Spacecraft charging

Title: Correcting moments of in situ particle distribution functions for spacecraft electrostatic charging

Authors: Benoit Lavraud, Davin E. Larson
Zotero link: Full Text

Abstract

Abstract
We first introduce previous works on spacecraft electrostatic charging and its effects on particle measurements and the calculation of moments from three‐dimensional distribution functions. We illustrate the fact that the lack of use, or misuse, of Liouville's theorem may lead to misinterpretations and inappropriate corrections to those effects. We emphasize in particular that its appropriate use naturally accounts for what is often called the “sheath focusing effect” in moment calculation. In the case of a “perfect” particle detector we show that there exists a trivial and essentially exact formulation for the calculation of moments of particle distribution functions that accounts for the spacecraft potential and that is particularly useful for onboard moment calculations. The main limitations, but that are not specific to this formulation, are inaccuracies in angle information (from blurring of acceptance angles at low energies or spacecraft‐skimming trajectory effects) and those arising from the detector properties (resolution, cutoffs, photoelectrons, etc.). We discuss this correction in the context of previous works and remind that it primarily affects low‐energy measurements and for populations whose temperature is comparable to the potential. Based on spacecraft observations, we show that this correction is most needed for regimes such as that of solar wind electrons but also for cold ions as often observed, for instance, in the magnetosphere near the Earth's magnetopause.
,
Key Points

Introduction of past work on spacecraft potential correction

Description of proper method to correct particle moments from spacecraft charging

Illustration of the impact of this correction from spacecraft data

Questions

Highlight (Page 2)

For a positive potential, ambient electrons will be bent in such a way that the fluxes measured at the detector at a given energy are higher than the actual fluxes in the ambient medium at the true (nonaccelerated) energy, owing to a focusing of the electron trajectories (the phase space density is conserved, however, as discussed in the next section). This phenomenon is generally called a “spacecraft sheath focusing” effect.

[!quote]+ Highlight (Page 2)
Scudder et al. [2000] [cf. also Pedersen, 1995; Laakso et al., 1995] use the bias voltage of electric field booms as a proxy of the spacecraft potential

Important points

Highlight (Page )

A spacecraft immersed in a collisionless plasma absorbs ambient electrons and ions and ejects photoelectrons, backscattered electrons, and secondary electrons.

[!quote]+ Highlight (Page 2)
Photoelectrons emitted from the spacecraft body with energies less than qΦ do not contribute to the net spacecraft current because they cannot escape the spacecraft electrostatic potential well and will return to the spacecraft surface. Therefore, for a positively charged spacecraft these photoelectrons can be measured by an electron analyzer on board the spacecraft. These returning photoelectrons necessarily have energies below qΦ. Therefore, in such a case a measured electron spectrum will be constituted of strong photoelectron fluxes at energies below qΦ and of the ambient electron spectrum above qΦ.

[!quote]+ Highlight (Page 2)
For a positive spacecraft potential, if an electron detector minimum measured energy Emin is lower than qΦ then it generally observes a break in the spectrum at low energy. As explained in section 1.1, this break separates the photoelectron population (below qΦ) from the ambient population (above qΦ) and allows an estimate of the spacecraft potential to be determined. The precision and accuracy of this estimate depend on the energy bin spacing and energy resolution of the instrument. If on the contrary qΦ < Emin then the photoelectron spectrum will not be observed and other means are required

[!quote]+ Highlight (Page 2)
the potential Φ can also be chosen such that the computed electron charge density is equal to the computed ion charge density or the density as determined by the plasma frequency...from an electric field wave experiment

[!quote]+ Highlight (Page 3)
It is also possible to determine empirical relationships for Φ as a function of the plasma properties [e.g., Thomsen et al., 1999; Scudder et al., 2000; Bouhram et al., 2002] and the relatively constant solar UV flux.

Solar UV radiation causes emission of photoelectrons and charges the spacecraft positively. When the spacecraft is in the nightside the Photoelectric effect reduces and it can get negatively charge by Diffusion on the walls (electrons have higher mobility). The balance of the Current Densitys determines the Floating potential and is dependent on the plasma density and temperature. @lavraudCorrectingMomentsSitu2016 .

#Motivation rojoElectronMomentsDerived2024#^VI9ZAHBF

For positive charge, all electrons will be measured but with an energy shift $q Φ$ . Photoelectrons with energies lower that that will return to the spacecraft and be measured by the Plasma analyzer.

#Explanation lavraudCorrectingMomentsSitu2016#^K4Z2BXZ3

Title: Electron moments derived from the Mercury Electron Analyzer during the cruise phase of BepiColombo

Authors: M. Rojo, M. Persson, J.-A. Sauvaud, S. Aizawa, G. Nicolaou, E. Penou, A. Barthe, N. André, C. Mazelle, A. Fedorov, S. Yokota, Y. Saito, D. Heyner, I. Richter, U. Auster, D. Schmid, D. Fischer, T. Horbury, C. J. Owen, M. Maksimovic, Y. Khotyaintsev, P. Louarn, G. Murakami
Zotero link: Full Text

Abstract

Aims.
We derive electron density and temperature from observations obtained by the Mercury Electron Analyzer on board Mio during the cruise phase of BepiColombo while the spacecraft is in a stacked configuration.

Methods.
In order to remove the secondary electron emission contribution, we first fit the core electron population of the solar wind with a Maxwellian distribution. We then subtract the resulting distribution from the complete electron spectrum, and suppress the residual count rates observed at low energies. Hence, our corrected count rates consist of the sum of the fitted Maxwellian core electron population with a contribution at higher energies. We finally estimate the electron density and temperature from the corrected count rates using a classical integration method. We illustrate the results of our derivation for two case studies, including the second Venus flyby of BepiColombo when the Solar Orbiter spacecraft was located nearby, and for a statistical study using observations obtained to date for distances to the Sun ranging from 0.3 to 0.9 AU.

Results.
When compared either to measurements of Solar Orbiter or to measurements obtained by HELIOS and Parker Solar Probe, our method leads to a good estimation of the electron density and temperature. Hence, despite the strong limitations arising from the stacked configuration of BepiColombo during its cruise phase, we illustrate how we can retrieve reasonable estimates for the electron density and temperature for timescales from days down to several seconds.

Blue

Highlight (Page 8)

electron temperature Te calculated using our method with the secondary electrons removed agrees remarkably well with those of Dakeyo et al. (2022) down to around 0.4 AU.

[!quote]+ Highlight (Page 9)
If photo emission is the main process producing secondary electrons, we should not observe a correlation between the SW electron density ne and the secondary electron density nesec. Indeed, PE depends only on the extreme ultraviolet photon intensity. On the contrary, if SEEE dominates, we should observe a strong correlation between ne and nesec.

[!quote]+ Highlight (Page 9)
we can conclude that the main secondary emission process is SEEE. The derived slope indicates that the nesec represents about one-third of the SW electron density

[!quote]+ Highlight (Page 10)
the electron density calculated from MEA 3D and the OMNI data products are highly correlated. It may therefore be possible to apply a corrective factor on the densities derived from the MEA OMNI data products in order to increase their time resolution significantly.

Questions

Note (Page 2)

Around the Earth a spacecraft can experience a negative potential (typically in the shadow region) or a positive potential (in the sunlight). During very energetic events like magnetic substorms, a spacecraft can experience negative potentials of several thousand volts. Typically, scientific spacecraft traveling through the SW have potentials varying between 0 and +10 volt (Matéo-Vélez et al. 2018; Sarno-Smith et al. 2016). Classical processes related to plasma-surface interactions in space include photo-emission (PE), secondary electron emission under electron (SEEE) or ion (SEEI) impact, or backscattered electrons (BEs). In the current equation, Φsc reaches a stationary state when the sum of all currents on the spacecraft is equal to zero. #Look-into

[!quote]+ Highlight (Page 3)
In this work we focus on the MEA 1 sensor because it is the only one that can provide 3D data products #Question

In general? Telemetry?

[!quote]+ Highlight (Page 3)
Therefore, in order to obtain the most accurate moments, we create a virtual channel that uses the maximum count rates between channels 6 and 7 of MEA 1 #Question

Why not take every non-obstracted direction? Doesn't this bias the direction of the beam? Bias in secondary electrons?

[!quote]+ Highlight (Page 3)
Then we assume that the main electron population is isotropic, which is a reasonable assumption for the core electron population of the SW #Question

Isn't it a beam?

[!quote]+ Note (Page 3)
The classical method to determine the spacecraft potential from electrostatic analyzer measurements consists of identifying a discontinuity in the observed count rates at low energies, which is caused by the secondary electron emitted with enough energy to escape...the spacecraft electric sheath. Then, using the Liouville theorem and assuming that the plasma sheath between the spacecraft and the undisturbed plasma is collisionless, it is possible to shift in energy the phase space density (PSD) in order to determine the electron moments

[!quote]+ Highlight (Page 4)
As a consequence channels 6 and 7 of the MEA instrument used in this work make an angle of ±45◦ with respect to the ecliptic plane at maximum, and are typically perpendicular to the interplanetary magnetic field. The limited pitch angle distributions of electrons observed by MEA during the cruise phase of BepiColombo prevent us from detecting anisotropic features on their distribution functions, as reported by Halekas et al. (2020) and Berciˇ c et al. ˇ (2019). #Question

Not even if we analyse each section separately? Does it mean that the plane of the sectionsis perpendicular?

[!quote]+ Highlight (Page 5)
During this time interval the two spacecraft are almost radially aligned, and are located at a close distance ranging from 225 to 290 Venus radii from each other. This unique two-point measurement configuration is particularly advantageous since the two spacecraft should have observed the same solar wind plasma populations. #Question

How do we calculate when they are close enough? How do we have mag data?

[!quote]+ Highlight (Page 5)
The three large data gaps observed are due to wheel off-loadings (WoLs) #Question

What

[!quote]+ Highlight (Page 5)
The RPW allows an accurate estimation of the electron density neRPW, which is anti-correlated to the SolO potential. As explained in Khotyaintsev et al. (2021), ΦSolO has a logarithmic dependence on neRPW. #Look-into

[!quote]+ Highlight (Page 5)
Khotyaintsev

[!quote]+ Highlight (Page 5)
In order to obtain neEAS, the counts below the spacecraft potential measured by RPW were removed, then the PSD was shifted to the cutoff energy of EAS.

[!quote]+ Highlight (Page 7)
We also note that the secondary electron density seems to be correlated with the SW density, showing that the nature of the secondary emission is likely SEEE. If it was produced by PE, no correlation would be observed

Why?

[!quote]+ Highlight (Page 7)
For each distance bin, the density distribution is normalized by its maximum value, where the solid black line links all the density maxima at each distance bin.

[!quote]+ Highlight (Page 9)
In order to adjust neOmni to ne3D without secondary electrons, we subtract ne3D-OMNI to ne3D. This difference with a time step of 640 s is interpolated for the real Omni data product where the time step is 4 s. Then we interpolate the difference for the time steps (4 s) of all the Omni data products

For this to work the deviation from linear correlation has to be a non- random process. How do we ensure that?

[!quote]+ Highlight (Page 9)
Between 10:30 and 13:30 we observe fluctuations of ne3D. These variations are correlated with the SW count rate measured in 20–40 eV energy range on the 3D virtual channel spectra. These fluctuations are barely visible in the Omni spectra. Hence, this shifted neOmni becomes closely related with the 3D virtual channel that is only open to space, and no longer with the Omni data products.

Important points

Note (Page 2)

two Mercury Electron Analyzers (MEA 1 and 2, shown in Fig. 1) that will detect electrons for the first time in the Mercury orbit over a low-energy range (from 3 eV to 26 keV).

[!quote]+ Note (Page 2)
electrostatic analyzers like MEA have a distorted FoV for low-energy charged particles when the spacecraft surfaces remain negatively or positively charged

[!quote]+ Highlight (Page 2)
Spacecraft charging strongly affects the determination of plasma moments, especially those of solar wind electrons. For instance, a positive spacecraft potential will accelerate electrons, and hence can shift the electron energy distribution function (EEDF) toward higher energies. In addition, secondary electrons emitted from the spacecraft’s charged surfaces can be re-collected and can contaminate the EEDF....fore necessary to remove the secondary electron contribution in order to obtain the most accurate estimation of the plasma moments (Lewis et al. 2008; Rymer 2004; Génot & Schwartz 2004; Lavraud & Larson 2016)

[!quote]+ Note (Page 3)
. In order to derive Et-OMNI (hereafter OMNI), the count rates from all channels are simultaneously integrated for each energy bin

[!quote]+ Highlight (Page 5)
we use the proton bulk velocity measured by SolO/PAS to time-shift the magnetic field vector B measured by SolO to the location of BepiColombo.

[!quote]+ Highlight (Page 5)
The main difference is due to the Venus bow shock crossing by BepiColombo around 14:00 UTC (Persson et al. 2022), represented by the vertical green dashed line. Since B is “frozen in” to the plasma, the two spacecraft should therefore have observed the same solar wind plasma populations.

[!quote]+ Note (Page 8)
Since only a limited dataset restricted to three days is obtained by BepiColombo in this region of the heliosphere, this discrepancy may be due to a colder than usual solar wind electron population observed by BepiColombo at that time

[!quote]+ Highlight (Page 8)
Because these observations are obtained when BepiColombo is in the shadow of Mercury, we deduce that the observed secondary electrons are produced by SEEE and confirm that they are not photoelectrons.

@rojoStructureDynamicsHermean2024

Measurement of spacecraft potential

#Motivation rojoElectronMomentsDerived2024#^Y725T2RB

Using an particle measurements for a positively charged spacecraft we can measure a break in the spectrum at low energies, separating the photolectrons and the ambient population.

#Explanation lavraudCorrectingMomentsSitu2016#^4QY7X9UY

Using field measurements we can set the electron charge density equal to the plasma density as calculated by the Plasma frequency. We can also use the bias voltage of electric field booms ( #Question How? )

lavraudCorrectingMomentsSitu2016#^PGKY32LX
lavraudCorrectingMomentsSitu2016#^H2K2VURY

We can also use empirical models of $Φ$ as a function of plasma properties and UV Flux Density

@lavraudCorrectingMomentsSitu2016

differential charging of spacecraft --> nno photoelectron in MEA1
precipitating electrons --> shoulnt we measure X-rays?
gradial acceleration by whistler waves - time scale?
time dealy between waves and electrons - if one generated the other isnt it normal?