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Estimation and subtraction of spurious sunward electric field component in double probe observation by GEOTAIL/EFD in tenuous space plasmas

This paper presents a method to estimate and subtract spurious sunward electric field components from GEOTAIL/EFD double-probe observations in tenuous plasmas by leveraging the relationship between the spurious field and spacecraft potential, thereby enabling the retrieval of accurate natural electric fields in the Earth's magnetosphere and solar wind.

Original authors: Tomoko Nakagawa, Yasumasa Kasaba, Ayako Matsuoka, Iku Shinohara, Yoshifumi Saito

Published 2026-09-01

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CC BY 4.0

Original authors: Tomoko Nakagawa, Yasumasa Kasaba, Ayako Matsuoka, Iku Shinohara, Yoshifumi Saito

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Space is not empty; it is a vast ocean of invisible, charged particles called plasma. To understand how this ocean moves and behaves, scientists need to measure the electric fields that drive it, much like a meteorologist needs to measure wind speed to predict a storm. One of the most reliable ways to do this is by stretching out long wires from a spinning satellite, with small metal spheres at the ends to act as sensors. As the satellite spins, these sensors sweep through the plasma, measuring the voltage difference between them to calculate the electric field. However, in the thin, sparse regions of space far from Earth, this method often produces a ghostly error. The sensors pick up a false electric field that always points toward the Sun, even when no such field exists. This phantom signal is caused by the satellite itself: sunlight hits the metal spheres, knocking electrons loose, and the positively charged body of the satellite pulls some of those electrons back in a way that tricks the sensors into seeing a force that isn't there.

For decades, this error has forced researchers to ignore certain directions when studying space weather, leaving gaps in our understanding of how energy flows through the solar system. A team of scientists led by Tomoko Nakagawa has now developed a way to see through this illusion. By analyzing data collected over more than a decade by the Geotail satellite, they found a predictable pattern linking the size of the error to the electrical charge of the satellite itself. They discovered that as the satellite's charge increases, the false electric field grows in a specific, calculable way. Using this relationship, they created a method to estimate the size of the error and subtract it from the raw data, revealing the true, natural electric fields hidden beneath the noise.

The researchers focused on data gathered between 1994 and 2005, a period when the Geotail satellite was exploring the distant tail of Earth's magnetic field and the solar wind. In these regions, the plasma is so thin that the satellite often builds up a significant positive electrical charge, much like a balloon rubbed against hair. This charge attracts the electrons that the satellite's own sensors emit when hit by sunlight, creating an imbalance between the two sensors. The sensor on the side facing away from the Sun loses more electrons than it can regain, causing it to register a higher voltage than the sensor on the sunward side. This difference creates a fake electric field pointing toward the Sun. The team realized that if they could measure the satellite's charge, they could calculate exactly how large this fake field was.

To test their idea, the scientists first looked for moments when the natural electric field and the magnetic field were aligned in a way that allowed them to calculate the error directly. They found that in these specific conditions, the error was indeed a sunward force, typically ranging from zero to five millivolts per meter. This is a small number, but in the context of space physics, it is large enough to distort the entire picture. More importantly, they noticed that when they plotted the size of this error against the satellite's electrical charge, the points fell along a straight line. The relationship was not perfectly simple; the line bent slightly when the charge reached about three to four volts. Below this threshold, the error grew as the charge increased. Above it, the error began to shrink and even reverse direction in some cases.

This bend in the line revealed a second, competing force at work. When the satellite's charge became high enough, it started to push away the cold, slow-moving ions of plasma flowing past it. This created a wake, a region of depleted plasma behind the satellite, similar to the low-pressure area behind a boat moving through water. In this wake, the electric field pointed away from the Sun, effectively canceling out some of the false sunward signal. By understanding this interplay, the team could create a mathematical model that estimated the error based solely on the satellite's charge, without needing the special magnetic alignment required for the initial calculation.

The result was a powerful new tool for cleaning up the data. When the researchers applied their correction to the raw measurements, the false sunward signal disappeared, leaving behind the true electric fields of the magnetosphere and solar wind. In many cases, the corrected data matched the expected motion of plasma driven by the solar wind, confirming that the error had been successfully removed. They could now see the natural electric fields in three dimensions, rather than being limited to just one direction. However, the method also highlighted the limits of their approach. In the extremely thin plasma of the magnetic tail lobes, where the satellite's charge was very high and the plasma density was incredibly low, the ion wake became so strong that it sometimes overwhelmed the correction, causing the error to flip direction entirely.

This work does not just fix old data; it opens a window into regions of space that were previously difficult to study. By removing the artifact caused by the satellite's own interaction with the environment, scientists can now get a clearer view of how energy moves through the Earth's magnetic shield. The study suggests that while the error is a persistent challenge in thin space plasmas, it is not an unsolvable mystery. With the right understanding of how the satellite charges and how the surrounding plasma reacts, the ghostly signals can be identified and subtracted, allowing the true voice of the cosmos to be heard. The findings confirm that the natural electric fields are indeed perpendicular to the magnetic field, as theory predicts, once the interference of the spacecraft itself is accounted for. This clarity is essential for understanding the complex dance of particles that protects our planet and shapes the space environment around us.

Technical Summary: Estimation and Subtraction of Spurious Sunward Electric Field Component in GEOTAIL/EFD Observations

Problem Statement
Space-borne electric field measurements using the double-probe method in tenuous plasmas frequently suffer from a spurious, sunward-directed electric field artifact. This phenomenon is primarily attributed to an imbalance in sheath potentials between the two probes caused by spacecraft charging. Under solar UV illumination, photoelectrons emitted from the anti-solar-side probe are attracted toward the positively charged spacecraft body and wire booms, preventing their return. This asymmetry elevates the potential of the anti-solar probe relative to the sunward probe, generating an artificial sunward electric field. Additionally, spacecraft-induced ion wakes formed by cold ion flows deflected by the spacecraft potential can create anti-sunward electric fields, particularly in low-density regions like the magnetotail lobes. These artifacts have historically restricted electric field analyses to specific directions (e.g., dawn–dusk) and hindered coordinate transformations to geophysical systems.

Methodology
This study utilizes data from the Geotail Electric Field Detector (EFD), specifically the Spherical Probe Antenna (PANT), covering the period from January 1994 to December 2005. The authors propose a method to estimate and subtract the spurious sunward component ( $E_{sp}$ ) from the observed electric field ( $E_{obs}$ ) based on three primary assumptions:

The observed field is the sum of the natural field ( $E_{nat}$ ) and the spurious component ( $E_{obs} = E_{nat} + E_{sp}$ ).
The natural electric field is perpendicular to the background magnetic field ( $B$ ), such that $E_{nat} \cdot B = 0$ .
The spurious electric field is directed sunward (parallel to the sun–spacecraft line).

Direct Calculation: When the background magnetic field lies parallel to the spacecraft spin plane (where $B_z \approx 0$ ), the spurious sunward component ( $E_{spx}$ ) can be directly calculated using the inner product of the observed electric field and the magnetic field vectors within the antenna plane:
$E_{spx} = \frac{E_{obsx}B_x + E_{obsy}B_y}{B_x}$
This calculation is performed only when the angle between the magnetic field and the spin plane is less than 3 degrees ( $\theta < 0.05$ ).

Indirect Estimation: To extend this correction to periods where the magnetic field is not parallel to the spin plane, the authors established a relationship between the calculated spurious field and the spacecraft potential ( $\phi_{sc}$ ). Analysis revealed a piecewise linear relationship between $E_{spx}$ and $\log(\phi_{sc})$ with a distinct bend at approximately 3–4 V:

Low Potentials ( $\phi_{sc} < 3\text{--}4$ V): A positive slope indicates the spurious field increases with spacecraft potential, driven by photoelectron asymmetry.
High Potentials ( $\phi_{sc} > 3\text{--}4$ V): A negative slope indicates the spurious field decreases (or becomes anti-sunward), attributed to the formation of an ion wake that counteracts the photoelectron-induced field.

Using these regression fits derived from monthly data windows, the spurious component is estimated from the spacecraft potential and subtracted from the raw data to retrieve the corrected natural electric field.

Key Results

Magnitude: The estimated spurious components from 1994 to 2005 were mostly in the range of 0–5 mV/m, comparable to the magnitude of the observed sunward components.
Correction Success: In the Earth's magnetosphere and solar wind, where plasma densities were sufficient to prevent strong ion wakes, the subtraction successfully retrieved natural electric fields that aligned well with the convective $-V \times B$ fields derived from Low Energy Particle (LEP) and Magnetic Field (MGF) data.
Ion Wake Effects: In the magnetotail lobe region, characterized by extremely low plasma density ( $\sim 10^{-2}$ cm $^{-3}$ ) and high spacecraft potentials ( $>25$ V), the spurious field occasionally became anti-sunward. This was consistent with the formation of an ion wake behind the spacecraft, where the spacecraft potential exceeded the bulk energy of the cold ion flow.
Z-Component Recovery: By removing the spurious sunward component, the authors successfully estimated the electric field component parallel to the spin axis ( $E_z$ ), assuming $E_{nat} \cdot B = 0$ . This allowed for more complete coordinate transformations in regions where $B_z$ was not negligible.

Significance and Claims
The paper claims to provide a robust method for estimating and subtracting spurious sunward electric field components in double-probe observations, thereby retrieving the natural electric field in tenuous space plasmas. The significance of this work lies in:

Data Recovery: Enabling the use of electric field data in regions and coordinate systems previously restricted due to spurious artifacts.
Physical Insight: Validating the dual nature of the artifact—photoelectron asymmetry at lower potentials and ion wake effects at higher potentials—by correlating the spurious field with spacecraft potential.
Methodological Extension: Demonstrating that the relationship between the spurious field and spacecraft potential allows for the estimation of the artifact even when the magnetic field configuration does not permit direct calculation (i.e., when $B_z \neq 0$ ).

The authors note that while the method is highly effective for Geotail due to its specific spin axis orientation relative to the sun and magnetic field, its application to other spacecraft may be limited by their specific attitude and orbital trajectories, particularly in the inner magnetosphere where cold ion flow directions may deviate from the sunward-anti-sunward alignment.

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