Supplementary Materials for "Direct Forcing of the Collisional Auroral Ionosphere by Kinetic Alfvén Turbulence"

Supplementary Materials for “Direct Forcing of the Collisional Auroral Ionosphere by Kinetic Alfv´en Turbulence” Magnus F Ivarsen,∗Jean-Pierre St-Maurice,†Brian Pitzel, Saif Marei, and Glenn C Hussey Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Canada Kaili Song and P. T. Jayachandran Physics Department, University of New Brunswick, Fredericton, Canada Luca Spogli Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy Devin R Huyghebaert‡ Leibniz Institute of Atmospheric Physics, K¨uhlungsborn, Germany Yangyang Shen Department of Earth and Space Sciences, University of California, Los Angeles, USA Satoshi Kasahara and Kunihiro Keika Department of Earth and Planetary Science, University of Tokyo, Tokyo, Japan Yoshizumi Miyoshi and Tomo Hori Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Japan David R Themens School of Engineering, University of Birmingham, Birmingham, UK Yoichi Kazama and Shiang-Yu Wang Academia Sinica Institute of Astronomy and Astrophysics, Taipei, Taiwan Ayako Matsuoka Data Analysis Center for Geomagnetism and Space Magnetism, Kyoto University, Kyoto, Japan Iku Shinohara and Takefumi Mitani Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara, Japan Shoichiro Yokota Department of Earth and Space Science, Osaka University, Toyonaka, Japan This document contains a detailed description of the instrumentation, data, and analysis techniques applied in the the paper “Direct Forcing of the Collisional Auroral Ionosphere by Kinetic Alfv´en Turbulence”, referred to as the Main Paper. We likewise provide a detailed theoretical foundation for the D-region ‘chemical etching’ processes that we evoke to explain such low-altitude turbulence observations. I: INTRODUCTION This document supports the findings of the Main Paper, by providing technical, theoretical, and observational details concerning the many multi-instrumental conjunctions that we analyze, detailing the data analysis techniques that we have applied, and we also provide a a theoretical foundation for the chemical etching mechanism that we evoke to explain low-altitude (<90 km) HF echoes. The document is organized as follows. Section II (Figure S1) describes the core dataset used in the Main Paper, namely the ten ground-ground conjunctions between the experimental HF radar icebear and the Rabbit Lake GPS receiver in the chain network of ionospheric scintillation monitoring receivers (ISMRs). Section III (Fig- 2 Figure S 1. Six simultaneous ground-ground conjunctions between the icebear radar and observations from the CHAIN ISMR in Rabbit Lake. Each panel compares the spectral density measurements, the internal structure of the radar point-clouds denoted by a black line and the spectrum of GPS amplitude fluctuations in red and gray colors. The spectral indices are calculated automatically following Ref. [1] and are indicated, as is the Fresnel-scale. ure S2) describes an extended space-ground-ground conjunction between icebear,chain, and two European Swarm satellites. Section IV (Figures S3, S4) describes a total of ten conjunctions between icebear and the Japanese spacecraft Arase, of which one includes observations from chain. Finally, Section V provides a detailed theoretical foundation for the chemical etching mechanism, supported by the analysis of an icebear-Arase conjunction (Figure S5). II: TEN ICEBEAR-CHAIN CONJUNCTIONS Figure S1 showcases six simultaneous icebear-chain conjunctions, occurring in rapid succession during two extended events that took place on 7 July 2023 and 18 August 2022. Each panel of Figure S1 shows the composite powerspectrum for each conjunction event. We normalize the power amplitude to facilitate a direct spectral shape comparison, and we apply an automatic spectral slope- & break-point detection algorithm based on piecewise linear Hermite polynomials [4], with close details described in, e.g., Ref. [1] and Ref. [5]. For scale-sizes between 750 m and 3000 m the spectral shapes from the 3 Figure S 2. Two space-ground-ground conjunctions, and one ground-ground-conjunction, between icebear, a chain ISMR, and the Swarm A and C satellites, on 6 May 2023. Panel b) shows the spatial distribution of echoes (black point-cloud), with the Swarm satellite orbits (blue lines) and GPS pierce-point (red circle) superposed. Panels a) and f) show the magnitude of the perpendicular magnetic fluctuations observed by the Swarm satellites (black line and blue colorscale), with the latitudinal distribution of icebear echoes superposed in red. Panels b,d,e, and g) show various composite powerspectra, with icebear clustering spectra (black), compared to textscchain k-spectra (red, gray) and field-aligned current structuring spectra (blue) measured by Swarm. Panel e) shows an enlarged portion of the composite icebear-chain spectrum in panel d). two different methods are observed to match strikingly well. What is more, the steep slopes at the larger scales (>1 km) are highly consistent with the steep slopes seen at smaller scales (<100 m), with observed spectral index values between −2.6 and −3.1. A prominent break-point is observed near the Fresnel-scale, and similar prominent features are visible at scale-sizes around 1–10 km, both in accordance with expectations based on plasma instabilities from the literature [6–11]. The remaining four composite spectra that we analyze are presented in Figures 2, 3, and 6 in the Main Paper. III: EXTENDED ICEBEAR-CHAIN-SWARM CONJUNCTION We shall describe two successive space-ground-ground conjunctions that offer a clear, physical interpretation of the composite spectra. Figure S2 details two triple conjunctions between icebear,chain, and the European Space Agency’s Swarm mission [12, 13], consisting of three polar orbiting satellites (inclination 87◦, altitude ∼450 km, and orbital period of 90 minutes). The conjunctions, with their geospatial coordinates detailed in Figure S2c), exhibited very strong magnetic fluctuations perpendicular to Earth’s magnetic field, produced by field-aligned currents, and what follows is a 4 Figure S 3. A space-ground-ground conjunction between icebear,chain, and the Japanese inner magnetosphere spacecraft Arase that took place on 2 August 2023. Panels a,b) show the satellite location in the magnetosphere, while Panel c) shows the geospatial distribution of radar echoes, with Arase’s northern hemisphere orbital footprint in green dashed lines (using the Tsy04 mapping method [2]) and the GPS pierce-point as a red cross, all using the AACGM coordinate system mapped along Earth’s magnetic field-lines [3]. The conjunction is detailed in Figure 2d–g) in the Main Paper. treatment of the structure, or filamentation, of those currents. Following Ref. [14] and Ref. [15], we Fourier analyze the Swarm 50 Hz magnetic field fluctuations transformed into a mean-field-aligned coordinate system [16, 17], and this Fourier analysis yields information on electrical current filamentation, the degree to which the observed currents are non-laminar, or anomalous. The quantity is analogous to the structuring of magnetic field-tubes in the plane perpendicular to the geomagnetic field. Figure S2a, f) detail the observed magnitude of the perpendicular magnetic fluctuations, with the distribution of simultaneously observed icebear echoes superposed with a red line. As the Swarm satellites orbit through the topside (Fregion) ionosphere with a velocity of vs= 7.62 km/s, we apply Taylor’s “frozen-in”-hypothesis to convert the temporal powerspectra to k-spectra. These are superposed on the icebear echo clustering spectra in Figure S2b, g), showing reasonably good agreement on a wide range of spatial scales between 105m and 750 m (below 750 m, the Swarm spectra drop off, indicating an effective Nyquist frequency of 12.5 Hz for the Swarm magnetic field instrument). We note a very good shape-wise agreement between the radar clustering spectra and the observed field-aligned current structuring, echoing recent studies [14, 15]. The implications are that the spatial characteristics of turbulence in the E-region are contained, or communicated, by filaments in the field-aligned currents. In Figure S2d, e), we compare the icebear and GPS spectra, for which the simultaneous conjunction took place between the two satellites’ orbit, and which again exhibit excellent shape-wise agreement down to individual spectral features around 1 kilometer (inset panel e). IV: NINE ICEBEAR-ARASE CONJUNCTIONS On 2 August 2023, an extended conjunction took place between icebear and the Japanese inner magnetosphere satellite Arase. During this conjunction, two additional icebear–chain conjunctions took place. Results from this events are presented in Figure 2d–g) in the Main Paper. What follows is an overview of the geospatial locations of the various instruments during this event. Arase orbits Earth at a maximum distance (semimajor axis) of around 5 Earth radii, with a magnetospheric orbit that keeps the satellite relatively close to equator with an ionospheric footprint that routinely sample auroral latitudes [21]: it has an apogee of 32,000 km and a perigee of 400 km, an inclination angle of 31◦, and a period of 570 minutes. The satellite’s orbit in the magnetosphere is shown in Figure S3a, b), while its ionospheric footprint is shown with a dashed line in Figure S3c). The satellite was located some 19◦equatorward of magnetospheric equator, and it was observing a considerable flux of electrons with pitch angles lower than or equal to 5◦. Figure 2e, f) in the Main Paper present these observations. The observed flux of particles is a proxy of the real precipitating particle flux [22], producing the characteristic diffuse aurora that we infer to have occurred during the event. Next, Figure S4 shows seven conjunctions between icebear and Arase, akin to Figure 1 in the Main Paper, where we use the foregoing analysis to infer ionization curves (green profile), and compare those curves to the altitude distribution of HF echoes (black profiles). For each conjunction event, we confirm the geospatial proximity of Arase’s northern hemisphere footprint with the distribution of HF echoes, and we show the total, observed energy flux observed by Arase in inset panels. Figure 4 is a unique dataset of low-altitude HF echoes coincident with highly energetic particle precipitation, and in the next section we provide a new theoretical foundation to explain low (<90 km) plasma turbulence observations. 5 Figure S 4. Seven space-ground conjunctions between icebear and Arase, showing altitude profiles of precipitation-induced ionization rate (green profiles) and the altitude distribution of HF echoes (black profiles). Inset plots shows the combined precipitating electron energy flux through the LEP-e [18], MEP-e [19], and HEP [20] instruments onboard Arase. V: THE DRIVEN-DISSIPATIVE PHOTOCHEMICAL FORCING: “CHEMICAL ETCHING” The persistence of fine-scale plasma density structures (<10 m) in the highly collisional D-region (<90 km) presents a fundamental challenge to classical diffusion theory. Building on the thermal attachment instability framework identified in artificial heating experiments [23], we identify driven-dissipative photochemical forcing as the primary structuring mechanism. This mechanism exploits the dominance of rapid electron attachment to neutrals (formation of negative ions) in D-region loss processes. The evolution of an electron density perturbation δNe is governed by the continuity equation coupled with the electron energy equation, where the linearized loss term Lis determined by the attachment frequency νatt [24, 25], ∂(δNe) ∂t ≈ − ∂νatt ∂Te δTeNe−Da∇2(δNe),(1) where Dais the ambipolar diffusion coefficient and Teis the electron temperature. In this note, we describe the conditions when the loss mechanism, τchem ≈∂νatt ∂Te δTe−1 ≈1 νeff att ,(2) works faster than the smoothing mechanism, τdiff ≈1 k2Da .(3) Crucially, we invoke a “pre-conditioned” nonequilibrium neutral background, provided by broadband energetic electron precipitation (1 keV–100 keV, with a tail exceeding 600 keV). This precipitation functions as a ’seedbed,’ sustaining a high population of vibrationally excited oxygen O2(v) and metastable O2(a1∆g) via impact excitation and cascade by secondary electrons [26]. While Alfv´en wave absorption elevates Te, the increase is insufficient to drive dissociative attachment to ground-state oxygen (threshold ∼3.7 eV). However, for the vibrationally excited population O2(v), the reaction threshold effectively vanishes. As vincreases, the neutral wave function overlaps favorably with the repulsive potential curve of the negative ion (O− 2) [27]. For 6 O2(v≥10) or O2(a1∆g), the peak cross-section increases by factors of 102to 103. Consequently, a modest rise in plasma temperature (e.g., Te∼0.03 eV to Te∼0.1 eV) broadens the electron Maxwellian distribution sufficiently to access these resonant channels, e+O∗ 2→(O− 2)∗→O−+O. (4) The resonant nature of this process causes the attachment frequency νatt to spike instantaneously with Te, converting mobile free electrons into heavy, slow negative ions. We can test this quantitatively at 85 km altitude. Using standard atmospheric parameters (NRLMSISE-00) for the background neutral density (Nn≈1020 m−3) and ambipolar diffusion (Da≈4 m2/s), we compare the timescales for a λ= 3 m structure (the icebear backscatter wavelength). For τchem, we calculate the effective rate for the resonant channel e+O∗ 2→O−+O. With excited state densities predicted by precipitation models [26] and resonant rates from [27], the effective attachment frequency during heating spikes to, νeff att ≈101−102s−1.(5) Comparing this to the diffusive smoothing time: τchem ≈1 νeff att ≈10 ms < τdiff ≈1 k2Da ≈50 ms. (6) Since τchem < τdiff , the chemical ’etching’ dominates, allowing fine-scale structures to persist against diffusion. Validation – The validity of the chemical etching mechanism is supported by experimental measurements of the reaction cross-sections. Ref. [28] confirms that for the metastable O2(a1∆g) state, the dissociative attachment cross-section is enhanced by a factor of 3.5 and the energy threshold is shifted lower by 0.98 eV compared to the ground state. Furthermore, modeling of energetic electron precipitation events (40–100 keV) by Ref. [29] demonstrates the efficient production of these metastable states in the D-region, providing the necessary ’seedbed’ density ([O∗ 2]≳108cm−3). Finally, while electron impact ionization of metastables is possible [30], the high energy threshold for ionization (>10 eV) compared to the resonant attachment threshold ensures that plasma loss dominates over production in the range of electron temperatures (Te∼0.1–0.5 eV) generated by Alfv´enic heating. The 13 March 2021 event – In Figure 1 of the Main Paper, we show an event during which highly energetic electron precipitation observed by Arase coincided with low-altitude HF echoes observed by icebear, with matching altitude profiles. In Figure S5 we show data Figure S 5. Panel a) shows icebear echo altitude distribution (red line) superposed on the ionization altitude profile (green line), inferred from the Arase-measured electron precipitation (panel b).Panel c) shows the HF echoes in an altitude-time-intensity diagram (with colorscale denoting echo signal-to-noise ratio (SNR), with the peak ionization altitude (±one standard deviation) shown in green. Panel d) shows a cross-correlation analysis between the echo detection rates and the 60 keV electron flux. Panel e) shows timeseries of the electron energy fluxes through the three particle detectors (red) and the echo detection rates (black). from this event, for a 16-minute interval that features 90-second periodic bursts in both energy flux and echo detection rates, corresponding to Pc3-5 (Alfv´en) pulsations. 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