On the Applicability of Single‐Spacecraft Interferometry Methods Using Electric Field Probes

Abstract

When analyzing plasma waves, a key parameter to determine is the phase velocity. It enables us to, for example, compute wavelengths, wave potentials, and determine the energy of resonant particles. The phase velocity of a wave, observed by a single spacecraft equipped with electric field probes, can be determined using interferometry techniques. While several methods have been developed to do this, they have not been documented in detail. In this study, we use an analytical model to analyze and compare three interferometry methods applied on the probe geometry of the Magnetospheric Multiscale spacecraft. One method relies on measured probe potentials, whereas the other two use different E‐field measurements: one by reconstructing the E‐field between two probes and the spacecraft, the other by constructing four pairwise parallel E‐field components in the spacecraft spin‐plane. We find that the potential method is sensitive both to how planar the wave is, and to spacecraft potential changes due to the wave. The E‐field methods are less affected by the spacecraft potential, and while the reconstructed E‐field method is applicable in some cases, the second E‐field method is almost always preferable. We conclude that the potential based interferometry method is useful when spacecraft potential effects are negligible and the signals of the different probes are very well correlated. The method using two pairs of parallel E‐fields is practically always preferable to the reconstructed E‐field method and produces the correct velocity in the spin‐plane, but it requires knowledge of the propagation direction to provide the full velocity.

Slow Electron Holes in the Earth's Magnetosheath

“…The use of the time delay between V 1 and − V 2 provides the speed estimate of only a few km/s, but these voltage signals were poorly correlated, and the solitary wave was barely propagating along this antenna ( L 12 ≈ − 0.01), which makes the speed estimate highly uncertain (Wang et al., 2021). The revealed solitary wave velocity of about 60 km/s is consistent with the results of electric field interferometry (SM), which is another technique for estimating wave velocities (for example, Graham et al., 2016; Steinvall et al., 2022). Using solitary wave velocity V s = 60 km/s, we compute the electrostatic potential φ = ∫E L V dt and also translate temporal solitary wave profiles into spatial ones.…”

Waves in Magnetosheath Jets—Classification and the Search for Generation Mechanisms Using MMS Burst Mode Data

“…In order to determine the electric potential from $$\vec{E}$$ of the ESW, the propagation direction must be known. Single‐spacecraft timing (Steinvall et al., 2022) fails, since the magnetic field (and hence the wave propagation direction) is mainly along the shorter axial probes, resulting in an unmeasurable time lag. The ESWs are not observed by all four spacecraft, so we cannot use multi‐spacecraft timing to determine their velocity.…”

Short‐Wavelength Electrostatic Wave Measurement Using MMS Spacecraft

“…Unfortunately, the E80 interferometry technique is restricted to the spin plane, so we cannot use it to get the axial component of the wave vector. Other quantities can be timed in the axial direction, such as the potential measured at probes 5 and 6, but such timing is often unreliable (Steinvall et al., 2022).…”

“…For electrostatic waves measured by MMS, one can apply interferometry on both the probe potentials or electric fields. Using synthetic data, Steinvall et al (2022) found that one particular electric field configuration, what they call "diagonal electric field" and what we will call E80 electric field, is the most reliable quantity to apply interferometry on. In order to explain the E80 interferometry, we show in Figure 4 a schematic of MMS in the spin plane, using probes 2 and 4 we calculate the electric field E 42 , and using probes 3 and 1 we calculate the electric field E 13 .…”