H. Brace, R. F. Theis, W. H. Pinkus, and R. B. Kaplan, The Dynamics Explorer Langmuir probe instrument, Space Science Instrumentation, 5, 493–502, 1981. Kutiev, I., K. I. Oyama, and T. Abe, Analytical representation of the plasmasphere electron temperature distribution based on Akebono data, J. Geophys. Res., 107, A12, 1459, doi:10.1029/2002JA009494, 2002. Langmuir, I., Positive ion currents from the positive column of Mercury arcs, Science, 58, 290–291, 1923. Langmuir, I. and H. Mott-Smith, Jr., Studies of electric discharges in gas at low pressures, Gen. Elec. Rev., 616, Sept., 1924. Lebreton, J.-P., Micro-satellite DEMETER, DCI-ISL, Technical note, ESTEC SCI-SO, 2002. Olson, J., N. Brenning, J.-E. Wahlund, and H. Gunell, On the interpretation of Langmuir probe data inside a spacecraft sheath, Rev. Sci. Instrum., 81, No. 10, 105106–105108, 2010. Oyama, K. and K. Hirao, Application of a glass-sealed Langmuir probe to ionosphere study, Rev. Sci. Instrum., 47, No. 1, 101–107, 1976. Oyama, K.-I. and K. Hirao, Energy gain of thermal electrons from the excited neutral gases, J. Geomag. Geoelectr., 37, 913–926, 1985. Oyama, K.-I., K. Hibino, T. Abe, R. Pfaff, T. Yokoyama, and J. Y. Liu, Energetics and structure of the lower E region associated with sporadic E layer, Ann. Geophys., 26, 2929–2936, 2008. Piel, A., M. Hirt, and C. T. Steigies, Plasma diagnostics with Langmuir probes in the equatorial ionosphere: I. The influence of surface contamination, J. Phys. D: Appl. Phys., 34, No. 17, 2643–2649, doi:10.1088/0022-3727/34/17/311, 2001. Reifman, A. and W. G. Dow, Dynamics probe measurements in the ionosphere, Phys. Rev., 76, 987–988, 1949. Schunk, R. W. and A. F. Nagy, Electron temperatures in the F region of the ionosphere : Theory and observations, Rev. Geophys. Space Phys., 16, 355–399, 1978. S´eran, E., J.-J. Berthelier, F. Z. Saouri, and J.-P. Lebreton, The spherical segmented Langmuir probe in a flowing thermal plasma: numerical model of the current collection, Ann. Geophys., 23, 1723–1733, 2005. Spencer, N. W., L. H. Brace, G. R. Carignan, D. R. Taeusch, and H. Niemann, Electron and molecular nitrogen temperature and density in the thermosphere, J. Geophys. Res., 70, No. 11, 2665–2698, 1965. T. Abe (e-mail: [email protected]) and K. Oyama