Quasi-thermal Noise Research Articles

Electron Temperatures in the Venusian Ionosphere From Parker Solar Probe Using Quasi‐Thermal Noise Spectroscopy

AbstractParker Solar Probe (PSP) uses Venus gravity assists (VGA) to achieve the closest orbits to the Sun by a spacecraft. During the third (VGA3) and fourth (VGA4) Venus gravity assists, the PSP entered the Venusian ionosphere. The core electrons could not be detected as they were below the SWEAP/SPAN electrostatic analyzer instrument energy threshold. However, there is another way to estimate the core temperature using quasi‐thermal noise (QTN) data measured by the PSP/FIELDS Radio Frequency Spectrometer instrument. QTN spectroscopy offers an effective tool for measuring electron temperature and density when the electrons are too cold for other instruments to measure, as is the case with VGA3 and VGA4. Low‐frequency plasma wave data from the closest approach during VGA3 and VGA4 was analyzed with the QTN spectroscopy technique to determine the density and first‐ever in‐situ thermal electron temperature of the Venusian ionosphere at solar minimum.

On the Plasma Quasi-thermal Noise in the Outer Heliosphere

The recent paper by Li et al. on electron quasi-thermal noise (QTN) in the outer heliosphere is flawed. It assumes the plasma drift speed to be much smaller than the electron thermal speed, even though both quantities are of the same order of magnitude in the outer heliosphere inward of the termination shock, because of the low plasma temperature. In this case, the Langmuir wave dispersion equation and the QTN in the antenna frame are completely changed. Furthermore, these calculations neglect the shot noise, which should produce a large contribution below the plasma frequency with the Voyager antennas in the outer heliosphere.

Solar Wind Density and Core Temperature Derived from the PSP Quasi-thermal Noise Measurements

Quasi-thermal noise (QTN) spectroscopy is a valuable method to deduce important parameters in space plasma, such as plasma density and temperature, especially when direct particle measurements are not available. The present study develops a new fitting method to fit the QTN spectra observed by the Parker Solar Probe (PSP) with a comprehensive theoretical QTN spectral model. By combining the steepest descent and Levenberg–Marquardt algorithms, the new method is more flexible with initial guess values but still yields reliable solar wind electron density and temperature values. The new method is applied to derive the solar wind density and core temperature from the QTN measurements during 10 encounters of PSP. The electron density and temperature values obtained vary with the radial distance from the Sun as n e ∝ r −2.12 and T e ∝ r −0.71, both of which are consistent with existing models and previous results.

Radial Distribution of Electron Quasi-thermal Noise in the Outer Heliosphere

Voyager 1 and 2 are only the two spacecraft that have arrived and passed through the heliospheric boundaries. Based on the plasma data from the Voyager 2 spacecraft, the electron quasi-thermal noise (QTN) is investigated by using of the electron population model consisting of a core with Maxwellian distribution and a halo with kappa distribution. The power spectra of the electron QTN is calculated at different heliocentric distances from 1 to 110 au. The parametric dependence of the QTN power spectra and the effective Debye length on the model parameters, such as the density ratio and temperature ratio of the halo to the core, kappa index and the antenna length, are discussed further. The results show that the electron QTN spectrum consists of a plateau in the low frequency band f < f pt , a prominent peak at the plasma frequency f pt , and a rapid decreasing part in the high frequency band f > f pt . The QTN plateau level basically falls down outwards until the termination shock crossing at about 84 au, after which the plateau rebounds a little near the heliopause. Although the model parameters can be very variable, the QTN plateau level does not present more than the double change in a fairly wide range of the model parameters. The presented results can be useful for future deep-space explorations in the heliosphere and can provide valuable references for the design of onboard detectors.

Voyager 1 Electron Densities in the Very Local Interstellar Medium to beyond 160 au

The two Voyager spacecraft have been exploring the interstellar medium beyond the heliopause since 2012 (Voyager 1) and 2018 (Voyager 2). Electron plasma oscillations and a quasi-thermal noise line at the electron plasma frequency have enabled the determination of the electron density in this region, revealing a radial density gradient convolved with shocks and pressure fronts. Voyager 1 has a functioning wideband receiver that provides high-spectral-resolution observations allowing the detection of the quasi-thermal noise line and has now provided electron densities to 161.4 au. Since a pressure pulse observed in 2020 around day 146 at about 149 au, the density has remained relatively constant at 0.147 cm−3 based on the most recent observations from 2023, suggesting that Voyager 1 has reached a broad density peak and possibly a new regime.

Plasma line detected by Voyager 1 in the interstellar medium: Tips and traps for quasi-thermal noise spectroscopy

The quasi-thermal motion of plasma particles produces electrostatic fluctuations, whose voltage power spectrum induced on electric antennas reveals plasma properties. In weakly magnetised plasmas, the main feature of the spectrum is a line at the plasma frequency – proportional to the square root of the electron density – whose global shape can reveal the electron temperature, while the fine structure reveals the suprathermal electrons. Since it is based on electrostatic waves, quasi-thermal noise spectroscopy (QTN) provides in situ measurements. This method has been successfully used for more than four decades in a large variety of heliosphere environments. Very recently, it has been tentatively applied in the very local interstellar medium (VLISM) to interpret the weak line discovered on board Voyager 1 and in the context of the proposed interstellar probe mission. The present paper shows that the line is still observed in the Voyager Plasma Wave Science data, and concentrates on the main features that distinguish the plasma QTN in the VLISM from that in the heliosphere. We give several tools to interpret it in this medium and highlight the errors arising when it is interpreted without caution, as has recently been done in several publications. We show recent solar wind data, which confirm that the electric field of the QTN line in a weakly magnetised stable plasma is not aligned with the local magnetic field. We explain why the amplitude of the line does not depend on the concentration of suprathermal electrons, and why its observation with a short antenna does not require a kappa electron velocity distribution. Finally, we suggest an origin for the suprathermal electrons producing the QTN and we summarise the properties of the VLISM that could be deduced from an appropriate implementation of QTN spectroscopy on a suitably designed instrument.

Quasi-thermal Noise Spectroscopy Analysis of Parker Solar Probe Data: Improved Electron Density Model for Solar Wind

We present a comprehensive analysis of electron density measurements in the solar wind using quasi-thermal noise (QTN) spectroscopy applied to data from the first 15 encounters of the Parker Solar Probe mission (2018 November–2023 March). Our methodology involves the identification of the plasma line frequency and the calculation of plasma density based on in situ measurements. By analyzing over 2.1 million data points, we derive a power-law model for electron density as a function of radial distance from the Sun in the range of 13 to 50 R ☉: n e(r) = (343,466 ± 19921) × r (−1.87±0.11). This model provides improved estimates for localizing interplanetary solar radio bursts. Moreover, obtained electron densities can be used for calibrating particle instruments on board the Parker Solar Probe. We discuss its limitations and potential for further refinement with additional Parker Solar Probe encounters.

Precision electron measurements in the solar wind at 1 au from NASA’s Wind spacecraft

Context. The non-equilibrium characteristics of electron velocity distribution functions (eVDFs) in the solar wind are key to understanding the overall plasma thermodynamics as well as the origin of the solar wind. More generally, they are important in understanding heat conduction and energy transport in all weakly collisional plasmas. Solar wind electrons are not in local thermodynamic equilibrium, and their multicomponent eVDFs develop various non-thermal characteristics, such as velocity drifts in the proton frame and temperature anisotropies as well as suprathermal tails and heat fluxes along the local magnetic field direction. Aims. This work aims to characterize precisely and systematically the nonthermal characteristics of the eVDF in the solar wind at 1 au using data from the Wind spacecraft. Methods. We present a comprehensive statistical analysis of solar wind electrons at 1 au using the electron analyzers of the 3D-Plasma instrument on board Wind. This work uses a sophisticated algorithm developed to analyze and characterize separately the three populations – core, halo and strahl – of the eVDF up to super-halo energies (2 keV). This algorithm calibrates these electron measurements with independent electron parameters obtained from the quasi-thermal noise around the electron plasma frequency measured by Wind’s Thermal Noise Receiver (TNR). The code determines the respective set of total electron, core, halo, and strahl parameters through non-linear least-square fits to the measured eVDF, properly taking into account spacecraft charging and other instrumental effects, such as the incomplete sampling of the eVDF by particle detectors. Results. We use four years, approximately 280 000 independent measurements, of core, halo, and strahl electron parameters to investigate the statistical properties of these different populations in the slow and fast solar wind. We discuss the distributions of their respective densities, drift velocities, temperature, and temperature anisotropies as functions of solar wind speed. We also show distributions with solar wind speed of the total density, temperature, temperature anisotropy, and heat flux of the total eVDF, as well as those of the proton temperature, proton-to-electron temperature ratio, proton-β and electron-β. Intercorrelations between some of these parameters are also discussed. Conclusions. The present data set represents the largest, high-precision collection of electron measurements in the pristine solar wind at 1 au. It provides a new wealth of information on electron microphysics. Its large volume will enable future statistical studies of parameter combinations and their dependences under different plasma conditions.

Total electron temperature derived from quasi-thermal noise spectroscopy in the pristine solar wind from Parker Solar Probe observations

Aims. We applied the quasi-thermal noise (QTN) method to Parker Solar Probe (PSP) observations to derive the total electron temperature (Te). We combined a set of encounters to make up a 12-day period of observations around each perihelion from encounter one (E01) to ten (E10), with E08 not included. Here, the heliocentric distance varies from about 13 to 60 solar radii (R⊙). Methods. The QTN technique is a reliable tool to yield accurate measurements of the electron parameters in the solar wind. We obtained Te from the linear fit of the high-frequency part of the QTN spectra acquired by the RFS/FIELDS instrument. Then, we provided the mean radial electron temperature profile, and examined the electron temperature gradients for different solar wind populations (i.e. classified by the proton bulk speed, Vp, and the solar wind mass flux). Results. We find that the total electron temperature decreases with the distance as ∼R−0.66, which is much slower than adiabatic. The extrapolated Te based on PSP observations is consistent with the exospheric solar wind model prediction at ∼10 R⊙, Helios observations at ∼0.3 AU, and Wind observations at 1 AU. Also, Te, extrapolated back to 10 R⊙, is almost the same as the Strahl electron temperature, Ts (measured by SPAN-E), which is considered to be closely related to or even almost equal to the coronal electron temperature. Furthermore, the radial Te profiles in the slower solar wind (or flux tube with larger mass flux) are steeper than those in the faster solar wind (or flux tube with smaller mass flux). The more pronounced anticorrelation of Vp–Te is observed when the solar wind is slower and located closer to the Sun.

Wind/Waves Antenna Length Determined Using Quasi-Thermal Noise Spectroscopy

The Wind/Waves instrument has been collecting in situ electric field measurements in the solar wind as well as Earth's magnetosphere and geotail since 1994. The Thermal Noise Receiver (TNR) sub-instrument uses a wire dipole made of very long and thin whip antennas, highly convenient for Quasi-Thermal Noise (QTN) measurements. The instrument team has determined that twice during the mission, in 2000 and 2002, one of the antenna arms broke, changing the antenna response to plasma fluctuations. In this note, we use the QTN spectroscopy method developed specially for the TNR to determine the antenna length after each of these breaks. By parametrically varying the value of the antenna length used in the QTN calculation, we find that initial 50 m long antenna arm was initially shortened to ∼25.5 m in 2000, and then to ∼20 m in 2002.

Weak line discovered by Voyager 1 in the interstellar medium: Quasi-thermal noise produced by very few fast electrons

A weak continuous line has been recently discovered onboard Voyager 1 in the interstellar medium, whose origin raised two major questions. First, how can this line be produced by plasma quasi-thermal noise on the Voyager short antenna? Second, why does this line emerge at some distance from the heliopause? We provide a simple answer to these questions, which elucidates the origin of this line. First, a minute quantity of supra-thermal electrons, as generally present in plasmas – whence the qualifier ‘quasi-thermal’ – can produce a small plasma frequency peak on a short antenna, of amplitude independent of the concentration of these electrons; furthermore, the detection required long spectral averages, alleviating the smallness of the peak compared to the background. We therefore attribute the observed line to a minute proportion of fast electrons that contribute negligibly to the pressure. Second, we suggest that, up to some distance from the heliopause, the large compressive fluctuations ubiquitous in this region prevent the line to emerge from the statistical fluctuations of the receiver noise because it is blurred out by the averaging required for detection, especially in the presence of short-wavelength density fluctuations. These results open up novel perspectives for interstellar missions, by showing that a minute proportion of fast electrons may be sufficient to measure the density even with a relatively short antenna, because the quietness of the medium enables a large number of spectra to be averaged.

Origin of the Weak Plasma Emission Line Detected by Voyager 1 in the Interstellar Medium: Evidence for Suprathermal Electrons

Abstract Recently, a very weak, nearly continuous plasma wave emission line has been discovered in the nearby interstellar medium at the electron plasma frequency. The new observations were made by the plasma wave instrument on the Voyager 1 spacecraft, which crossed into the interstellar medium in 2012 August. Several questions remained unanswered after the initial discovery. Why was the emission line not observed until several years after Voyager 1 entered the interstellar medium, what is the wavelength of the plasma oscillations responsible for the emission line, and what is the origin of the oscillations? Here, we provide answers to these questions. On the most important question, namely the origin of the oscillations, the evidence strongly suggest that the emission is driven by suprathermal electrons that excite plasma oscillations comparable to the quasi-thermal noise (QTN) that is commonly observed by space plasma wave instruments with long, thin electric dipole antennas. These results imply the existence of a relatively dense population of suprathermal electrons that could contribute significantly to the overall pressure in the interstellar medium. Although the similarities to the previous QTN observations are impressive, there is no certainty that the emissions are driven by thermal excitation, and other sources should be explored, such as the possibility that they are driven by pressure fluctuations associated with the short-wavelength cascade of interstellar turbulence.

Solar wind energy flux observations in the inner heliosphere: first results from Parker Solar Probe

Aims.We investigate the solar wind energy flux in the inner heliosphere using 12-day observations around each perihelion of Encounter One (E01), Two (E02), Four (E04), and Five (E05) of Parker Solar Probe (PSP), respectively, with a minimum heliocentric distance of 27.8 solar radii (R⊙).Methods.Energy flux was calculated based on electron parameters (densityne, core electron temperatureTc, and suprathermal electron temperatureTh) obtained from the simplified analysis of the plasma quasi-thermal noise (QTN) spectrum measured by RFS/FIELDS and the bulk proton parameters (bulk speedVpand temperatureTp) measured by the Faraday Cup onboard PSP, SPC/SWEAP.Results.Combining observations from E01, E02, E04, and E05, the averaged energy flux value normalized to 1R⊙plus the energy necessary to overcome the solar gravitation (WR⊙) is about 70 ± 14 W m−2, which is similar to the average value (79 ± 18 W m−2) derived by Le Chat, G., Issautier, K., &amp; Meyer-Vernet, N. (2012, Sol. Phys., 279, 197) from 24-yr observations by Helios, Ulysses, and Wind at various distances and heliolatitudes. It is remarkable that the distributions ofWR⊙are nearly symmetrical and well fitted by Gaussians, much more so than at 1 AU, which may imply that the small heliocentric distance limits the interactions with transient plasma structures.

Narrowband oblique whistler-mode waves: comparing properties observed by Parker Solar Probe at &lt;0.3 AU and STEREO at 1 AU

Aims.Large amplitude narrowband obliquely propagating whistler-mode waves at frequencies of ~0.2fce(electron cyclotron frequency) are commonly observed at 1 AU, and they are most consistent with the whistler heat flux fan instability. We want to determine whether similar whistler-mode waves occur inside 0.3 AU and how their properties compare to those at 1 AU.Methods.We utilized the waveform capture data from the Parker Solar Probe Fields instrument from Encounters 1 through 4 to develop a data base of narrowband whistler waves. The Solar Wind Electrons Alphas and Protons Investigation (SWEAP) instrument, in conjunction with the quasi-thermal noise measurement from Fields, provides the electron heat flux, beta, and other electron parameters.Results.Parker Solar Probe observations inside ~0.3 AU show that the waves are often more intermittent than at 1 AU, and they are interspersed with electrostatic whistler-Bernstein waves at higher-frequencies. This is likely due to the more variable solar wind observed closer to the Sun. The whistlers usually occur within regions when the magnetic field is more variable and often with small increases in the solar wind speed. The near-Sun whistler-mode waves are also narrowband and large amplitude, and they are associated with beta greater than 1. The association with heat flux and beta is generally consistent with the whistler fan instability. Strong scattering of strahl energy electrons is seen in association with the waves, providing evidence that the waves regulate the electron heat flux.

Persistent plasma waves in interstellar space detected by Voyager 1.

In 2012, Voyager 1 became the first in situ probe of the very local interstellar medium1. The Voyager 1 Plasma Wave System has given point estimates of the plasma density spanning about 30 au of interstellar space, revealing a large-scale density gradient2,3 and turbulence4 outside the heliopause. Previous studies of the plasma density relied on the detection of discrete plasma oscillation events triggered ahead of shocks propagating outwards from the Sun and used to infer the plasma frequency and hence density5,6. We present the detection of a class of very weak, narrowband plasma wave emission in the Voyager 1 data that persists from 2017 onwards and enables the first steadily sampled measurement of the interstellar plasma density over about 10 au with an average sampling distance of 0.03 au. We find au-scale density fluctuations that trace interstellar turbulence between episodes of previously detected plasma oscillations. Possible mechanisms for the narrowband emission include thermally excited plasma oscillations and quasi-thermal noise, and could be clarified by new findings from Voyager or a future interstellar mission. The emission's persistence suggests that Voyager 1 may be able to continue tracking the interstellar plasma density in the absence of shock-generated plasma oscillation events.

Impedance and Voltage Power Spectra of a Monopole Antenna in a Warm Plasma—Derivation and Application to CubeSats

AbstractThe impedance for a monopole antenna in a warm plasma is derived and compared with the cases for wire dipole and double‐sphere antennas. This derivation produces a new expression for the monopole antenna response function, Fm1(x), which is very similar to the double‐sphere antenna response function. The monopole, wire dipole, and double‐sphere response functions are compared by modeling an antenna in Earth's ionospheric plasma (i.e., electrostatic and collisionless) and predicting the antenna capacitance and voltage power spectra for quasi‐thermal noise (QTN) and shot noise. Specifically, we assume the antennas are part of a CubeSat, which has spurred this research as most interplanetary craft carry a dipole or more complicated antenna designs on board (Imbriale, 2006, https://doi.org/10.1002/0470052783.ch3; Imbriale, Gatti et al., 2006, https://doi.org/10.1002/0470052783.ch5). The monopole antenna current distribution is assumed to be a half‐triangular current distribution (considering only the positive half of the triangular distribution), which follows that of prior authors (Balmain, 1965, https://doi.org/10.6028/jres.069D.065; Kuehl, 1966, https://doi.org/10.1002/rds196618971; Couturier et al., 1981, https://doi.org/10.1029/JA086iA13p11127) and simplifies comparison. The predictions for the shot noise and capacitance presented problems, as the integral over wave number space or k space did not converge for large values of k. The derived expression therefore remains a current problem in these situations, and no alternative has been found in the existing literature, necessitating future work to determine a more general expression. In this paper we bring the problem of an appropriate analytic monopole antenna response function to the attention of the community and outline a number of tests that can be used to verify any future expression.

First In Situ Measurements of Electron Density and Temperature from Quasi-thermal Noise Spectroscopy with Parker Solar Probe/FIELDS

Abstract Heat transport in the solar corona and wind is still a major unsolved astrophysical problem. Because of the key role played by electrons, the electron density and temperature(s) are important prerequisites for understanding these plasmas. We present such in situ measurements along the two first solar encounters of the Parker Solar Probe, between 0.5 and 0.17 au from the Sun, revealing different states of the emerging solar wind near the solar activity minimum. These preliminary results are obtained from a simplified analysis of the plasma quasi-thermal noise (QTN) spectrum measured by the Radio Frequency Spectrometer (FIELDS). The local electron density is deduced from the tracking of the plasma line, which enables accurate measurements, independent of calibrations and spacecraft perturbations, whereas the temperatures of the thermal and suprathermal components of the velocity distribution, as well as the average kinetic temperature, are deduced from the shape of the plasma line. The temperature of the weakly collisional thermal population, similar for both encounters, decreases with the distance as R −0.74, which is much slower than adiabatic. In contrast, the temperature of the nearly collisionless suprathermal population exhibits a virtually flat radial variation. The 7 s resolution of the density measurements enables us to deduce the low-frequency spectrum of compressive fluctuations around perihelion, varying as f −1.4. This is the first time that QTN spectroscopy is implemented with an electric antenna length not exceeding the plasma Debye length. As PSP will approach the Sun, the decrease in the Debye length is expected to considerably improve the accuracy of the temperature measurements.

Thermodynamic, Non-Extensive, or Turbulent Quasi-Equilibrium for the Space Plasma Environment

The Boltzmann–Gibbs (BG) entropy has been used in a wide variety of problems for more than a century. It is well known that BG entropy is additive and extensive, but for certain systems such as those dictated by long-range interactions, it is speculated that the entropy must be non-additive and non-extensive. Tsallis entropy possesses these characteristics, and is parameterized by a variable q ( being the classic BG limit), but unless q is determined from microscopic dynamics, the model remains a phenomenological tool. To this day, very few examples have emerged in which q can be computed from first principles. This paper shows that the space plasma environment, which is governed by long-range collective electromagnetic interaction, represents a perfect example for which the q parameter can be computed from microphysics. By taking the electron velocity distribution function measured in the heliospheric environment into account, and considering them to be in a quasi-equilibrium state with electrostatic turbulence known as quasi-thermal noise, it is shown that the value corresponding to , or alternatively , may be deduced. This prediction is verified against observations made by spacecraft, and it is shown to be in excellent agreement. This paper constitutes an overview of recent developments regarding the non-equilibrium statistical mechanical approach to understanding the non-extensive nature of space plasma, although some recent new developments are also discussed.

Quasi‐thermal noise spectroscopy: The art and the practice

AbstractQuasi‐thermal noise spectroscopy is an efficient tool for measuring in situ macroscopic plasma properties in space, using a passive wave receiver at the ports of an electric antenna. This technique was pioneered on spinning spacecraft carrying very long dipole antennas in the interplanetary medium—like ISEE‐3 and Ulysses—whose geometry approached a “theoretician's dream.” The technique has been extended to other instruments in various types of plasmas on board different spacecraft and will be implemented on several missions in the near future. Such extensions require different theoretical modelizations, involving magnetized, drifting, or dusty plasmas with various particle velocity distributions and antennas being shorter, biased, or made of unequal wires. We give new analytical approximations of the plasma quasi‐thermal noise (QTN) and study how the constraints of the real world in space can (or cannot) be compatible with plasma detection by QTN spectroscopy. We consider applications to the missions Wind, Cassini, BepiColombo, Solar Orbiter, and Parker Solar Probe.

Quasi‐thermal noise and shot noise spectroscopy on a CubeSat in Earth's ionosphere

AbstractWe investigate the practicality of using quasi‐thermal noise (QTN) and shot noise spectroscopy on a CubeSat in the Earth's ionosphere and constrain the satellite antenna length for optimal detection of these signals. The voltage spectra predicted for thermal Langmuir waves (QTN) and particle “shot noise” are modeled, and it is shown that the signals detected can provide two very good, independent, passive, in situ methods of measuring the plasma density and temperature in the ionosphere. The impact of the antenna potential ϕ is also discussed, and we show that the negative potential calculated for the ionosphere due to natural current flows has a significant impact on the voltage power level of the shot noise spectrum. The antenna configuration is also shown to play an important role in the shot noise, with a monopole configuration enhancing the spectrum significantly compared with a dipole. Antenna lengths on the order of 20–40 cm are found to be ideal for ionospheric plasma conditions, nicely matching CubeSat sizes and producing detectable thermal Langmuir waves and shot noise at the microvolt level. Further, with a continuous stream of data points at different latitudes and longitudes an orbiting CubeSat can produce a global picture for the ionospheric plasma density and temperature using QTN and shot noise signals. If implemented, especially in a constellation, these data would be more frequent and cover a much greater domain than current ground‐based or single‐satellite methods. This could lead to improved ionospheric models, such as the empirically based International Reference Ionosphere.