Sheath capacitance observed by impedance probes onboard sounding rockets: Its application to ionospheric plasma diagnostics
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2010
Received: 18 August 2009
Accepted: 28 January 2010
Published: 31 August 2010
Ion sheath which is formed around an electrode significantly affects the impedance of the probe immersed in a plasma. The sheath capacitances obtained from impedance probe measurements were examined for application to plasma diagnoses. We compared analytical calculations of the sheath capacitance with measurements from impedance probes onboard ionospheric sounding rockets. The S-520-23 sounding rocket experiment, which was carried out in mid-latitude, demonstrated that the observed sheath capacitances agreed well with those of the calculations. We concluded that the sheath capacitance measurements allow for estimation of the electron temperature and the electron density of a Maxwellian plasma. On the other hand, the sheath capacitances obtained from the S-310-35 rocket experiment in the auroral ionosphere showed lower values than expected. Auroral particles precipitations should modify the probe potential.
In-situ plasma diagnoses are essential for clarifying various aspects of phenomena found in space and laboratory plasmas. A radio frequency (RF) probe technique is a powerful tool for measuring the plasma parameters (e.g., Jackson and Kane, 1959). Over the past several decades, numerous investigations have been conducted on the impedance of an electrode immersed in a plasma in order to achieve accurate plasma diagnoses.
The observed antenna impedance reflects various physical properties of the ambient plasma as well as the electron density. Evaluations of the observed impedance are actively discussed subjects these days. Tsutsui et al. (1997) examined antenna impedance measured by the Geotail spacecraft in the Earth’s magnetosphere, where the electron densities are too low to observe the resonances. Béghin et al. (2005) computed the self-impedance and mutual-impedance to model the electric antennas onboard the Cluster satellites. Impedance measurements in a laboratory plasma showed resonances of a long dipole antenna (Blackwell et al., 2007). Miyake et al. (2008) developed an analysis tool of antenna impedance via Particle-In-Cell (PIC) simulation. A Plasma-Fluid Finite-Difference Time Domain (PF-FDTD) simulation was applied to estimate the collision frequency in the ionosphere (Ward et al., 2005; Spencer et al., 2008). In addition, unique characteristics of the probe impedance in a thermal magnetized plasma were found by laboratory experiments (Suzuki et al., 2009).
In actual situations, for evaluating the probe impedance it is essential to consider the effect of an ion sheath surrounding the probe. This paper deals with the capacitance of the ion sheath measured by impedance probes. The ion sheath is formed around the probe due to the difference between the thermal velocity of electrons and ions. The sheath capacitance significantly affects the probe impedance at lower frequencies in comparison to that around the UHR frequency. Derivation of the electron temperature from the sheath capacitance was originally proposed by Oya and Aso (1969). Watanabe (2000) reported that sheath thickness was changed with the auroral energetic electron flux. Sheath capacitance has also been studied in terms of its capacitively coupled plasma (e.g., Chen, 2006).
The purpose of this study is to evaluate the sheath capacitance obtained from impedance probe measurements in order to utilize it for ionospheric plasma diagnostics. We applied an analytical formula of the sheath capacitance with a step sheath model. Although our calculation method of the sheath capacitance is fundamentally the same as that of the report by Oya and Aso (1969), we have made some modifications on the evaluation of the probe potential. We examined the sheath capacitance observed from impedance probes onboard the two sounding rockets, S-520-23 and S-310-35. First, we show analysis of the sheath capacitance in a quiet state of the ionospheric plasma to confirm the validity of the analytical model. We also provide observations of the sheath capacitance under disturbed conditions.
2. Sheath Capacitance in Impedance Probe Measurements
3. Outline of the Sounding Rocket Experiments and Instruments
3.1 Sounding rocket S-520-23 experiment
Wind measurement for Ionized and Neutral atmospheric Dynamics study (WIND) campaign was carried out to investigate the momentum transfer between the ionospheric plasma and the neutral atmosphere. The S-520-23 sounding rocket was launched from the Uchinoura Space Center (31.15°N, 131.04°E in geodetic coordinates), Japan on 2nd September 2007, at 19:20 LT (LT = UT + 9 h). The pay-load reached an apex altitude of 279 km at 268 sec after the launch. The Lithium Ejection System (LES) installed on the S-520-23 rocket was designed to release Li gas three times in the descending phase. The resonantly scattered light of the Li clouds was successfully observed from several ground sites to measure thermospheric neutral wind accurately.
All instruments performed successfully during the rocket flight. Many interesting results were achieved by the neutral wind, the electron density, the electron temperature, the plasma wave, and the electric field measurements. The present paper focuses on the sheath capacitance measured by the impedance probe instrument.
3.2 Sounding rocket S-310-35 experiment
The sounding rocket S-310-35 experiment was performed as a part of the Dynamics and Energetics of the Lower Thermosphere in Aurora (DELTA) campaign, whose objectives and results were described in detail in Abe et al. (2006a) and references therein. The sounding rocket was launched from the Andøya rocket range (69.29°N, 16.01°E in geodetic coordinates) in Norway on 13th December 2004, at 01:33 LT (LT = UT + 1 h).
While an auroral breakup was occurring simultaneously with the launch, the sounding rocket flew through the auroral active region. There were two auroral active arcs which crossed the rocket trajectory. The second arc around 124–131 km altitude was within the range of sheath analysis. We should also mention that observations by the N2 temperature instrument (NTV), which emitted the artificial electron beam (Kurihara et al., 2006), onboard the rocket affected the electron densities and the probe potentials below about 115 km altitude in the ascent (see Wakabayashi and Ono, 2006).
3.3 Impedance probe onboard the sounding rockets
While other impedance measurement system found that for sufficiently dense plasma, the parallel circuit resonance appeared at less than the UHR frequency due to the stray capacitance (Kiraga, 2003), the NEI systems from the rocket flights S-520-23 and S-310-35 have not observed the parallel circuit resonance. Pre-flight environmental tests performed in the space plasma simulation chamber at ISAS/JAXA also ensured the reproducibility of the results with well defined, sharp absolute minimum which can be assigned to the upper hybrid frequency. Data pertinent to space ambient plasma show up the same signature of the upper hybrid frequency. The NEI instruments onboard the S-520-23 and S-310-35 rockets therefore realized the accurate measurements of the electron density without the effect of the stray capacitance.
The NEI systems of S-310-35 and S-520-23 are designed to measure the equivalent probe capacitance over the frequency ranges of 300 kHz–10.3 MHz and 300 kHz–12.0 MHz, respectively. The frequency resolution of the impedance probe onboard S-310-35 was 10.0 kHz from (0.3–4.3) MHz and 20 kHz from (4.3–10.3) MHz. In the case of S-520-23, the frequency resolution was 9.4 kHz from (0.3–2.0) MHz, 20.0 kHz from (2.0–4.0) MHz, 50.0 kHz from (4.0–8.0) MHz, and 100.0 kHz from (8.0–12.0) MHz. The time resolution of the impedance probes was about 500 msec.
The observed frequency variations of the equivalent probe capacitance provide the sheath capacitances and the UHR frequencies. In the following analysis, we identified the equivalent probe capacitance measured at around the 300 kHz, which was sufficiently lower than the observed SHR frequencies, as the sheath capacitance. Electron densities along the rocket trajectory were calculated from the observed UHR frequencies and International Geomagnetic Reference Field (IGRF) model. We also used the electron temperature data measured by the fast Langmuir probes onboard the rockets to obtain the Debye length. The Langmuir probe data were running averaged to reduce the effects of the rocket wake.
4. Observations of the Sheath Capacitance
4.1 Observations during the ascent of the S-520-23 sounding rocket
The sensor of the impedance probe was extended at 56.5 sec after the rocket launch, and measurements were successfully operated above 93.1 km. During the ascending phase of the S-520-23 sounding rocket, measurements were performed under quiet plasma conditions. Although the impedance probe was exposed to the sun during the observations, the effects of photoelectrons on the probe potential are negligible in the ionosphere.
4.2 Observations during the descent of the S-520-23 sounding rocket
In the descent of the S-520-23 sounding rocket, LES released Li gas. As the Li releases were strongly disturbing the equivalent probe capacitance, it became difficult to deduce the electron densities by detecting the UHR frequencies after the each Li release. On the other hand, the equivalent probe capacitances measured at lower frequency than SHR frequency were not so fluctuated as capacitance curves around the UHR frequency even after the Li releases.
The most likely interpretation is that Li release caused increases of the plasma density. The observed sheath capacitance variation corresponded to the increase of the electron density of about 1–2 orders of magnitude. The effects of the chemical release on the ionosphere are intriguing (e.g., Szuszczewicz et al., 1996). Uemoto et al. (2010) includes detailed observations and discussion of the electron density after the Li releases.
Here, we should emphasize the practicality of the plasma diagnosis from the sheath capacitance. In rocket observations, instruments sometimes fail to measure plasma parameters due to artificial interferences. Analysis of the sheath capacitance in addition to the UHR frequency will contribute to improvement of the success rate of plasma measurements.
4.3 Observations in the auroral ionosphere
5.1 Validation of the calculation method
We also found a slight difference of the sheath capacitance in the plasma frequency range of more than 4.5 MHz, even though fpe> fce was satisfied (see Fig. 7(b)). The difference appeared periodically around the apex of the rocket flight. The periodic variation was caused by the rocket spin. The effect of rocket wake became significant near the apex and descending phase due to the rocket attitude. Since the electron temperature data were running averaged, the calculated sheath capacitances do not reflect the electron temperatures in the wake. There are some physical issues regarding how to evaluate the temperature in the wake. It is beyond the scope of this article to examine the sheath capacitance measured in the wake region.
5.2 Effect of the auroral particles precipitation
As shown in Fig. 6, the sheath capacitances measured by the S-310-35 rocket were significantly lower than that of the calculations. Note that the plasma frequencies were higher than the cyclotron frequencies except for the altitudes below 100 km, due to the ionization by auroral particles precipitation (Wakabayashi and Ono, 2006). This indicates that the difference between the observations and calculations was not derived from the condition fpe< fce as discussed in Section 5.1.
We examined the sheath capacitance measured by using impedance probe techniques. The sheath capacitance was analytically calculated from the Debye length. Such calculations are a simpler method in comparison with the PIC simulations (Miyake et al., 2008), and as a result, our method does not then require enormous computer facility.
We have compared the sheath capacitances observed by the impedance probes onboard the sounding rockets with the calculated sheath capacitances. When a condition of fpe> fce was satisfied, the equivalent probe capacitance observed at a sufficiently lower frequency than the SHR frequency showed a constant value which equaled to the sheath capacitance. The observed sheath capacitances agreed well with the calculations. This indicates that the calculation methodology of the sheath capacitance described in Section 2 is valid; and the Debye length can be estimated from the observed sheath capacitance. The advantages of this technique are summarized as follows: (a) the sheath capacitance in addition to the UHR frequency provides plasma parameters, (b) the electron density, the electron temperature and the probe potential measured via other instruments can be cross-checked with analysis of the sheath capacitance, and (c) the analysis method is simple. Since the detection of the UHR frequencies sometimes becomes hard due to plasma disturbances (e.g., effect of Li release and electron beam emission) in sounding rocket experiments, plasma diagnosis technique from the sheath capacitance is valuable. In future experiments, we propose to design the impedance probe to measure the sheath capacitance with high time resolution. This improvement allows the impedance probe to realize both high-accurate measurements of the electron density from the UHR frequency and high-resolution plasma diagnostics from the sheath capacitance.
In the case of fpe < fce, the plasma resonance clearly appeared. As a result, it became difficult to separate the sheath capacitance from the observed the equivalent probe capacitance. For accurate plasma diagnostics from the sheath capacitance obtained by the impedance probe, it is necessary that the plasma frequency is larger than the cyclotron frequency.
Observations in the auroral ionosphere indicated that the probe potential was shifted from the analytical solution of the floating potential due to the non-Maxwellian velocity distribution. Strong precipitation of energetic electrons in the auroral arc should have caused the lower probe potential. Quantitative discussion of the response of the probe potential to the total flux of precipitating auroral particles remains a future issue to examine.
The sounding rocket experiments were conducted by the Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency (ISAS/JAXA) as international projects. We thank all members of the rocket experiments. Pre-flight operation tests of the impedance probes were supported by the Space Plasma Laboratory, ISAS/JAXA. The impedance probes were manufactured by System Keisoku Co., Ltd. This work is supported by the Global COE Program “Global Education and Research Center for Earth and Planetary Dynamics” at Tohoku University.
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