# Spatial Distribution and Plasmaspheric Ducting of Auroral Kilometric Radiation Revealed by Wind, Polar, and Arase

Siyuan Wu, Daniel Whiter, Sai Zhang, Ulrich Taubenschuss, Philippe Zarka, Georg Fischer, Laurent Lamy, Shengyi Ye, James Waters, Baptiste Cecconi, et al.

► To cite this version:

Siyuan Wu, Daniel Whiter, Sai Zhang, Ulrich Taubenschuss, Philippe Zarka, et al. Spatial Distribution and Plasmaspheric Ducting of Auroral Kilometric Radiation Revealed by Wind, Polar, and Arase. AGU Advances, 2025, 6 (4), 10.1029/2025AV001743. http://dx.doi.org/10.1101/2025-03-04

HAL Id: hal-05490663

https://hal.science/hal-05490663v1

Submitted on 2 Mar 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
RESEARCH ARTICLE

10.1029/2025AV001743

**Peer Review** The peer review history for this article is available as a PDF in the Supporting Information.

**Key Points:**

* Global occurrence maps of Auroral Kilometric Radiation are established, showing high latitude and nightside preferences

* The plasmasphere creates an equatorial shadow zone, but high frequency AKR fills this region immediately outside of the plasmasphere

* Low-density ducts inside the plasmasphere act as wave guides for AKR propagation

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

S. Wu,
Siyuan.Wu@soton.ac.uk

**Citation:**

Wu, S., Whiter, D. K., Zhang, S., Taubenschuss, U., Zarka, P., Fischer, G., et al. (2025). Spatial distribution and plasmaspheric ducting of auroral kilometric radiation revealed by Wind, Polar, and Arase. *AGU Advances, 6*, e2025AV001743. https://doi.org/10.1029/2025AV001743

Received 20 MAR 2025
Accepted 16 JUN 2025

**Author Contributions:**

**Conceptualization:** Siyuan Wu, Daniel K. Whiter, Ulrich Taubenschuss, Laurent Lamy

**Data curation:** Siyuan Wu, Sai Zhang, James Waters, Ping Li, Caitriona M. Jackman, Alexandra R. Fogg, Yoshiya Kasahara, Yasumasa Kasaba

**Formal analysis:** Siyuan Wu

**Funding acquisition:** Daniel K. Whiter

**Investigation:** Siyuan Wu, Daniel K. Whiter

**Methodology:** Siyuan Wu, Sai Zhang, Claire Baskevitch

© 2025. The Author(s).
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

<figure><img src="image_2.png" /></figure>

# Spatial Distribution and Plasmaspheric Ducting of Auroral Kilometric Radiation Revealed by Wind, Polar, and Arase

Siyuan Wu¹ ID, Daniel K. Whiter¹ ID, Sai Zhang² ID, Ulrich Taubenschuss³ ID, Philippe Zarka⁴ ID, Georg Fischer⁵ ID, Laurent Lamy⁴,⁶ ID, Shengyi Ye⁷ ID, James Waters⁶ ID, Baptiste Cecconi⁴ ID, Ping Li², Caitriona M. Jackman⁸ ID, Alexandra R. Fogg⁸ ID, Claire Baskevitch⁴ ID, Yoshiya Kasahara⁹ ID, and Yasumasa Kasaba¹⁰

¹School of Physics and Astronomy, University of Southampton, Southampton, UK, ²School of Physics and Electronic Sciences, Changsha University of Science and Technology, Changsha, China, ³Department of Space Physics, Institute of Atmospheric Physics of the Czech Academy of Sciences, Prague, Czech Republic, ⁴LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris Meudon, Meudon, France, ⁵Institute of Physics, University of Graz, Graz, Austria, ⁶Aix Marseille University, CNRS, CNES, LAM, Marseille, France, ⁷Department of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen, People's Republic of China, ⁸School of Cosmic Physics, Dublin Institute for Advanced Studies, Dublin, Ireland, ⁹Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa, Japan, ¹⁰Planetary Plasma and Atmospheric Research Center, Graduate School of Science, Tohoku University, Sendai, Japan

**Abstract** Auroral Kilometric Radiation (AKR), the dominant radio emission from Earth, has been extensively studied, though previous analyses were constrained by limited spacecraft coverage. This study utilizes long-term observations from Polar, Wind, and Arase spacecraft to generate comprehensive global AKR occurrence rate maps, revealing a high-latitude and nightside preference. A detailed investigation of the equatorial shadow region confirms that the dense plasmasphere blocks AKR emissions across all wave frequencies. Low-frequency emissions (<100 kHz) are presents outside the shadow region at larger radial distance, which is attributed to magnetosheath reflection, while higher-frequency emissions (>100 kHz) propagate via plasmaspheric ducting and leakage, filling the equatorial region immediately outside the plasmasphere. Ray-tracing simulations identify low-density ducts within the plasmasphere as crucial channels that enable AKR to penetrate the dense plasmasphere, particularly at higher frequencies. These results align with meridional AKR observations, offering new insights into AKR propagation patterns.

**Plain Language Summary** Auroral Kilometric Radiation (AKR) is a type of radio wave emitted from Earth's auroral regions, linked to energetic electron precipitation processes in space. Although AKR has been studied for decades, earlier research was limited by data from spacecraft with constrained orbital coverage. This study combines long-term observations from three spacecraft—Polar, Wind, and Arase—to create detailed maps showing where AKR occurs most frequently. These maps reveal that AKR is most common at high latitudes and on Earth's nightside. A significant finding is that the dense plasmasphere—a region of high-density plasma around Earth—blocks AKR from traveling freely, forming an equatorial shadow zone around the plasmasphere. This shadow region outside the plasmasphere is observed to be “filled” with AKR emissions. This filling is explained by AKR traveling through less dense “ducts” within the plasmasphere, which act as pathways for the waves to escape and reach surrounding regions. Simulations of AKR propagation confirm that these low-density ducts serve as critical wave guides, enabling AKR to bypass dense plasma regions. These findings enhance our understanding of how AKR propagates through Earth's space environment and emphasize the need for further studies into the specific properties of these radio waves and the plasma structures that guide them.

## 1. Introduction

Auroral Kilometric Radiation (AKR) is Earth's most intense natural radio emission, first identified in the 1960s (Benediktov et al., 1965; Dunckel et al., 1970; Gurnett, 1974). These emissions span frequencies from approximately 30 kHz to nearly 1 MHz (Figure 1), with a primary band between 100 and 400 kHz and peak power levels reaching $10^9$ W (Benson & Calvert, 1979; Gurnett, 1974; Waters et al., 2022; Zhao et al., 2019 and references therein). Predominantly observed in the right-hand extraordinary (R-X) mode (Kaiser et al., 1978), AKR is also accompanied by weaker left-hand ordinary (L-O) mode components and Z mode emissions, which contribute to
**Project administration:** Daniel K. Whiter

**Resources:** Siyuan Wu, Sai Zhang,

Yoshiya Kasahara, Yasumasa Kasaba

**Software:** Siyuan Wu, Claire Baskevitch

**Supervision:** Daniel K. Whiter,

Ulrich Taubenschuss, Philippe Zarka

**Validation:** Siyuan Wu, Sai Zhang

**Visualization:** Siyuan Wu

**Writing – original draft:** Siyuan Wu

**Writing – review & editing:** Siyuan Wu,
Daniel K. Whiter, Sai Zhang,

Ulrich Taubenschuss, Philippe Zarka,
Georg Fischer, Laurent Lamy, Shengyi Ye,
James Waters, Baptiste Cecconi, Ping Li,
Caitriona M. Jackman, Alexandra R. Fogg,
Claire Baskevitch, Yoshiya Kasahara,
Yasumasa Kasaba

its spectral complexity (Benson, 1985; De Feraudy et al., 1987; Hanasz et al., 2003; Mellott et al., 1984; Sha-
whan & Gurnett, 1982; Zhang et al., 2024). AKR is found to be mostly circularly polarized with a marginal linear
component (Panchenko et al., 2008), and R-X mode AKR from the northern hemisphere is left-handed, whereas it
is right-handed from the southern hemisphere where the magnetic field is pointing toward higher altitudes (Kaiser
et al., 1978).

The generation of AKR is attributed to the cyclotron maser instability (CMI), a relativistic electron cyclotron
resonance process that amplifies waves at frequencies near the local electron cyclotron frequency ($f_{ce}$ = 28*B in
Hertz, where B is the magnetic field strength in nT; C. S. Wu & Lee, 1979; Louarn et al., 1990). This mechanism
localizes the AKR source region along high-latitude magnetic field lines at radial distances of approximately ~1.2
to ~3.7 Earth radii (Re, where 1 Re = 6,371 km), where the local $f_{ce}$ matches the observed AKR frequencies.
Observations in the AKR source region suggest the AKR sources are within the high latitude auroral cavity—a
low-density plasma region bordered by denser plasma (Calvert, 1981; Hilgers, 1992). Inside the cavity and in the
AKR source region, auroral electrons exhibit a “horseshoe” (shell-like) velocity distribution due to acceleration
and pitch-angle spreading along magnetic field lines, providing the free energy required for CMI wave ampli-
fication (Ergun et al., 1998; Strangeway et al., 2001).

AKR emissions are initially generated perpendicular to the local magnetic field (Benson & Calvert, 1979; Strangeway et al., 2001) but undergo significant refraction due to, for example, strong near-source refraction for the R-X mode emissions as the wave frequency is close to the local $f_{ce}$, which itself is approximately the R-X mode cut-off frequency when the electron density in the source region is low ($f_X = \frac{1}{2}f_{ce} + \sqrt{f_{pe}^2 + \frac{f_{ce}^2}{4}}$, with $f_X$ the R-X mode cut-off frequency and $f_{pe}$ the electron plasma frequency, $f_{pe} = 8980\sqrt{n_e}$ in Hz, where $n_e$ is the electron number density in $cm^{-3}$). There is also strong refraction of both R-X and L-O emissions due to density gradients in the source region (Louarn & Le Quéau, 1996a, 1996b; Mutel et al., 2008; Schreiber et al., 2017). Consequently, AKR exhibits distinct spatial and directional propagation patterns. The spatial distribution of AKR statistically favors high latitudes and nightside local times (Fogg et al., 2022; Gurnett, 1974; Hanasz et al., 2003; Kasaba et al., 1997; Louis et al., 2023; Xiao et al., 2022). Additionally, AKR's propagation is further constrained by the equatorial shadow zone formed by the dense plasmasphere (a region of plasma extending out from the ionized upper part of the atmosphere to distances of 2–6 Earth Radii, also see illustrations in the following Sections), which blocks the radio emissions due to its higher electron density (Gurnett, 1974; Lamy, Schippers, et al., 2010; Louis et al., 2023; Morioka et al., 2011). Although blocking by the plasmasphere is very strong, the emissions are still observed inside the equatorial radiation belt region occasionally, which is possibly influenced by plasmaspheric compression during magnetic storms (Deng et al., 2022; Xiao et al., 2016) and also the ducted propagation through the low-density ducts inside plasmasphere (AKR emissions propagate inside wave guide structures, see discussion in the following Sections; Calvert, 1982, 1995; Kolpak et al., 2024).

The link between AKR emissions and auroral processes underscores its importance in studying magnetospheric
dynamics. AKR originates along magnetic field lines where electron precipitation also generates optical auroras
(Benson & Akasofu, 1984; Hanasz et al., 2001; Huff et al., 1988; C. S. Wu & Lee, 1979). Observations indicate
that AKR intensifications often precede auroral breakups by 1–2 min, with higher-frequency enhancements
detectable up to 20 min before substorm onset (Liou et al., 1999; Morioka et al., 2010; Waters et al., 2022).
Beyond auroras, AKR correlates with various magnetospheric phenomena, including magnetic storms, bursty
bulk flows, field-aligned currents, solar wind speed, X-ray auroras, and PC pulsations, highlighting its utility as a
diagnostic tool for magnetospheric activity (Green et al., 1982; Gallagher & D'Angelo, 1981; Hanasz et al., 2006,
2008; Imhof et al., 2000; Morioka et al., 2008, 2010). AKR emissions emitted from the northern and southern
sources are modulated with a period of 24 hr, and this variation might be connected with diurnal changes of the
ambient plasma density in the auroral region (Lamy, Zarka, et al., 2010; Panchenko et al., 2009).

Despite decades of research, many aspects of AKR remain unresolved. For example, questions remain about the
origins of harmonic emissions in O- and X-modes (Benson, 1984; Gurnett & Inan, 1988), the mechanisms
responsible for fine structures such as “striated” emissions (Mutel et al., 2006; Taubenschuss et al., 2023), and the
processes that enable “leaked” AKR to penetrate the ionosphere and reach ground-level (LaBelle et al., 2022).
Previous studies have primarily relied on case studies or statistical analyses constrained by spacecraft orbit
coverage, leaving substantial gaps in the understanding of AKR's global distribution and propagation. Therefore,
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Examples of AKR observations by Wind, Polar, and Arase spacecraft. (a) Wind WAVES electric field spectrogram, showing intensity color-coded as a function of time and frequency, recorded from 2003-10-18 00:00 UT to 2003-10-18 23:55. Solar type III bursts, extending from high frequencies (top edge of the spectrogram), are marked by white arrows. (b) Polar PWI electric field spectrogram, recorded from 1997-04-21 00:00 to 1997-04-22 00:00. The white line represents the local f<sub>ce</sub>. Horizontal lines in the spectrogram are due to receiver interferences. (c) Arase PWE electric field spectrogram, recorded from 2017-07-17 00:00 to 2017-07-18 00:00. The intense emission line in the spectrogram, marked by a white arrow, corresponds to local upper hybrid emissions. The time resolution of these spectrograms varies, ranging from approximately 3 min for Wind (Panel (a)), to about 2 s for Polar (Panel (b)), and around 1 s for Arase (Panel (c)).</figcaption></figure>

several studies only examine the equatorial occurrence distribution, not the latitudinal distribution (Hanasz et al., 2003; Xiao et al., 2022).

To address these gaps, this study combines long-term observations from three spacecraft—Wind, Polar, and Arase—with ray-tracing simulations to construct global occurrence maps of AKR emissions. The distinct orbital configurations and observational environments of these spacecraft provide complementary perspectives. As shown by Figure 1, Wind (Panel (a)) is operating at large radial distances, providing observations of AKR over a 10-year period. Meanwhile, Polar and Arase, with closer orbits, capture more detailed variations of AKR in the inner magnetosphere, such as observations near the source region as indicated by the local f<sub>ce</sub> (white lines in Panel
(b) from Polar) and observations near the dense plasmasphere as indicated by the local upper hybrid resonance emissions ($f_{uh} = \sqrt{f_{ce}^2 + f_{pe}^2}$, upper hybrid emissions in Panel (c) from Arase). By investigating these data sets with ray-tracing techniques, this study uncovers new insights into AKR's global behavior.

This paper is organized as follows: Section 2 describes the data and methods. Sections 3 and 4 present the derived global occurrence maps and theoretical AKR propagation features. Sections 5 and 6 discuss AKR propagation near the plasmasphere using both spacecraft observations and ray-tracing simulations. Finally, Section 7 discusses the results and summarizes the conclusions.

## 2. Data and Methodology

### 2.1. Spacecraft Data and AKR Selection

This study utilizes data from three spacecraft: Polar, Wind, and Arase:

1. Polar Plasma Wave Instrument (PWI; Gurnett et al., 1995): The data set spans from 1996-03-25 to 1997-09-16. The PWI provides radio wave electric field and magnetic field spectrograms covering frequencies from approximately 13.0 to 807.8 kHz, with a time resolution of ~2 s.

2. Wind WAVES (Bougeret et al., 1995): Data from the Wind spacecraft spans from 1995-04-23 to 2004-12-30. The WAVES instrument records wave electric field spectrograms with frequencies from ~20.0 to ~1040.0 kHz, and a time resolution of ~3 min.

3. Arase Plasma Wave Experiment (PWE; Kasahara, Kasaba, et al., 2018; Kumamoto et al., 2018): Data from the High Frequency Analyzer (HFA) is used from 2017-03-23 to 2023-03-30. The PWE HFA instrument covers a frequency range of ~2.4–~1003.5 kHz. Due to varying operational modes, the time resolution ranges from 1 s to 1 min. For analysis, these modes are merged and averaged, producing a data set with an effective time resolution of ~4 s per frequency sweep.

Figure 2 illustrates the spatial coverage of each spacecraft. Wind provides extensive radial distance coverage up to 330 Re (Panel (a)) and almost all local times (Panel (b)). Polar samples high-latitude regions above the polar caps (Panel (c)) at all local times (Panel (d)), and Arase offers detailed equatorial observations (Panels (e) and (f)), enabling a comprehensive analysis of AKR emissions across the magnetosphere.

The selection of AKR was conducted using different methodologies tailored to data from different spacecraft. For Wind spacecraft data, we utilized previously published selection results by Waters, Jackman, et al. (2021) and Fogg et al. (2024). The identification method in these works relies on the characteristic rapid amplitude fluctuations of AKR, which are captured by the Wind/WAVES instrument over the spacecraft spin timescale. Each set of flux density measurements within a spin period is normalized by its mean, and then the standard deviation of the normalized values, denoted as $\sigma$, is computed. This $\sigma$ represents the degree of temporal variability. AKR signals typically exhibit a significantly higher $\sigma$ compared to background emissions such as solar radio emissions, which are more stable. An empirical threshold is applied to $\sigma$, and only intervals with values exceeding this threshold are classified as AKR (See details in Waters, Jackman, et al. (2021)).

AKR selection from Arase spacecraft data was performed following the method described by Zhang et al. (2021), which involves applying an intensity threshold of $10^{-14} \text{ V}^2\text{m}^{-2}\text{Hz}^{-1}$ to the wave spectra within the theoretical AKR frequency range determined from the local electron density and magnetic field strength. Readers are referred to these references for comprehensive methodological details.

For the Polar spacecraft data, we applied a selection method by integrating electric and magnetic field spectrogram information from the PWI instrument. The detailed steps of the Polar AKR data processing are as follows:

1. Removal of electrostatic emissions and noise: signals with $E/cB > 2$ were excluded to eliminate electrostatic emissions and other noise sources in the wave electric field data, as illustrated in Figure 3c (where E is wave electric field power spectral density, B is the magnetic field power spectral density, and c is the speed of light).

2. Thresholding for weak magnetic emissions: emissions with magnetic field strengths below $10^{-13} \text{ nT}^2/\text{Hz}$ were removed. This threshold was chosen empirically.

3. Application of a 2D Median Filter: a two-dimensional median filter with a kernel size of [3 × 3] (time × frequency) was applied to the electric field spectrogram to smooth the data across both time and frequency dimensions. This step mitigated the presence of isolated pixels on the spectrogram.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Spacecraft dwell time distributions. (a) Wind spacecraft orbits projected onto the magnetic meridional plane. (b) Wind spacecraft orbits projected onto the magnetic equatorial plane. (c)–(d) Polar spacecraft dwell time distributions projected onto the magnetic meridional and equatorial planes, respectively. (e)–(f) Arase spacecraft dwell time distributions projected onto the magnetic meridional and equatorial planes, respectively.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Figure 3.** AKR selection results from the Polar PWI instrument. (a) Polar PWI electric field spectrogram from 1996-08-01 00:00 to 1996-08-02 00:00. (b) Polar PWI magnetic field spectrogram for the same time interval. (c) E/cB spectrogram calculated from Panels (a) and (b). (d) Wave electric field spectrogram with the selected AKR emissions, identified using the criteria described in the Methodology section.</figcaption></figure>

4. Thresholding for weak electric field emissions: emissions with electric field strengths below $10^{-16}$ V²m⁻²Hz⁻¹ were further excluded, based on empirical thresholds.

5. Manual removal of residual electrostatic emissions: residual electrostatic emissions, particularly upper hybrid emissions not entirely removed by the E/cB criterion, were manually identified and eliminated. These emissions often displayed saturation patterns in Polar PWI data, as depicted in Figure 1 Panel (b). An example of the final selection results is given in Figure 3 Panel (d).

Note that automatic detection algorithms applied to all these three data sets occasionally produced spurious results, particularly due to low-frequency emissions such as the kilometric continuum emissions (Matsumoto et al., 1994, 2000) and the emission lines like the upper hybrid emissions. All these erroneous detections were manually reviewed and removed to ensure the selection accuracy. The final selection results include AKR emissions corresponding to a total effective duration of 492 days from Wind (out of ~10 years of observations,
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Construction of the electron density model of Earth's inner magnetosphere. (a) Electron density profile constructed as described in Methodology. (b) Zoomed-in version of the same electron density profile as in (a) but with $f_x$ contours (white contours indicating the $f_x$ frequencies in kHz) and AKR source regions (red squares) superimposed. The plasmapause is introduced at $L = 4.5$. At the plasmapause, the density gradient is characterized by a fivefold decrease in density from the inner to the outer region.</figcaption></figure>

with an approximate occurrence rate of ~13.5%), 270.2 days from Polar (out of ~1.5 years of observations, with an approximate occurrence rate of ~50%), and 417.9 days from Arase (out of ~6.5 years of observations, with an approximate occurrence rate of ~17.5%), reflecting differences in AKR observations due to the varying orbits of the spacecraft.

## 2.2. Construction of Ray-Tracing Environment

To carry out ray-tracing simulations of AKR propagation in the magnetic meridian plane, we first constructed the electron density profile by combining several existing models. The empirical plasmasphere model of Ozhogin et al. (2012) derived from radio propagation features is used. This model provides the plasmasphere density from $L = 1.6$ to $L = 4$ and accounts for a well-defined density decay beyond the $L = 4$ region, as shown in Figure 4 Panel (a). A plasmapause is introduced at $L = 4.5$, corresponding to moderate geomagnetic conditions (Ripoll et al., 2022). The electron density outside the plasmapause is set to be five times lower than that within the plasmapause. For the ionosphere, electron density below 1.5 Re was calculated using the model by Kletzing et al. (1998), which is based on Langmuir probe measurements at high latitudes. This model is valid within an altitude range of 1,000–8,000 km (~1.15–2.25 Re), and 1.5 Re was chosen as the transition point to ensure a smooth variation between the plasmasphere and ionosphere (Note that for the overlap region of the two models, the higher electron density value is chosen). Additionally, the field-aligned density duct model from Fung and Green (2005), designed to simulate ducted radio propagation in the plasmasphere, was used. The ducts are modeled as follows:

$$N_e(r, \theta) = N_e \left( 1 - \frac{\delta N}{Ne} \exp \left[ - \left( \frac{r - L \cos^2(\lambda)}{\sigma} \right)^2 \right] \right) \quad (1)$$

where $N_e$ is the electron density given by the merged model of the plasmasphere and ionosphere. The term $\delta N/Ne$ gives the fractional density variation at the center of the ducts. The exponential term gives the exponential decay of duct density as a function of $r$, $\lambda$ and $\sigma$, where $r$ is radial distance of a field location, $\lambda$ is the magnetic latitude of the field location at $r$, and $\sigma$ is the “width” of the density duct. The duct center position is given by $L$, where $L$
denotes the central L-shell value of the duct. As shown in Figure 4 Panel (a), low-density ducts are introduced at L-shells from $L = 2$ to $L = 8$ with a step of 0.3. Note that in real observations, the fractional density variation $\delta N/N_e$ can vary significantly, typically ranging from ~10% to 80% (Thomas et al., 2021; Darrouzet et al., 2009, and references therein). Additionally, it may also vary as a function of latitude, exhibiting a much more complex behavior than the simplified configuration assumed here. A value of 80% is used here to facilitate the ray-tracing simulations to let the rays propagate inside the ducts as this provides stronger density gradients. To further enhance the realism of the model, we introduce sinusoidal modulations of the duct width by applying a sinusoidal function to $\sigma$ with amplitude of 0.03 Re. The obtained width of the ducts is then varying sinusoidally along the magnetic field line within a range of 0.1 ± 0.03 Re, as indicated by the white text arrows in Figure 4a.

The AKR emissions are generated within the auroral cavity, where the electron density is low (Calvert, 1981; Hilgers, 1992; Louarn & Le Quéau, 1996a). To model this, we adopt the density cavity model from Hashimoto et al. (1998):

$$P = 1 - \exp\left\{-\alpha\left(\frac{\Lambda - \Lambda_0}{W}\right)^{\kappa}\right\} \quad (2)$$

$$\Lambda = \sin^{-1}\left(\sqrt{\frac{R_e}{r}} \sin \theta\right) \quad (3)$$

$$G = \frac{1}{\pi} \tan^{-1} \left( \frac{r - R_{\text{ref}}}{\Delta R} \right) \quad (4)$$

$$N_c = \{(0.5 - G) + (0.5 + G)P\}N_e \quad (5)$$

The empirical parameters $\alpha = 2.77$ and $\kappa = 6$ are retained as used in previous studies (Hashimoto et al., 1998; Xiao et al., 2016). The width of the cavity, denoted as $W$, is set to 15, and $r$ and $\theta$ represent the radial distance and magnetic colatitude for a field position, respectively. The center invariant latitude of the cavity, $\Lambda_0$, is chosen to be 67.8° (corresponding to dipole $L = 7$). The reference latitude for the earthward boundary of the cavity, $R_{\text{ref}}$, is set to 1.2 Re. We modify the cavity's width from 6 at 1.1 Re to 0 at 5 Re to let the cavity close at 5 Re, with the cavity starting at 1.1 Re and ending at 5 Re. The function $G$ is introduced to connect the cavity to the background electron density within $R_{\text{ref}}$ (1.2 Re), with a scaling factor $\Delta R$ chosen to be 0.001 Re. The density within the cavity ($N_e$) decreases exponentially from the background density ($N_e$, derived from the merged density of the plasmasphere and ionosphere model) at its edge to the center. Note that although this model has been adopted in many previous ray-tracing simulations, and the resulting ray paths exhibit good agreement with observations (e.g., Deng et al., 2022; Xiao et al., 2016). Detailed observations of the auroral cavity suggest that finer-scale density structures may exist within the cavity (Ergun et al., 1998; Singh et al., 2005). These small-scale features could potentially lead to more complex ray path behavior for AKR propagation within the cavity. Nevertheless, for large-scale simulations of AKR propagation, the current cavity model is sufficient to capture the overall propagation characteristics and provide meaningful insights into the global distribution of AKR. The final merged electron density profile is given in Figure 4 Panel (a).

The magnetic field used is a simple dipole field with a surface magnetic field strength of -0.31 Gauss. Since the magnetic field is only important in the radio source region, particularly between 1 and 5 Re at high latitudes, the use of the dipole magnetic model results in negligible differences compared to the International Geomagnetic Reference Field (IGRF) model (Alken et al., 2021). The determined AKR source region from the dipole model is marked by red squares (see Section 2.3 for details) and the R-X mode cut-off frequency surfaces ($f_x$ surfaces) are illustrated in Figure 4 Panel (b). The AKR sources are located along $L = 7$ (blue line) and positioned almost aligned with the $f_x$ contours.

## 2.3. ARTEMIS-P Ray-Tracing Simulations

The ray-tracing method employed in this study is the ARTEMIS-P algorithm (Anisotropic Ray Tracer for Electromagnetics in Magnetosphere, Ionosphere, and Solar Wind, including Polarization), developed by Gautier (2013) and previously utilized in several studies (Gautier et al., 2013; S. Wu, Taubenschuss, et al., 2024; S. Wu, Ye, et al., 2024). The code is based on the Haselgrove equations (Haselgrove, 1963; Haselgrove &
Haselgrove, 1960), which describe wave propagation and wave vector evolution derived from the wave dispersion relation. It solves the Altar-Appleton-Hartree dispersion relation under the cold plasma approximation (Appleton, 1928, 1932; Hartree, 1931). The resulting differential equations are numerically integrated using a fourth-order Runge-Kutta method, as detailed in Gautier (2013) and S. Wu, Taubenschuss, et al. (2024).

We trace the propagation of AKR rays launched at a discrete set of wave frequencies covering the entire AKR frequency range—[800, 600 400, 200, 100, 60, 40, 30, 20] kHz—along L-shell = 7, corresponding to an invariant latitude of 67.8°, which approximates the typical latitude of AKR sources. The source positions for each wave frequency are determined based on local $f_{ce}$ of [720, 570, 390, 190, 95, 56, 37, 27, 18] kHz. The selection of source positions with $f_{ce}$ values slightly lower than the launched wave frequencies addresses a technical limitation of the ARTEMIS-P algorithm. As it relies on the cold plasma dispersion relation (Gautier, 2013), the algorithm cannot initiate R-X mode rays at positions where the wave frequency equals or falls below the local $f_{ce}$ (Lamy, Schippers, et al., 2010; Roux et al., 1993). However, this adjustment does not significantly affect the simulation results, as it introduces negligible differences in the source positions on a global scale. This is a widely accepted procedure, as employed in earlier studies (Hashimoto et al., 1998; Ladreiter & Leblanc, 1990; S. Wu, Ye, et al., 2024). The calculated source positions are marked by nine red squares in Figure 4, Panel (b), where the AKR source regions are positioned near the $f_x$ contour lines corresponding to each wave frequency.

The initial beaming angles of the AKR rays are systematically ranging from 0° to 359° in 1° increments to account for the diverse directional propagation paths of AKR. As shown by the previous observations (Mutel et al., 2008; Schreiber et al., 2017), the rays propagate outward from the source region, significant refraction occurs due to density gradients, with the refraction angles exceeding 80° in some cases. Consequently, a wide range of beaming angles is tested in our simulations to evaluate how AKR rays interact with and enter into density ducts, as discussed in subsequent sections.

# 3. Occurrence Rates of AKR From Polar, Wind, and Arase

## 3.1. Confirmation of Earlier Findings on AKR Occurrence Rates

The global occurrence rates of AKR, derived from data collected by the Wind, Polar, and Arase spacecraft, are presented in Figure 5 and projected onto the magnetic meridian plane (z-axis parallel to the magnetic dipole axis) and magnetic equatorial plane (x-y plane parallel to the dipole magnetic equator). Panel (a) illustrates a strong preference for AKR emissions at higher magnetic latitudes (MLAT), predominantly above 10° in both hemispheres. A clear magnetic local time (MLT) asymmetry is evident in Panel (b), with peak occurrence rates concentrated on the nightside, consistent with earlier findings (e.g., Fogg et al., 2024; Gurnett, 1974; Hanasz et al., 2003; Waters, Jackman, et al., 2021). Zoomed-in views in Panels (c) and (d) reveal a more detailed distribution, highlighting a prominent peak in occurrence rates above 30° MLAT and a low-occurrence region within 8 Re near the equator.

In the equatorial plane in Panel (d), AKR occurrence rates exhibit a pronounced nightside preference, forming a spiral-like distribution with a higher occurrence rate that extends from approximately 15 MLT to 8 MLT. While some emissions are detected on the dayside, their occurrence rates are significantly lower. The zoomed-in views in Panels (e) and (f) provide finer spatial details, particularly as bin sizes decrease from 3 Re in Panels (a)–(b) to 0.2 Re in Panels (e)–(f). To improve statistical reliability, bins with spacecraft dwell times of less than 1 hr were excluded. Consequently, many bins containing only Wind data were removed due to Wind's limited observation time in the inner magnetosphere. High-latitude observations in Panel (e) predominantly reflect data from Polar, while equatorial observations are primarily derived from Arase, supplemented by Polar.

The low-occurrence region observed in Panels (c) and (e) near the equator and close to Earth aligns with the position of the dense plasmasphere extending from magnetic equator to MLAT ~30°. This region effectively hinders the propagation of AKR. However, emissions persist outside the plasmasphere, indicating that while the plasmasphere impedes AKR propagation, the surrounding regions remain filled with emissions. This observation will be explored further in Section 3.2.

Finally, the equatorial occurrence rates in Panel (f) reaffirm the nightside dominance of AKR. Within the circular region corresponding to a radial distance of 1 Re, as shown in Panel (f), high occurrence rates of AKR are detected, representing emissions observed by Polar above the polar cap region, which suggests a wide range of beaming angles for AKR emissions, with significant activity observed across all latitudes.
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Occurrence rate maps of AKR in the magnetic meridian and equatorial planes. (a) Global AKR occurrence rates projected onto the magnetic meridian plane. The occurrence rates at larger radial distances are primarily derived from Wind data. A bin size of 3 Re is used, and bins with dwell times shorter than 1 hr are removed. (b) AKR occurrence rates projected onto the magnetic equatorial plane. (c)–(d) Occurrence rates presented in the same format as (a)–(b), but with a zoomed-in view and a smaller bin size of 1.2 Re. (e)–(f) Occurrence rates shown in the same format as (a)–(b), with an even finer zoomed-in view and a bin size of 0.2 Re.</figcaption></figure>

## 3.2. Novel and Unexplained Findings

The plasmasphere's shadowing effect on AKR emissions is illustrated in Figure 5 Panel (c) and further analyzed in Figure 6. AKR occurrence rates were examined across four frequency bands: 30–100 kHz (Figure 6 Panel (a)), 100–200 kHz (Panel (b)), 200–400 kHz (Panel (c)), and 400–800 kHz (Panel (d)). The possible propagation directions of AKR rays in the meridional plane are depicted with red arrows for perpendicular propagation relative to the source magnetic field and yellow arrows for parallel propagation. White contour lines represent the $f_x$ cutoff frequencies, delineating regions where the dense plasmasphere inhibits AKR propagation for the corresponding wave frequencies.

AKR emissions are initially beamed perpendicular to the magnetic field (red arrows) at their source regions (red squares in Figure 6). However, within the plasmasphere, high plasma density causes strong refraction or reflection near the $f_x$ contours (white contour lines), redirecting the emissions toward higher latitudes with a reduced beaming angle, approaching parallel propagation (yellow arrows). This refraction effect creates a plasmaspheric shadowing region, where the plasmasphere itself acts as a wave barrier, leading to significantly lower occurrence rates within it, as shown in Figure 5 (Panels c, e) and Figure 6. Additionally, an extended equatorial shadow zone is expected outside the plasmasphere due to the continued refraction of emissions toward higher latitudes.

Beyond the plasmasphere as shown by Figure 6, additional shadowing regions emerge at low equatorial latitudes, where wave occurrence rates remain suppressed. This effect is particularly pronounced for emissions below 100 kHz (Figure 6 Panel (a)), where the equatorial region is expected to be devoid of emissions due to strong refraction toward higher latitudes. However, contrary to expectations, Figure 6 reveals that some emissions persist within these equatorial shadowed regions especially for AKR emissions at higher frequencies (>100 kHz
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Occurrence rate maps of AKR in the magnetic meridian plane across different wave frequency ranges. (a) Occurrence rates of AKR within the 30–100 kHz frequency range, projected onto the magnetic meridian plane. White contour lines indicate the $f_x$ frequencies ($f_x$ = [20, 30, 40, 60, 100] kHz) derived from the electron density profile and magnetic field model outlined in the Methods section. Contours progress from large radial distances ($f_x$ = 20 kHz) to smaller ones ($f_x$ = 100 kHz). The blue line represents the magnetic field line corresponding to the AKR sources at L = 7. Red squares denote the AKR source locations for $f_{wave}$ = [20, 30, 40, 60, 100] kHz, with red arrows indicating perpendicular propagation directions and yellow arrows showing parallel propagation directions (relative to the background magnetic field direction). The white box, which includes the average occurrence rate, highlights the variations in occurrence rates across different regions around Earth. The shadow zone outside the plasmasphere at low latitudes is indicated by the middle white box, which contains a lower average occurrence value. Panels (b)–(d) present similar wave occurrence rate maps for AKR within the frequency ranges of [100–200] kHz, [200–400] kHz, and [400–800] kHz, respectively. The color scale is saturated to 0.6 for clarity.</figcaption></figure>

as shown in Panels (b)–(d)), indicating that wave propagation is more complex than simple refraction scenarios suggest.

For low-frequency emissions (<100 kHz), the shadowing effect is most prominent. Figure 6 Panel (a) shows that these emissions are strongly refracted and reflected toward high latitudes, leaving the equatorial region largely devoid of AKR signals. This is evident from the middle white box, where the average occurrence rate is only 0.11, compared to 0.21 at higher latitudes (outer two white boxes). This suggests that approximately 52% (0.11/0.21) of the emissions penetrate the plasmasphere and reach the equatorial shadowed region despite plasmaspheric obstruction. The shadowing effect extends outward to ~23 Re, beyond which emissions reappear with higher occurrence rate (We only show the occurrence map to 25 Re for format consistency), likely due to reflections at the magnetosheath boundary—a phenomenon similar to Saturn's Kilometric Radiation (SKR) (S. Wu, Ye, et al., 2024; see also the Discussion).

By contrast, higher-frequency AKR emissions (Figure 6 Panels (b)–(d)) exhibit a less pronounced shadowing effect. These emissions are still detected immediately outside the plasmasphere, as indicated by the white boxes. The strong shadowing is confined to within ~8 Re. While plasmaspheric inhibition affects AKR across all
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Ray-tracing simulations of AKR propagation. (a) Simulated AKR rays in magnetic meridian plane. The calculations in (a) are carried out using the plasmasphere model without incorporating the low-density ducts structures described in Method Section. AKR rays are launched with a wave frequency at [800, 600, 400, 200, 100, 60, 40, 30, 20] kHz (shown by red squares from left to right hand side of (a)), separately. AKR rays at different frequencies are presented via different colors as given by the colorbar on the right-hand corner of the figure. The electron density is color-coded as background colors. The $f_x$ contour lines are marked by the white lines. The beaming of AKR varies from 0° to 359° with a step size of 1°. For clarity, only 60 rays with an increment of 6° are plotted for each AKR source. (b) Zoomed-in view of northern hemisphere in (a).</figcaption></figure>

frequencies (Figure 5 Panels (c) and (e)), higher-frequency emissions exhibit a greater ability to penetrate the plasmaspheric barrier. As shown in Figure 6 Panel (b), approximately 72% (0.32/0.44) of the high-frequency emissions penetrate the plasmasphere, with even higher fractions of 85% (0.46/0.54) and 85% (0.39/0.46) observed in Panels (c) and (d), respectively. These findings suggest that high-frequency AKR emissions experience more efficient propagation through the plasmaspheric barrier compared to their low-frequency counterparts.

## 4. ARTEMIS Ray-Tracing Simulations on Theoretical AKR Propagation

To further illustrate the features of the AKR occurrence maps shown in Figures 5 and 6, a ray-tracing simulation of theoretical AKR propagation is presented in Figure 7. The propagation of AKR is simulated using the Artemis-P ray-tracing algorithm, considering only R-X mode emissions. Initially, ray paths were calculated using the electron density model described in Section 2, excluding low-density ducts (will be discussed in the following Sections). The results are presented in Panels (a)–(b) of Figure 7. AKR rays were launched from red squares with initial beaming angles ranging from 0° to 359° in 1° increments (rays are only launched within the meridian plane, i.e., 2D simulations). For clarity, Panels (a)–(b) show a subset of the rays at 6° intervals, with Panel (b) offering a zoomed-in view of Panel (a).

The simulations reveal that AKR rays are immediately refracted or reflected toward higher latitudes upon leaving their source region (indicated by red squares), moving away from the cutoff frequency surfaces ($f_x$ contours in white). The results demonstrate that AKR emissions spanning frequencies from 800 kHz (red rays) to 20 kHz (green rays) are all refracted and are unable to propagate to low latitudes. This behavior is attributed to the higher electron density within the plasmasphere, which acts as a barrier, effectively blocking these emissions. As a result, no AKR emissions are observed in low-latitude regions outside the plasmasphere, aligning well with higher occurrence rates observed at higher latitudes as shown in the observational data presented in Figures 5 and 6 (except for the filled shadow zone). This scenario of existence of a shadow zone at large distances and low latitudes has already been found by many previous AKR ray-tracing calculations (e.g., Green, 1988). A direct comparison of the results in Figures 6 and 7 reveals clear differences between the observations and theoretical predictions, particularly in the presence of AKR in the shadow region. How do these AKR emissions reach the shadow region? The answer may lie in the observations of AKR in the vicinity of the plasmasphere, as discussed in the next section.
## 5. AKR Observations Revealing Ducts in the Plasmasphere

The plasmasphere exhibits a range of density structures, from large-scale features such as plumes, notches, shoulders, and fingers, to small-scale field-aligned density irregularities (Darrouzet et al., 2009, and references therein). The R-X and L-O mode emissions are characterized by a lower cutoff frequency at $f_X$ or $f_{pe}$, which depend on the local electron density, particularly in the plasmasphere where the magnetic field is relatively weak. Consequently, both R-X and L-O mode AKR emissions experience significant refraction or reflection when approaching the cutoff frequency surface around the plasmasphere, as illustrated in Figures 6 and 7.

The observations of AKR near the plasmasphere provide critical insights into their interactions with plasma-spheric density structures. Figure 8 Panels (a)–(b) show that the Arase spacecraft was positioned in the northern hemisphere (MLAT = 38°), on the early morning side (MLT = 4.5), at a radial distance of 2.8 Re, and near the northern edge of the plasmasphere. The wave electric field spectrogram reveals a distinct low-frequency cutoff in the AKR emissions, which correlates with variations in the local $f_{uh}$ line (approximately $f_X$, as $f_{ce}$ is small). Notably, the local $f_{uh}$ line lies slightly below the lower cutoff of AKR, separated by a frequency gap. For instance, at ~11:05:16 UT, the local $f_{uh}$ is ~170 kHz, while the AKR lower cutoff frequency is ~240 kHz, creating a ~70 kHz gap. This gap can be attributed to the angular dependence of the cutoff frequency, expressed as $f_{cutoff}(\theta) = f_X/\cos(\theta)$, where $\theta$ is the angle between the wave incident direction and the normal direction to the density gradient. The estimated angle $\theta$ for observations around ~11:05:16 UT is ~44°.

The cutoff feature extends up to 300 kHz, with higher-frequency emissions remaining unaffected, suggesting that the low-frequency emissions are reflected somewhere else and not being detected by the spacecraft. The higher-frequency emissions correspond to L-O mode harmonics of R-X mode fundamental emissions, as inferred from the axial ratio data in Panel (b). The axial ratio data illustrated in Panel (b), representing the wave's circular polarization defined on the Arase antenna plane, of which the axis is aligned with the anti-sunward direction, is influenced by the wave magnetoionic mode and the spacecraft's orientation. The axial ratio indicates left-hand polarization (positive in red in Panel (b)) on the nightside and northern hemisphere, where the magnetic field lines are roughly Sunward. When Arase is located in the southern hemisphere on the nightside, the magnetic field at the source region (southern polar region) is approximately anti-sunward. In this case, the positive axial ratio would indicate right-hand polarization. The observed cutoff near the plasmasphere highlights the role of wave reflection at lower frequencies.

Panels (c)–(d) illustrate a distinct AKR emission feature that diverges from the cutoff behavior observed in Panels (a)–(b). The emissions are well confined within the low-density region as indicated by the decreases in $f_{uh}$, with their lowest frequency close to the local $f_{uh}$. If we explain the lowest frequency of these emissions similar to Panel (a) as cut-off features, then this suggests a small incident angle of the emissions relative to the normal direction of the density gradient (where $\cos(\theta)$ approaches 1 and $f_{cutoff}$ is close to $f_{wave}$). However, emissions are entirely absent in the adjacent high-density regions (indicated by an increase in $f_{uh}$). If there are emissions in these high-density regions but being reflected, then the reflection of these emissions with frequencies up to 400 kHz and above, would require the $\theta$ angle to approach 90° ($\cos(\theta)$ close to 0), resulting in a much higher cutoff frequency that would preclude emissions above the $f_{uh}$ line and up to 400 kHz.

Given that the overall AKR emission incidence angles should remain consistent without large variations during this short observation period, this apparent contradiction suggests that instead of the emission incidence angle, the normal direction of the density gradient itself suddenly changed, leading the $\theta$ angle to vary significantly. Such a reorientation suggests the presence of low-density ducts as indicated by a decrease of the local $f_{uh}$, where AKR emissions are guided along the duct boundaries. Then the observed lowest frequency of the emissions within these low-density ducts are not due to cutoff but rather the geometries of the density duct. This is further demonstrated in the following ray-tracing calculations in Section 6. These ducted emissions may originate elsewhere, propagate along the ducts, and become detectable only within the low-density regions. Outside the ducts, no emissions are observed, either due to reflection preventing their detection or the absence of emissions in these regions.

The synchronous modulation of whistler-mode emissions (below both the $f_{ce}$ (white line) and $f_{pe}$ (not shown as $f_{pe} \approx f_{uh}$ here) in Panels (c)–(d)) in these low-density regions further supports this interpretation. As shown in Figure 8 Panels (c)–(d), the whistler-mode emissions are also confined to the low-density regions and exhibit intensity variations similar to those of AKR. The alignment of these emissions with the low-density ducts
<figure><img src="image_10.png" /><figcaption>**Figure 8.** Observations of AKR behavior near the plasmasphere. (a) Arase PWE wave electric field spectrogram from 2019-07-02 11:04 to 11:13. The enhanced line emissions are $f_{uh}$ emissions as indicated by the white arrow. (b) Axial ratio (circulation polarization) parameters at same time range as (a), given by PWE measurements with blue for the right-hand polarized emissions and red for left-hand polarized waves. (c) Arase PWE wave electric field spectrogram from 2018-12-08 07:25 to 08:41. The white line gives the local $f_{ce}$. The pink lines indicate the time interval shown in greater detail in panel (d). (d) Zoomed-in view of wave electric field spectrogram from 2018-12-08 07:37 to 07:50. (e) Arase PWE wave electric field spectrogram from 2021-02-23 21:00 to 21:20. The pink lines indicate the time interval shown in greater detail in panel (f). (f) Zoomed-in view of wave electric field spectrogram from 2021-02-23 21:05 to 21:13 with different scaling of intensity compared to panel (e). (g) Arase PWE wave electric field spectrogram from 2019-09-15 18:34 to 18:57. (h) Axial ratio spectrogram at same time range as (g).</figcaption></figure>
suggests a shared ducted propagation mechanism, where both AKR and whistler-mode waves are guided within
these structured density irregularities.

Sometimes, ducted emissions are observed overlapping with background unducted emissions, as shown in Panels (e)–(f). These ducted emissions manifest as localized intensity enhancements relative to the background and are synchronized with low-electron-density regions, indicated by local decreases in the $f_{uh}$ line. The zoomed-in view in Panel (f), with adjusted intensity saturation for clarity, reveals fine structures within the ducted emissions that at higher frequencies occasionally connect with emissions outside the ducts. This suggests that these unducted emissions are entering the ducts, with the intensification in the ducts resulting from the superposition of waves continuously captured and guided by the duct structures.

Panels (g)–(h) present another example of ducted AKR emissions, incorporating polarization measurements. The observed duration of these ducted emissions varies on the spectrogram, ranging from less than 1 min (as seen near 18:36 UT) to approximately 2 min (as seen near 18:46 UT). This variation corresponds to the spacecraft's traversal across the cross-section of the density ducts, suggesting that the spatial scale of the ducts can vary. The polarization data in Panel (h) reveals that both R-X mode (red) and L-O mode (blue) emissions are ducted by these low-density structures, aligning with theoretical predictions (Calvert, 1995). The low-frequency L-O mode emissions near 18:50 UT are identified as trapped kilometric continuum emissions (Matsumoto et al., 1994, 2000) confined within large density depletion regions in the plasmasphere.

These observations emphasize the critical role of plasmaspheric density structures, particularly low-density ducts, in shaping the propagation and observation of AKR. The existence of these low-density field-aligned ducts in the plasmasphere is widely accepted in previous studies of ground-based detections of whistler-mode waves, which are guided by these ducts (Bakharev et al., 2010; Chen et al., 2021; Ke et al., 2021; Ohta et al., 1996; Shen et al., 2021). The exact generation mechanism remains unclear but has been attributed to processes such as flux tube interchange (Ferrière et al., 1999; Loi et al., 2015), instabilities in the plasmapause region (Richmond, 1973), and hot plasma injections from the outer magnetosphere (Morioka & Oya, 1996). A recent statistical study of density irregularities using data from Arase and the Van Allen Probes suggests that these ducts are present across all MLT sectors and span an L-shell range from $L = 2$ to $L = 8$ (the upper limit constrained by Arase's orbit, though ducts may extend to larger radial distances). Thus these ducts have been observed both inside and outside the plasmapause (Thomas et al., 2021). Their occurrence rate increases at higher L-shells ($L > 4$). The density drop within these ducts varies widely, ranging from 10% to 80%, and exhibits dependence on local time and latitude. Detailed ray-tracing simulations of AKR propagation incorporating these density ducts are presented in the next section.

## 6. ARTEMIS Ray-Tracing Simulations on AKR Propagation Within Ducts

Figure 9 presents simulations of AKR propagation in the presence of low-density ducts. As specific parameters for these ducts are unavailable, the simulations provide a qualitative assessment of AKR propagation in a plasma environment with such structures. Based on observations indicating that density ducts span a wide L-shell range ($L = 2–8$; Thomas et al., 2021), the model incorporates ducts at this interval with $\Delta L = 0.3$. A uniform density reduction of 80% relative to the ambient electron density is applied along these ducts. However, in reality, the density drop likely varies with L-shell and latitude. These simulations, therefore, serve as an initial qualitative analysis rather than a fully representative physical model. The actual propagation of AKR within these ducts depends on the three-dimensional dynamics of both the wave and ducts structures, as well as the relative positioning of AKR sources and density ducts, which can vary over time.

The simulation results in Figure 9 immediately highlight that many rays become ducted within the low-density regions and are guided along magnetic field lines. Some emissions can propagate within the ducts and subsequently leak out under appropriate conditions. High-frequency rays (e.g., above 100 kHz) tend to exhibit partial guidance and leakage, whereas low-frequency rays (e.g., below 100 kHz) are more effectively guided over long distances, with some even traveling from the northern hemisphere to the southern hemisphere. Leakage occurs when the rays encounter duct boundaries at suitable angles. Interestingly, the ducted emissions are not strictly confined by ducts with high-density boundaries corresponding to the wave cutoff frequencies. Rays with frequencies as high as 800 kHz can be guided even within regions of relatively low density as shown in Panel (a) and the zoomed-in view in Panel (b). However, these lower-density ducts exhibit weaker confinement, particularly for
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Ray-tracing simulations of AKR propagation incorporating the density ducts. (a) AKR rays in magnetic meridian plane carried out using the plasmasphere model with the low-density ducts structures, in similar format as Figure 7. (b) Zoomed-in view of northern hemisphere of (a). (c) Ducted AKR ray paths in magnetic meridian plane launched only in northern hemisphere. Only the ray paths reaching an MLAT below 20° are selected and shown. (d) Zoomed-in view of Panel (c) as indicated by the white box in (c).</figcaption></figure>

high-frequency emissions, which are more prone to leakage. In contrast, low-frequency emissions are more easily ducted, enabling ducted propagation over a long distance.

Rays of different frequencies can enter the same ducts, directly accounting for the broad frequency range of ducted emissions observed in Figure 8. These emissions are further examined in Panels (c)–(d), where rays are launched exclusively from the northern hemisphere. Note that in Panels (a)–(b), rays are plotted with a 6° increment for clarity, while in Panels (c)–(d), all calculated rays with paths reaching latitudes below 20° are shown. The results illustrate that high-frequency emissions tend to leak through the ducts and propagate toward low-latitude regions. In contrast, low-frequency emissions are more effectively guided through the ducts, traveling significant distances toward the southern hemisphere. Leakage occurs only when the emissions encounter duct boundaries at suitable incidence angles or when they ultimately escape from the southern hemisphere auroral cavity.
The simulation results confirm that low-density ducts provide viable pathways for AKR emissions to penetrate the dense plasmasphere. This supports a consistent explanation for the AKR ducting observed near the plasmasphere (Figure 8) and aligns with the global occurrence patterns derived from our statistical analyses (Figure 6). Notably, the ducted propagation and leakage of AKR rays can account for the filling of the shadow region observed in Figure 6.

For high-frequency AKR (>100 kHz), ray paths are efficiently guided through the ducts for a certain distance before leaking into the equatorial shadow region, consistent with the features seen in Figure 6 Panels (b)–(d). In contrast, low-frequency AKR (<100 kHz) exhibits more complex behavior. Many rays remain strongly confined within the ducts due to the stronger density gradient around the ducts, as seen in Figure 9 (e.g., green rays in Panel (c)), while others experience a short time ducting before leaking toward higher latitudes (e.g., rays at 30–60 kHz in Panel (c)). This short duration ducting may explain the lower occurrence of low-frequency AKR in the shadow region. Note that the results from observations in Figure 6 suggest that low-frequency AKR is less effectively ducted, with ~52% of low-frequency emissions penetrating the plasmasphere, compared to ~85% for high-frequency emissions.

However, the results cannot explain why the low-frequency emissions are less ducted compared to the high-frequency emissions. Rather than adjusting the ray-tracing parameters to fit the observations, we acknowledge that the actual plasma environment is far more complex. Several factors could influence the reduced ducting of low-frequency AKR, including cavity properties (e.g., width and connectivity to ducts), duct density gradients at larger L-shells and their latitude-dependent variations (which determine whether ducts effectively guide low-frequency emissions), and the spatial distribution of ducts (e.g., more ducts at lower L-shells favoring high-frequency AKR ducting). Alternatively, stronger refraction may also prevent low-frequency AKR from entering the ducts in the first place. Further investigation is needed to determine whether ducting or alternative propagation mechanisms, such as enhanced refraction, primarily govern the behavior of low-frequency AKR in the equatorial shadow region.

# 7. Discussion and Summary

The propagation of AKR in the equatorial shadow region can be interpreted through multiple mechanisms. While ducted propagation through density cavities presents a comprehensive explanation for higher wave frequencies (>100 kHz), two alternative models—plasmaspheric compression and magnetosheath reflection—offer additional insights into specific cases of AKR propagation:

1. Xiao et al. (2016) proposed that during geomagnetically active conditions, enhanced convection electric fields compress the plasmasphere, shifting the position of the $f_X$ cutoff surface inward. This displacement may allow low-frequency AKR emissions, originating at larger radial distances, to propagate into the equatorial region. However, high-frequency emissions generated closer to Earth are more likely to undergo refraction due to increased plasma densities, limiting their equatorial penetration.

2. S. Y. Wu et al. (2022) and S. Wu, Ye, et al. (2024) described a mechanism in which radio emissions are reflected from the magnetosheath back to the equatorial region, which depends on the local electron density in the magnetosheath. For R-X mode emissions at 100 kHz: $f_X = \frac{1}{2}f_{ce} + \sqrt{f_{pe}^2 + \frac{f_e^2}{4}} \approx f_{pe} \approx 8980\sqrt{n_e} = f_{wave} = 100$ kHz. Assuming $f_{ce}$ is negligible in the magnetosheath, for $f_{wave} = 100$ kHz, the corresponding $n_e$ would be ~124 cm$^{-3}$, which significantly exceeds typical magnetosheath densities (several tens of electrons per cm$^{-3}$; Ma et al., 2020). This mechanism is plausible only under extreme conditions, such as during magnetospheric compressions. It may explain the filling effect for low-frequency emissions observed at large radial distance (Figure 6 Panel (a)), but is less applicable to higher frequencies.

While plasmaspheric compression and magnetosheath reflection provide viable explanations under specific conditions, their applicability remains limited to low-frequency AKR. In contrast, ducted propagation (Calvert, 1982, 1995) offers a general framework capable of explaining AKR distributions at higher wave frequencies.

The propagation of radio emissions through high-density plasma structures is well-documented in planetary magnetospheres, including Earth's plasmasphere, Saturn's plasma torus, and Jupiter's plasma disk (Boudjada et al., 2001; S. Wu, Taubenschuss, et al., 2024; S. Wu, Ye, et al., 2024; S. Y. Wu et al., 2022; Ye et al., 2010). Similar propagation pathways have been observed in SKR, where emissions escape from the plasma torus due to
variations in the torus density and geometry (S. Wu, Ye, et al., 2024). This phenomenon parallels AKR propa-
gation at Earth, where plasmaspheric compression influences ray trajectories (Xiao et al., 2007, 2016). Notably,
high-frequency SKR can traverse Saturn's plasma torus due to its relatively low density (S. Wu, Ye, et al., 2024).
While observations as shown in Figures 5–7 indicate that Earth's plasmasphere is sufficiently dense to obstruct
AKR across all wave frequencies. Saturn's narrowband (NB; Gurnett et al., 1981) emissions at 5 kHz can undergo
magnetosheath reflection, redirecting them toward equatorial regions (S. Y. Wu et al., 2022). A similar mech-
anism may explain the presence of low-frequency AKR in Earth's equatorial shadowing region at large radial
distances (Figure 6 Panel (a)). Specifically, for an average magnetosheath electron density of 10 cm⁻³,
$f_x \approx f_{pe} \approx 8980\sqrt{n_e} = f_{wave} \approx 28$ kHz, and for a density of 30 cm⁻³, magnetosheath reflections could occur
below ~50 kHz.

The ducted propagation mechanism verified in this study offers fresh insights into radio wave propagation and its interactions with plasmaspheric structures. Given its potential relevance beyond Earth, similar mechanisms should be investigated at Saturn and Jupiter, where low-density ducts may exist within their plasma tori (Azari et al., 2018; Daly et al., 2024). Additionally, further examination of density ducts using AKR observations (e.g., similar observations as illustrated in Figure 8) may provide important insights into their properties and the constraints they impose on radio wave propagation. In parallel, exploring the formation and evolution of such ducts under varying geomagnetic conditions could enhance our understanding of both AKR propagation and the dynamics of the plasmasphere. A limitation of the ray-tracing simulations in this study is that they are based on a simplified electron density model and consider only ray propagation in the magnetic meridian plane (i.e., a 2D simulation). In reality, the plasmasphere exhibits local time asymmetries (Darrouzet et al., 2009), and AKR emissions display a clear nightside preference (Gurnett, 1974), as also shown in this work. Additionally, the granularity of the density duct and cavity structures remains largely unknown, with many of their physical characteristics yet to be determined. These structures also co-rotate with the plasmasphere, further complicating their influence on AKR propagation. The auroral cavity may not be a uniform density depletion but rather a filamentary structure (Ergun et al., 1998), which could affect how AKR interacts with density ducts. Moreover, the full 3D beaming of AKR could introduce new perspectives on how emissions enter and propagate within these ducts. A comprehensive 3D modeling approach, incorporating a more realistic auroral cavity and duct structures, would be required to fully capture these effects. However, such an endeavor would be significantly more complex and is left for future studies.

To summarize, we derived the global occurrence rate maps of AKR using data from the Polar, Wind, and Arase
spacecraft. The occurrence maps show a high-latitude and nightside preference in AKR occurrence rates. We also
provide a detailed analysis of the equatorial shadow region of AKR generated by the dense plasmasphere. The
plasmaspheric ducting of AKR emissions through low-density cavities is discussed and verified through ray-
tracing simulations. It is important to note that in the statistical occurrence maps, all AKR emissions were
used without separating wave modes due to the lack of polarization measurements. In the ray-tracing simulations,
only R-X mode emissions were considered, as they are the most dominant wave components. Further studies
focusing on the distributions and propagation of L-O mode and Z mode AKR emissions are needed. The ducting
and leakage of emissions also introduce new scenarios for AKR observations, for example, the propagation of
AKR emissions to the opposite hemisphere and the characteristics of the duct-leaked AKR emissions, which
warrant further exploration.

Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

Data Availability Statement

The Polar PWI data are obtained at Gurnett et al. (2023). The Arase PWE data are obtained at Kasahara, Kumamoto, et al. (2018). The Wind Waves data are obtained at Waters, Cecconi, et al. (2021) and Fogg et al. (2023). The Polar magnetic field data (Russell et al., 1995) are obtained at Russell (2023). The Arase magnetic field data are obtained from the Magnetic Field Experiment (MGF; Matsuoka, Teramoto, Imajo, et al., 2018) at Matsuoka, Teramoto, Nomura, et al. (2018). The Artemis-P source code can be found at Gautier et al. (2023).
Acknowledgments

This work was supported by the Science and Technology Facilities Council (STFC) of the UK under Grant ST/Y002121/1. JEW's work at LAM was supported by the Center National d'Études Spatiales (CNES). CMJ and ARF's work at DIAS was supported by Taighe Éireann—Research Ireland award 18/FRL/6199. GF was supported by the Austrian Science Fund FWF (project https://doi.org/10.55776/16710). UT acknowledges support from the Czech Science Foundation (GACR) under Grant 24-11046L.

References

Alken, P., Thébault, E., Beggan, C. D., Amit, H., Aubert, J., Baerenzung, J., et al. (2021). International geomagnetic reference field: The thirteenth generation. *Earth Planets and Space*, 73(1), 49. https://doi.org/10.1186/s40623-020-01288-x

Appleton, E. V. (1928). The influence of the earth's magnetic field on wireless transmission (summary). In *U.R.S.I. Proc.* 1927.

Appleton, E. V. (1932). Wireless studies of the ionosphere. *Journal of the Institution of Engineers: Electronics*, 71(21), 257–265. https://doi.org/10.1049/pws.1932.0027

Azari, A. R., Liemohn, M. W., Jia, X., Thomsen, M. F., Mitchell, D. G., Sergis, N., et al. (2018). Interchange injections at Saturn: Statistical survey of energetic H+ sudden flux intensifications. *Journal of Geophysical Research: Space Physics*, 123(6), 4692–4711. https://doi.org/10.1029/2018JA025391

Bakharev, P. V., Zaboronkova, T. M., Kudrin, A. V., & Krafft, C. (2010). Whistler waves guided by density depletion ducts in a magnetoplasma. *Plasma Physics Reports*, 36(11), 919–930. https://doi.org/10.1134/S1063780X10110012

Benediktov, E. A., Getmantsev, G. G., Sazonov, Y. A., & Tarasov, A. F. (1965). Preliminary results of measurements of the intensity of distributed extraterrestrial radio-frequency emission at 725 and 1525-kHz frequencies by the satellite electron-2. *Kosmicskie issledovania*, 3(6), 1.

Benson, R. F. (1984). Ordinary mode auroral kilometric radiation, with harmonics, observed by ISIS 1. *Radio Science*, 19(2), 543–550. https://doi.org/10.1029/RS019i002p00543

Benson, R. F. (1985). Auroral kilometric radiation: Wave modes, harmonics, and source region electron density structures. *Journal of Geophysical Research*, 90(A3), 2753–2784. https://doi.org/10.1029/JA090iA03p02753

Benson, R. F., & Akasofu, S.-I. (1984). Auroral kilometric radiation/aurora correlation. *Radio Science*, 19(2), 527–541. https://doi.org/10.1029/RS019i002p00527

Benson, R. F., & Calvert, W. (1979). ISIS 1 observations at the source of auroral kilometric radiation. *Geophysical Research Letters*, 6(6), 479–482. https://doi.org/10.1029/GL006i006p00479

Boudjada, M. Y., Galopeau, P. H. M., & Rucker, H. O. (2001). Jovian hectometric beam observed by PWS and WAVES experiments on board Galileo and Wind spacecraft. *Planetary and Space Science*, 49(10), 1151–1158. https://doi.org/10.1016/S0032-0633(01)00022-8

Bougeret, J.-L., Kaiser, M. L., Kellogg, P. J., Manning, R., Goetz, K., Monson, S. J., et al. (1995). WAVES: The radio and plasma wave investigation on the Wind spacecraft. *Space Science Reviews*, 71(1), 231–263. https://doi.org/10.1007/BF00751331

Calvert, W. (1981). The auroral plasma cavity. *Geophysical Research Letters*, 8(8), 919–921. https://doi.org/10.1029/GL008i008p00919

Calvert, W. (1982). Ducted auroral kilometric radiation. *Geophysical Research Letters*, 9(1), 56–59. https://doi.org/10.1029/GL009i001p00056

Calvert, W. (1995). Wave ducting in different wave modes. *Journal of Geophysical Research*, 100(A9), 17491–17497. https://doi.org/10.1029/95JA01131

Chen, R., Gao, X., Lu, Q., Chen, L., Tsurutani, B. T., Li, W., et al. (2021). In situ observations of whistler-mode chorus waves guided by density ducts. *Journal of Geophysical Research: Space Physics*, 126(4), e2020JA028814. https://doi.org/10.1029/2020JA028814

Daly, A., Li, W., Ma, Q., Shen, X.-C., Capannolo, L., Huang, S., et al. (2024). Statistical survey of interchange events in the Jovian magnetosphere using Juno observations. *Geophysical Research Letters*, 51(19), e2024GL110300. https://doi.org/10.1029/2024GL110300

Darrouzet, F., Gallagher, D. L., André, N., Carpenter, D. L., Dandouras, I., Décréau, P. M. E., et al. (2009). Plasmaspheric density structures and dynamics: Properties observed by the CLUSTER and IMAGE missions. *Space Science Reviews*, 145(1), 55–106. https://doi.org/10.1007/s11214-008-9438-9

de Feraudy, H., Pedersen, B. M., Bahnsen, A., & Jespersen, M. (1987). Viking observations of auroral kilometric radiation from the plasmasphere to night auroral oval source regions. *Geophysical Research Letters*, 14(5), 511–514. https://doi.org/10.1029/GL014i005p00511

Deng, Z., Xiao, F., Zhou, Q., Zhang, S., Liu, S., Yang, Q., et al. (2022). Direct evidence for auroral kilometric radiation propagation into radiation belts based on Arase spacecraft and Van Allen Probe B. *Geophysical Research Letters*, 49(19), e2022GL100860. https://doi.org/10.1029/2022GL100860

Dunckel, N., Ficklin, B., Rorden, L., & Helliwell, R. A. (1970). Low-frequency noise observed in the distant magnetosphere with OGO 1. *Journal of Geophysical Research*, 75(10), 1854–1862. https://doi.org/10.1029/JA075i010p01854

Ergun, R. E., Carlson, C. W., McFadden, J. P., Mozer, F. S., Delory, G. T., Peria, W., et al. (1998). FAST satellite wave observations in the AKR source region. *Geophysical Research Letters*, 25(12), 2061–2064. https://doi.org/10.1029/98GL00570

Ferrière, K. M., Zimmer, C., & Blanc, M. (1999). Magnetohydrodynamic waves and gravitational/centrifugal instability in rotating systems. *Journal of Geophysical Research*, 104(A8), 17335–17356. https://doi.org/10.1029/1999JA900167

Fogg, A. R., Jackman, C., Waters, J. E., Bonnin, X., Lamy, L., Cecconi, B., et al. (2023). Bursts of auroral kilometric radiation individually selected from Wind/WAVES data (1995-2004) (Version 1.1) [Dataset]. *PADC*. https://doi.org/10.25935/ayzp-1833

Fogg, A. R., Jackman, C. M., Chapman, S. C., Waters, J. E., Bergin, A., Lamy, L., et al. (2024). Quantification of magnetosphere-ionosphere coupling timescales using mutual information: Response of terrestrial radio emissions and ionospheric–magnetospheric currents. *Nonlinear Processes in Geophysics*, 31(2), 195–206. https://doi.org/10.5194/npg-31-195-2024

Fogg, A. R., Jackman, C. M., Waters, J. E., Bonnin, X., Lamy, L., Cecconi, B., et al. (2022). Wind/WAVES observations of Auroral Kilometric Radiation: Automated burst detection and terrestrial solar wind—Magnetosphere coupling effects. *Journal of Geophysical Research: Space Physics*, 127(5), e2021JA030209. https://doi.org/10.1029/2021JA030209

Fung, S. F., & Green, J. L. (2005). Modeling of field-aligned guided echoes in the plasmasphere. *Journal of Geophysical Research*, 110(A1). https://doi.org/10.1029/2004JA010658

Gallagher, D. L., & D'Angelo, N. (1981). Correlations between solar wind parameters and auroral kilometric radiation intensity. *Geophysical Research Letters*, 8(10), 1087–1089. https://doi.org/10.1029/GL008i010p01087

Gautier, A.-L. (2013). *Étude de la propagation des ondes radio dans les environnements planétaires* (Doctoral dissertation). Observatoire de Paris.

Gautier, A.-L., Baskevitch, C. A., & Cecconi, B. (2023). maserlib/ARTEMIS-P: Version 0.1.0 [Software]. *Zenodo*. https://doi.org/10.5281/zenodo.8055943

Gautier, A.-L., Cecconi, B., & Zarka, P. (2013). ARTEMIS-P: A general ray tracing code in anisotropic plasma for radioastronomical applications. In *Proceedings of the 2013 International Symposium on Electromagnetic Theory* (pp. 1–4).

Green, J. L. (1988). Ray tracing planetary radio emissions. In H. O. Rucker, S. J. Bauer, & B. M. Pedersen (Eds.), *Planetary radio emissions II*. Austrian Academy of Sciences Press.

Green, J. L., Saflekos, N. A., Gurnett, D. A., & Potemra, T. A. (1982). A correlation between auroral kilometric radiation and field-aligned currents. *Journal of Geophysical Research*, 87(A12), 10463–10467. https://doi.org/10.1029/JA087iA12p10463

Gurnett, D. A. (1974). The Earth as a radio source: Terrestrial kilometric radiation. *Journal of Geophysical Research*, 79(28), 4227–4238. https://doi.org/10.1029/JA079i028p04227
Gurnett, D. A., & Inan, U. S. (1988). Plasma wave observations with the Dynamics Explorer 1 spacecraft. *Reviews of Geophysics*, **26**(2), 285–316.
https://doi.org/10.1029/RG026i002p00285

Gurnett, D. A., Kurth, W. S., & Scarf, F. L. (1981). Narrowband electromagnetic emissions from Saturn's magnetosphere. *Nature*, **292**(5825), 733–737. https://doi.org/10.1038/292733a0

Gurnett, D. A., Menietti, J., & Douglas (2023). Polar plasma wave instrument (PWI), sweep frequency receivers A and B—2 sec resolution fields [Dataset]. NASA Space Physics Data Facility. https://doi.org/10.48322/k1kt-d028

Gurnett, D. A., Persoon, A. M., Randall, R. F., Odem, D. L., Remington, S. L., Averkamp, T. F., et al. (1995). The Polar plasma wave instrument. *Space Science Reviews*, **71**(1–4), 597–622. https://doi.org/10.1007/BF00751343

Hanasz, J., de Feraudy, H., Schreiber, R., & Panchenko, M. (2006). Pulsations of the auroral kilometric radiation. *Journal of Geophysical Research*, **111**(A3). https://doi.org/10.1029/2005JA011302

Hanasz, J., de Feraudy, H., Schreiber, R., Parks, G., Brittnacher, M., Mogilevsky, M. M., & Romantsova, T. V. (2001). Wideband bursts of auroral kilometric radiation and their association with UV auroral bulges. *Journal of Geophysical Research*, **106**(A3), 3859–3871. https://doi.org/10.1029/2000JA900098

Hanasz, J., Panchenko, M., de Feraudy, H., Schreiber, R., & Mogilevsky, M. M. (2003). Occurrence distributions of the auroral kilometric radiation ordinary and extraordinary wave modes. *Journal of Geophysical Research*, **108**(A11). https://doi.org/10.1029/2002JA009579

Hanasz, J., Schreiber, R., Pickett, J., & de Feraudy, H. (2008). Pulsations of auroral kilometric radiation at Pc1 frequencies. *Geophysical Research Letters*, **35**(15). https://doi.org/10.1029/2008GL034609

Hartree, D. R. (1931). The propagation of electromagnetic waves in a refracting medium in a magnetic field. *Mathematical Proceedings of the Cambridge Philosophical Society*, **27**(1), 143–162. https://doi.org/10.1017/s0305004100009440

Haselgrove, C. B., & Haselgrove, J. (1960). Twisted ray paths in the ionosphere. *Proceedings of the Physical Society*, **75**(3), 357–363. https://doi.org/10.1088/0370-1328/75/3/304

Haselgrove, J. (1963). The Hamiltonian ray path equations. *Journal of Atmospheric and Terrestrial Physics*, **25**(7), 397–399. https://doi.org/10.1016/0021-9169(63)90173-9

Hashimoto, K., Kudo, S., & Matsumoto, H. (1998). Source of auroral myriametric radiation observed with Geotail. *Journal of Geophysical Research*, **103**(A10), 23475–23483. https://doi.org/10.1029/98JA01920

Hilgers, A. (1992). The auroral radiating plasma cavities. *Geophysical Research Letters*, **19**(3), 237–240. https://doi.org/10.1029/91GL02938

Huff, R. L., Calvert, W., Craven, J. D., Frank, L. A., & Gurnett, D. A. (1988). Mapping of auroral kilometric radiation sources to the aurora. *Journal of Geophysical Research*, **93**(A10), 11445–11454. https://doi.org/10.1029/9A093iA10p11445

Imhof, W. L., Walt, M., Anderson, R. R., Chenette, D. L., Hawley, J. D., Mobilia, J., & Petrinec, S. M. (2000). Association of electron precipitation with auroral kilometric radiation. *Journal of Geophysical Research*, **105**(A1), 277–289. https://doi.org/10.1029/1999JA900394

Kaiser, M. L., Alexander, J. K., Riddle, A. C., Pearce, J. B., & Warwick, J. W. (1978). Direct measurements by Voyagers 1 and 2 of the polarization of terrestrial kilometric radiation. *Geophysical Research Letters*, **5**(10), 857–860. https://doi.org/10.1029/GL005i010p00857

Kasaba, Y., Matsumoto, H., Hashimoto, K., & Anderson, R. R. (1997). The angular distribution of auroral kilometric radiation observed by the GEOTAIL spacecraft. *Geophysical Research Letters*, **24**(20), 2483–2486. https://doi.org/10.1029/97GL02599

Kasahara, Y., Kasaba, Y., Kojima, H., Yagitani, S., Ishisaka, K., Kumamoto, A., et al. (2018). The plasma wave experiment (PWE) on board the Arase (ERG) satellite. *Earth Planets and Space*, **70**(1), 86. https://doi.org/10.1186/s40623-018-0842-4

Kasahara, Y., Kumamoto, A., Tsuchiya, F., Matsuda, S., Shoji, M., Nakamura, S., et al. (2018). The PWE/HFA instrument level-2 spectrum data of exploration of energization and radiation in geospace (ERG) Arase satellite [Dataset]. https://doi.org/10.34515/DATA.ERG-10000

Ke, Y., Chen, L., Gao, X., Lu, Q., Wang, X., Chen, R., et al. (2021). Whistler-mode waves trapped by density irregularities in the Earth's magnetosphere. *Geophysical Research Letters*, **48**(7), e2020GL092305. https://doi.org/10.1029/2020GL092305

Kletzing, C. A., Mozer, F. S., & Torbert, R. B. (1998). Electron temperature and density at high latitude. *Journal of Geophysical Research*, **103**(A7), 14837–14845. https://doi.org/10.1029/98JA00962

Kolpak, V. I., Mogilevsky, M. M., Chugunin, D. V., Chernyshov, A. A., & Moiseenko, I. L. (2024). Transfer of Auroral Kilometric Radiation through low-density channels at the boundary of plasmasphere. *Solar-Terrestrial Physics*, **10**(1), 19–28. https://doi.org/10.12737/stp-101202403

Kumamoto, A., Tsuchiya, F., Kasahara, Y., Kasaba, Y., Kojima, H., Yagitani, S., et al. (2018). High frequency analyzer (HFA) of plasma wave experiment (PWE) onboard the Arase spacecraft. *Earth Planets and Space*, **70**(1), 82. https://doi.org/10.1186/s40623-018-0854-0

LaBelle, J., Yearby, K., & Pickett, J. S. (2022). South Pole station ground-based and cluster satellite measurements of leaked and escaping auroral kilometric radiation. *Journal of Geophysical Research: Space Physics*, **127**(2), e2021JA029399. https://doi.org/10.1029/2021JA029399

Ladreiter, H. P., & Leblanc, Y. (1990). Source location of the Jovian hectometric radiation via ray-tracing technique. *Journal of Geophysical Research*, **95**(A5), 6423–6435. https://doi.org/10.1029/95JA095iA05p06423

Lamy, L., Schippers, P., Zarka, P., Cecconi, B., Arridge, C. S., Dougherty, M. K., et al. (2010). Properties of Saturn kilometric radiation measured within its source region. *Geophysical Research Letters*, **37**(12). https://doi.org/10.1029/2010GL043415

Lamy, L., Zarka, P., Cecconi, B., & Prangé, R. (2010). Auroral kilometric radiation diurnal, semidiurnal, and shorter-term modulations disentangled by Cassini. *Journal of Geophysical Research*, **115**(A9). https://doi.org/10.1029/2010JA015434

Liou, K., Meng, C.-I., Lui, T. Y., Newell, P. T., Brittnacher, M., Parks, G., et al. (1999). On relative timing in substorm onset signatures. *Journal of Geophysical Research*, **104**(A10), 22807–22817. https://doi.org/10.1029/1999JA900206

Loi, S. T., Murphy, T., Cairns, I. H., Menk, F. W., Waters, C. L., Erickson, P. J., et al. (2015). Real-time imaging of density ducts between the plasmasphere and ionosphere. *Geophysical Research Letters*, **42**(10), 3707–3714. https://doi.org/10.1002/2015GL063699

Louarn, P., & Le Quéau, D. (1996a). Generation of the auroral kilometric radiation in plasma cavities—I. Experimental study. *Planetary and Space Science*, **44**(3), 199–210. https://doi.org/10.1016/0032-0633(95)00121-2

Louarn, P., & Le Quéau, D. (1996b). Generation of the auroral kilometric radiation in plasma cavities—II. The cyclotron maser instability in small size sources. *Planetary and Space Science*, **44**(3), 211–224. https://doi.org/10.1016/0032-0633(95)00122-0

Louarn, P., Roux, A., de Feraudy, H., Le Quéau, D., André, M., & Matson, L. (1990). Trapped electrons as a free energy source for the auroral kilometric radiation. *Journal of Geophysical Research*, **95**(A5), 5983–5995. https://doi.org/10.1029/95JA095iA05p05983

Louis, C. K., Smith, K. D., Jackman, C. M., Fogg, A. R., Waters, J. E., O'Dwyer, E. P., & Granroth, L. (2023). Latitudinal distribution of auroral kilometric radiation based on Polar spacecraft observations. In C. K. Louis, C. M. Jackman, G. Fischer, A. H. Sulaiman, & P. Zucca (Eds.), *Planetary, solar and heliospheric radio emissions IX, DIAS and TCD*. https://doi.org/10.2554/103088

Ma, X., Nykyri, K., Dimmock, A., & Chu, C. (2020). Statistical study of solar wind, magnetosheath, and magnetotail plasma and field properties: 12+ years of THEMIS observations and MHD simulations. *Journal of Geophysical Research: Space Physics*, **125**(10), e2020JA028209. https://doi.org/10.1029/2020JA028209
Matsumoto, H., Nagano, I., Anderson, R. R., Kojima, H., Hashimoto, K., Tsutsui, M., et al. (1994). Plasma wave observations with GEOTAIL spacecraft. *Journal of Geomagnetism and Geoelectricity*, **46**(1), 59–95. https://doi.org/10.5636/jgg.46.59

Matsumoto, H., Nagano, I., & Kasaba, Y. (2000). Terrestrial continuum radiation in the magnetotail: Geotail observations. In *Radio astronomy at long wavelengths* (pp. 187–203). American Geophysical Union (AGU). https://doi.org/10.1029/GM119p0187

Matsuoaka, A., Teramoto, M., Imajo, S., Kurita, S., Miyoshi, Y., & Shinohara, I. (2018). The MGF instrument Level-2 spin-averaged magnetic field data of Exploration of energization and Radiation in Geospace (ERG) Arase satellite [Dataset]. https://doi.org/10.34515/DATA.ERG-06001

Matsuoaka, A., Teramoto, M., Nomura, R., Nosé, M., Fujimoto, A., Tanaka, Y., et al. (2018). The ARASE (ERG) magnetic field investigation. *Earth Planets and Space*, **70**(1), 43. https://doi.org/10.1186/s40623-018-0800-1

Mellott, M. M., Calvert, W., Huff, R. L., Gurnett, D. A., & Shawhan, S. D. (1984). DE-1 observations of ordinary mode and extraordinary mode auroral kilometric radiation. *Geophysical Research Letters*, **11**(12), 1188–1191. https://doi.org/10.1029/GL011i012p01188

Morioka, A., Miyoshi, Y., Miyashita, Y., Kasaba, Y., Misawa, H., Tsuchiya, F., et al. (2010). Two-step evolution of auroral acceleration at substorm onset. *Journal of Geophysical Research*, **115**(A11). https://doi.org/10.1029/2010JA015361

Morioka, A., Miyoshi, Y., Tsuchiya, F., Misawa, H., Kasaba, Y., Asozu, T., et al. (2011). On the simultaneity of substorm onset between two hemispheres. *Journal of Geophysical Research*, **116**(A4). https://doi.org/10.1029/2010JA016174

Morioka, A., Miyoshi, Y., Tsuchiya, F., Misawa, H., Yumoto, K., Parks, G. K., et al. (2008). AKR breakup and auroral particle acceleration at substorm onset. *Journal of Geophysical Research*, **113**(A9). https://doi.org/10.1029/2008JA013322

Morioka, A., & Oya, H. (1996). Plasmapause disturbances synchronized with magnetospheric disturbances. *Journal of Geomagnetism and Geoelectricity*, **48**(3), 309–318. https://doi.org/10.5636/jgg.48.309

Mutel, R. L., Christopher, I. W., & Pickett, J. S. (2008). Cluster multispacecraft determination of AKR angular beaming. *Geophysical Research Letters*, **35**(7), L07104. https://doi.org/10.1029/2008GL033377

Mutel, R. L., Menietti, J. D., Christopher, I. W., Gurnett, D. A., & Cook, J. M. (2006). Striated auroral kilometric radiation emission: A remote tracer of ion solitary structures. *Journal of Geophysical Research*, **111**(A10), A10203. https://doi.org/10.1029/2006JA011660

Ohta, K., Kitagawa, T., Shima, N., Hayakawa, M., & Dowden, R. L. (1996). Characteristics of mid-latitude whistler ducts as deduced from ground-based measurements. *Geophysical Research Letters*, **23**(23), 3301–3304. https://doi.org/10.1029/96GL03253

Ozhogin, P., Tu, J., Song, P., & Reinisch, B. W. (2012). Field-aligned distribution of the plasmaspheric electron density: An empirical model derived from the IMAGE RPI measurements. *Journal of Geophysical Research*, **117**(A6). https://doi.org/10.1029/2011JA017330

Panchenko, M., Hanasz, J., & Rucker, H. O. (2008). Estimation of linear wave polarization of the auroral kilometric radiation. *Radio Science*, **43**(1), RS1006. https://doi.org/10.1029/2006RS003606

Panchenko, M., Khodachenko, M. L., Kislykov, A. G., Rucker, H. O., Hanasz, J., Kaiser, M. L., et al. (2009). Daily variations of auroral kilometric radiation observed by STEREO. *Geophysical Research Letters*, **36**(6), L06101. https://doi.org/10.1029/2008GL037042

Richmond, A. D. (1973). Self-induced motions of thermal plasma in the magnetosphere and the stability of the plasmapause. *Radio Science*, **8**(11), 1019–1027. https://doi.org/10.1029/RS008i011p01019

Ripoll, J.-F., Thaller, S. A., Hartley, D. P., Cunningham, G. S., Pierrard, V., Kurth, W. S., et al. (2022). Statistics and empirical models of the plasmasphere boundaries from the Van Allen Probes for radiation belt physics. *Geophysical Research Letters*, **49**(21), e2022GL101402. https://doi.org/10.1029/2022GL101402

Roux, A., Hilgers, A., de Feraudy, H., le Queau, D., Louarn, P., Perraut, S., et al. (1993). Auroral kilometric radiation sources: In situ and remote observations from Viking. *Journal of Geophysical Research*, **98**(A7), 11657–11670. https://doi.org/10.1029/92JA02309

Russell, C. T. (2023). Polar magnetic field key parameters [Dataset]. NASA Space Physics Data Facility. https://doi.org/10.48322/VSKF-PH35

Russell, C. T., Snare, R. C., Means, J. D., Pierce, D., Dearborn, D., Larson, M., et al. (1995). The GGS/POLAR magnetic fields investigation. *Space Science Reviews*, **71**(1), 563–582. https://doi.org/10.1007/BF00751341

Schreiber, R., Panchenko, M., Hanasz, J., Mutel, R., & Christopher, I. (2017). Beaming of intense AKR seen from the Interball-2 spacecraft. *Journal of Geophysical Research: Space Physics*, **122**(1), 249–257. https://doi.org/10.1002/2015JA022197

Shawhan, S. D., & Gurnett, D. A. (1982). Polarization measurements of auroral kilometric radiation by Dynamics Explorer-1. *Geophysical Research Letters*, **9**(9), 913–916. https://doi.org/10.1029/GL009i009p00913

Shen, Y., Chen, L., Zhang, X.-J., Artemyev, A., Angelopoulos, V., Cully, C. M., et al. (2021). Conjugate observation of magnetospheric chorus propagating to the ionosphere by ducting. *Geophysical Research Letters*, **48**(23), e2021GL095933. https://doi.org/10.1029/2021GL095933

Singh, N., Deverapalli, C., Rajagiri, A., & Khazanov, I. (2005). Dynamical behavior of U-shaped double layers: Cavity formation and filamentary structures. *Nonlinear Processes in Geophysics*, **12**(6), 783–798. https://doi.org/10.5194/npg-12-783-2005

Strangeway, R. J., Ergun, R. E., Carlson, C. W., McFadden, J. P., Delory, G. T., & Pritchett, P. L. (2001). Accelerated electrons as the source of auroral kilometric radiation. *Physics and Chemistry of the Earth - Part C: Solar, Terrestrial & Planetary Science*, **26**(1), 145–149. https://doi.org/10.1016/S1464-1917(00)00100-8

Taubenschuss, U., Fischer, G., Pisa, D., Santolik, O., & Soucek, J. (2023). Classification of the spectral fine structure in auroral kilometric radiation. In C. K. Louis, C. M. Jackman, G. Fischer, A. H. Sulaiman, & P. Zucca (Eds.), *Planetary, solar and heliospheric radio emissions IX* (p. 103089). https://doi.org/10.2554/103089

Thomas, N., Shiokawa, K., Miyoshi, Y., Kasahara, Y., Shinohara, I., Kumamoto, A., et al. (2021). Investigation of small-scale electron density irregularities observed by the Arase and Van Allen Probes satellites inside and outside the plasmasphere. *Journal of Geophysical Research: Space Physics*, **126**(3), e2020JA027917. https://doi.org/10.1029/2020JA027917

Waters, J. E., Cecconi, B., Jackman, C. M., Whiter, D. K., Bonnin, X., Lamy, L., & Issautier, K. (2021). Wind/waves flux density collection calibrated for auroral kilometric radiation (Version 1.0) [Dataset]. PADC. https://doi.org/10.25935/wxv0-vr90

Waters, J. E., Jackman, C. M., Lamy, L., Cecconi, B., Whiter, D. K., Bonnin, X., et al. (2021). Empirical selection of auroral kilometric radiation during a multipoint remote observation with wind and Cassini. *Journal of Geophysical Research: Space Physics*, **126**(10), e2021JA029425. https://doi.org/10.1029/2021JA029425

Waters, J. E., Jackman, C. M., Whiter, D. K., Forsyth, C., Fogg, A. R., Lamy, L., et al. (2022). A perspective on substorm dynamics using 10 years of Auroral Kilometric Radiation observations from Wind. *Journal of Geophysical Research: Space Physics*, **127**(9), e30449. https://doi.org/10.1029/2022JA030449

Wu, C. S., & Lee, L. C. (1979). A theory of the terrestrial kilometric radiation. *Astrophysical Journal*, **230**, 621–626. https://doi.org/10.1086/157120

Wu, S., Taubenschuss, U., Ye, S., Fischer, G., Cecconi, B., Wang, M., et al. (2024). Ray-tracing analysis for the propagation of Saturn narrowband emission within the Saturnian magnetosphere. *Journal of Geophysical Research: Planets*, **129**(4), e2023JE008118. https://doi.org/10.1029/2023JE008118
Wu, S., Ye, S., Taubenschuss, U., Fischer, G., Jackman, C. M., Zarka, P., et al. (2024). Formation of an extended equatorial shadow zone for low-frequency Saturn kilometric radiation. *Geophysical Research Letters*, 51(15), e2023GL106652. https://doi.org/10.1029/2023GL106652

Wu, S. Y., Ye, S. Y., Fischer, G., Jackman, C. M., Wang, J., Menietti, J. D., et al. (2022). Reflection and refraction of the L-O mode 5 kHz Saturn narrowband emission by the magnetosheath. *Geophysical Research Letters*, 49(5), e2021GL096990. https://doi.org/10.1029/2021GL096990

Xiao, F., Chen, L., Zheng, H., & Wang, S. (2007). A parametric ray tracing study of superluminous auroral kilometric radiation wave modes. *Journal of Geophysical Research*, 112(A10), A10214. https://doi.org/10.1029/2006JA012178

Xiao, F., Tang, J., Zhang, S., Zhou, Q., Liu, S., He, Y., et al. (2022). Asymmetric distributions of auroral kilometric radiation in Earth's northern and Southern Hemispheres observed by the Arase Satellite. *Geophysical Research Letters*, 49(13), e2022GL099571. https://doi.org/10.1029/2022GL099571

Xiao, F., Zhou, Q., Su, Z., He, Z., Yang, C., Liu, S., et al. (2016). Explaining occurrences of auroral kilometric radiation in Van Allen radiation belts. *Geophysical Research Letters*, 43(23), 11911-971978. https://doi.org/10.1002/2016GL071728

Ye, S.-Y., Menietti, J. D., Fischer, G., Wang, Z., Cecconi, B., Gurnett, D. A., & Kurth, W. S. (2010). Z mode waves as the source of Saturn narrowband radio emissions. *Journal of Geophysical Research*, 115(A8). https://doi.org/10.1029/2009JA015167

Zhang, S., Liu, S., Li, W., He, Y., Yang, Q., Xiao, F., et al. (2021). A concise empirical formula for the field-aligned distribution of auroral kilometric radiation based on Arase Satellite and Van Allen Probes. *Geophysical Research Letters*, 48(8), e2021GL092805. https://doi.org/10.1029/2021GL092805

Zhang, S., Yin, Q., Yang, H., Xiao, F., Zhou, Q., Yang, Q., et al. (2024). Direct observation of L-X mode of auroral kilometric radiation in the lower latitude magnetosphere by the Arase Satellite. *Geophysical Research Letters*, 51(5), e2023GL105694. https://doi.org/10.1029/2023GL105694

Zhao, W., Liu, S., Zhang, S., Zhou, Q., Yang, C., He, Y., et al. (2019). Global occurrences of auroral kilometric radiation related to suprathelial electrons in radiation belts. *Geophysical Research Letters*, 46(13), 7230-7236. https://doi.org/10.1029/2019GL083944