Direct Observation of L‐X Mode of Auroral Kilometric Radiation in the Lower Latitude Magnetosphere by the Arase Satellite

Previous studies have shown that auroral kilometric radiation (AKR) can play an important role in the magnetosphere‐atmosphere coupling and has the right‐handed extraordinary (R‐X), left‐handed ordinary (L‐O) and left‐handed extraordinary (L‐X) modes. However, the L‐X mode has not been directly observed in the lower latitude magnetosphere yet, probably because of its very limited frequency range. Here, using observations of the Arase satellite on 6 September 2018, we present an AKR event with two distinct bands (8–20 and 300–1000 kHz) around the location: L = 8 and latitude = −37°. The low (high) band is identified as the L‐X (R‐X) mode based on the polarization and frequency ranges. Simulations of 3‐D ray tracing show that most of ray paths with 14 (11 and 18) kHz pass (miss) the location of Arase, basically consistent with observations. Our study provides direct evidence that the L‐X mode can propagate from high latitudes downward to lower latitudes.


Introduction
Auroral kilometric radiation (AKR) is one of the powerful terrestrial radio emissions that originates from the polar region (Ergun et al., 1998;Kurth et al., 1975;Zarka, 1998).Similar emissions have been observed on all of the solar system's magnetized planets (Fischer et al., 2009;Schippers et al., 2011;Ye et al., 2012Ye et al., , 2016;;Zarka, 1998).Gurnett (1974) has revealed that AKR is an electromagnetic wave with kilometric wavelength.The electron cyclotron maser instability (ECMI) has been recognized as an important production mechanism of AKR (Burinskaya, 2013;Calvert, 1995;Melrose et al., 1982;Pritchett, 1984;Wu & Lee, 1979).The downward suprathermal electrons provide the free energy for the generation of AKR (Delory et al., 1998;Ergun et al., 1998;Seki et al., 2005).A positive velocity gradient in the electron velocity distribution, which results in a significant nonlinear development of waves close to the electron cyclotron frequency, is typically required in simulations of AKR production (Mutel et al., 2007).Using the data of Hawkeye and Fast satellites, some researchers have confirmed the polar cavity as AKR source region (Calvert, 1981a;Ergun et al., 1998).
Previous works have shown that AKR primarily occurs in the right-handed extraordinary (R-X) mode, with a small contribution in the left-handed ordinary (L-O) and left-handed extraordinary (L-X) modes (Calvert, 1981a(Calvert, , 1981b;;Gurnett et al., 1983;Liou et al., 2000;Pritchett et al., 2002;Schreiber et al., 2017).Xiao et al. (2016) have proposed that R-X mode can propagate down to the equatorial plane from high latitudes by the 3-D ray tracing method.It is well known that wave-particle interaction is an important process of magnetosphere-ionosphereatmosphere coupling and has been studied widely by researchers (J.B. He et al., 2021;Q. He et al., 2022;Jin et al., 2018;Guo et al., 2020;Guan et al., 2020;Q. Yang et al., 2016;C. Yang et al., 2022).Several works have demonstrated that AKR may accelerate or scatter the energetic electrons under the proper conditions (Li et al., 2023;Summers et al., 2001;Xiao, Chen, & He, 2010;Xiao, Chen, He, & Yang, 2010;Xiao, Su, et al., 2010;Xiao et al., 2006;Zhang et al., 2020).Those accelerated (or scattered) electrons can lead to considerable damage to spacecrafts (or destruction of ozone) (Baker, 2002;Callis et al., 1998;Thorne, 1977;Thorne et al., 2005).Using the data of Van Allen Probes, Zhao et al. (2019) have suggested that R-X mode exists widely in the radiation belts.Recently, Zhang et al. (2021) have presented a concise model for the field-aligned distribution of R-X mode amplitude in the region of L = 3.0-6.2and Magnetic Latitude (MLAT) = 0-± 40°.Based on observations from spacecrafts, some works have found the annual and seasonal periodic variations of R-X mode (Green et al., 2004;Kumamoto et al., 2003;Kumamoto & Oya, 1998;Mogilevsky et al., 2005;Xiao et al., 2022).Recently, Kumamoto et al. (2018) have reported an AKR event with R-X and L-O modes simultaneously using the data from Arase satellite.Oya and Morioka (1983) have reported an L-X mode event (called the Z mode) observed by the Jikiken (EXOS-B) satellite near the source region of AKR.At low latitudes, previous studies have only reported observations of the R-X and L-O modes.However, due to its extremely limited frequency range, the L-X mode at lower latitudes has not been directly observed so far.We focus on the observation and simulation of L-X mode in this paper.

Correlation Satellites Data
Arase is a small scientific satellite for the exploration of energization and radiation in geospace projects.It was launched on 20 December 2016 by Japan Aerospace Exploration Agency and measured from March 2017.The orbital inclination of Arase satellite is ∼31°, the altitudes of perigee and apogee are 340-440 km and 32,200-32,300 km, respectively.The high elliptical orbit of Arase covers the region of MLAT = 0-±42°and L = 1.1-9.0(Miyoshi, Shinohara, Takashima, et al., 2018;Nakamura et al., 2018).The power spectral density (PSD) of wave electric field is measured by the High Frequency Analyzer (HFA) of the Plasma Wave Experiment (PWE), which explores the electric field component of plasma wave from 2 kHz to 10 MHz (Kasahara, Kasaba, et al., 2018;Kumamoto et al., 2018).The frequency ranges of each AKR mode are as follows: R-X mode : L-X mode : with: where f ce is the local electron gyro-frequency and can be calculated by the ambient magnetic field strength B 0 , f pe represents the electron plasma frequency and can be obtained by the local upper hybrid fre- Under the EE-LR mode of HFA, the right-hand E 2 R ) and left-hand E 2 L ) electric fields can be obtained at 8 s intervals.The axial ratio of wave can be obtained by the following formula: The sign of Ratio indicates the polarization respect to the spin axis of Arase (anti-sunward direction) (Kumamoto et al., 2018).The polarization of waves is defined with respect to the direction of magnetic field at the AKR source region.When Arase is located in the northern hemisphere on the nightside, the magnetic field at the source region (northern polar region) can be assumed to direct sunward.In this case, the positive (negative) axial ratio indicates left-hand (right-hand) polarization.In the same manner, when Arase is located in the southern hemisphere on the nightside, the positive (negative) axial ratio indicates right-hand (left-hand) polarization.
Figure 1 shows an AKR event observed by Arase on 6 September 2018.Figure 1a 1b, strong AKR (PSD ≥ 10 7 mV 2 m 2 Hz 1 ) was detected during the period by HFA.Obviously, there are two distinct AKR bands: low frequency waves (8-20 kHz) and high frequency waves (300-1000 kHz).Figure 1c presents the Ratio of waves with PSD ≥ 10 7 mV 2 m 2 Hz 1 based on Equation 6. White part denotes waves with PSD < 10 7 mV 2 m 2 Hz 1 .Since the direction of magnetic field at the source region is opposite to the sun, the positive axis ratio (red) denotes the right-hand polarization and the negative axis ratio (blue) denotes the left-hand polarization (Kumamoto et al., 2018).We assume the lower frequency edge of the L-X waves is the lower cutoff frequency f L , then obtain f pe based on Equation 5.At 18:20:15 UT, f L is about 12.1 kHz and f ce is about 9.8 kHz, then f pe is about 16.3 kHz.As shown in Figure 1b, low frequency waves at 18:20:15 UT are identified as the L-X modes.
This event shows that the R-X and L-X modes can be observed simultaneously away from the source region.As shown in Figure 1, there is not R-X mode below 300 kHz.The probable reason is the geomagnetic reflection or missing the satellite on propagation.ECMI has suggested that AKR is excited in the polar cavity.Previous works have confirmed that the R-X mode from high latitudes can propagate downward to low latitudes based on observations and simulations (Deng et al., 2022;Xiao et al., 2016).We assume that the L-X mode is generated at high latitudes in this event.Considering that the frequency range of L-X mode is very limited, we shall use the 3-D ray tracing method to examine whether the L-X mode can also propagate from high latitudes to lower latitudes in the following.

Numerical Simulation
In this study, we simulate ray paths using the 3-D ray tracing model (Horne, 1989;Xiao et al., 2007Xiao et al., , 2016)).First, two orthogonal coordinate systems with right-hand rule are defined in the program: the Earth-centered coordinate (OXYZ) system and the local coordinate (pxyz) system.In the OXYZ system, the center of the Earth is considered as the origin, the north of geomagnetic axis as the Z axis, the geomagnetic equatorial plane as the X and Y axis, the anti-solar direction as the X axis, and dusk to dawn as the Y axis.In the pxyz system, the direction of geomagnetic field at point p is defined as the z axis, the anti-earthward direction in the longitudinal plane as the x axis.The angle formed by the wave vector k and the background geomagnetic field B 0 is known as wave normal angle θ.
The angle that the projection of the wave vector onto the x-y plane makes with the x axis as the azimuth angle η.Second, we adopt the reasonable assumptions and parameters used in the ray-trace simulation: a dipole field model for the background magnetic field, the global core plasma density model and the cavity plasma density model for the background plasma density models (Gallagher et al., 2000;Hashimoto et al., 1998).Third, ray paths are simulated based on the dispersion relation of L-X mode.
We choose the point (MLT = 23.3,MLAT = 70°) at a distance of R = 4.5 R E (Earth's radii) from the center of the Earth as the source region of L-X mode AKR. Figure 2 shows the ray paths at different wave frequencies ( f = 11, 14 and 18 kHz).We choose initial wave normal angle θ = 110°and azimuthal angles η = 214°-222°( different color lines).The values of θ > 90°and η > 180°are chosen to ensure rays move downward and outward away from Earth.The Z axis in Figure 2 refers downward in the northern direction to more clearly illustrate the ray paths of L-X mode.The red asterisk designates the source region of L-X mode.The precise positions of satellite are shown by the center of black circles.As shown in Figure 2b, most of ray paths for 14 kHz pass the location of Arase.While ray paths for 11 kHz (Figure 2a) and 18 kHz (Figure 2c) from the above source region with the same θ and η miss the location of Arase.These results are consistent with that L-X mode is observed at lower latitudes and concentrated around 14 kHz.
Figure 3 displays the respective ray paths on the R XY Z plane and X Y plane with different wave frequencies or initial azimuthal angles.The dashed lines in Figures 3a-3c are magnetic field lines of L = 6-10.As shown in Figures 3b and 3e, ray paths for 14 kHz pass the position of Arase satellite.Before these ray paths reach the satellite, they are reflected due to encountering f L at Z ∼ 2R E .After these ray paths pass the satellite, they are reflected due to encountering f pe at Z ∼ 4R E .Ray paths with 11 (18) kHz can propagate downward to lower latitudes, but they are reflected earlier (later) and miss the position of Arase satellite.If there were more other satellites, more ray paths with 11 (18) kHz may also be observed.Wave frequency affects ray paths of L-X mode greatly.All ray paths are reflected around L = 6 during propagate downward due to encountering f L of L-X mode.
Because the difference of background magnetic field strength and plasma density, different frequency waves are reflected at different positions.The direction of L-X mode shall change again owing to the variety of wave group velocities exhibited in this mode.These simulations provide a reasonable explanation that the peak intensity of L-X mode is concentrated around 14 kHz.
In Figure 4, we further simulate ray paths by varying initial normal angles and source locations at fixed 14 kHz.The dashed lines in Figures 4a-4d are magnetic field lines of L = 6-10.Particularly, θ is specified to be in 100°-120°(Figures 4a and 4e), latitude λ is specified to be in 65°-75°(Figures 4b and 4f), R is specified to be in 4.4-4.6R E (Figures 4c and 4g) and MLT is specified to be in 22.9-23.7 (Figures 4e and 4h).As shown in Figure 4a, ray paths miss the Arase satellite even if θ varies 5°by each step.Ray paths from different sources (λ varies 3°in Figure 4f, R varies 0.05 R E in Figure 4c and MLT varies 0.4 in Figure 4h) shall miss the satellite.Results (shown in Figures 3 and 4) imply that the propagation characteristic of L-X mode is very sensitive to wave normal angle, wave frequency and the location of source.This is why it is difficult to observe the L-X mode in the lower latitude magnetosphere.
We have observed that the intensity of L-X mode corresponds to peaks of potential V. Previous work has obtained empirical formulas of plasma density Ne from the spacecraft potential V based on observations of Cluster ( Pedersen et al., 2008).However, the potential V is not only determined by plasma density but also other parameters (temperature, surface material, surface shape, etc.).Those empirical formulas relating the density to the spacecraft potential should not be directly applied to Arase satellite data.Because there are some possible errors in the plasma density from the spacecraft potential, it is hard to confirm that there is a density duct.Unlike whistler mode wave propagating along the magnetic field, previous works have confirmed that AKR tends to propagate across the magnetic field (Xiao, Chen, He, & Yang, 2010;Xiao et al., 2016).As mentioned above, we assume that the L-X mode is generated at high latitudes in this study.We plan to study whether the L-X mode can propagate along the magnetic field when there are direct observations available regarding a field aligned density irregularity in the future (Calvert, 1995).As shown in Figure 1b, there are waves of 11 and 18 kHz observed by the Arase satellite.There should be a set of solutions for rays at these frequencies to pass the satellite.The full space of source region and wave parameters will be explored in the next work.

Summary
AKR with frequency between 30 and 800 kHz is generated in the high latitude polar cavity (Deng et al., 2022;Fogg et al., 2022;Zhang et al., 2020).In this study, we present an AKR event in which two distinct frequency bands are observed simultaneously at lower latitude ( 37°): low frequency waves (8-20 kHz) and high frequency waves (300-1000 kHz).The polarization and frequency range indicate that the low and high frequency bands are the L-X and R-X modes, respectively.The L-X mode event (peak frequency ∼14 kHz) at lower latitudes observed by the Arase satellite is reported for the first time.Using the 3-D ray tracing method with suitable wave azimuthal angles and normal angles, we simulate L-X mode ray paths in the magnetosphere.All ray paths are reflected several times when they propagate downward.Most of ray paths for 14 kHz pass the position of Arase satellite, but those for 11 and 18 kHz miss the satellite.These simulations successfully explain the observations that L-X mode is observed at lower latitudes and concentrated around 14 kHz.We demonstrate that L-X mode ray paths are highly dependent on initial normal angles, wave frequency and the position of source.The observations and corresponding simulations first provide a direct evidence that the L-X mode from high latitudes can propagate downward to the lower latitude magnetosphere.The current results are also applicable to similar emissions on other magnetic planets of the solar system.

Figure 2 .
Figure 2. The ray paths of L-X mode at (a) 11, (b) 14 and (c) 18 kHz with different initial azimuth angles.The plasma density N e in the equatorial plane is superimposed in the color scale.The red asterisks indicate the AKR source cavity.The black circles denote the location of Arase satellite.

Figure 3 .
Figure 3.The projections of L-X mode ray paths, positions of satellites (black circles) and source cavity (red asterisks) on the (a-c) R XY Z plane and (d-f) X Y plane.The dashed lines indicate magnetic field lines of L = 6-10 on R XY Z plane.

Figure 4 .
Figure 4. L-X mode ray paths on the R XY Z plane and X Y plane with different initial wave normal angles or positions of source cavity.The meanings of asterisks, black circles and dashed lines are the same as those in Figure 3.
exhibits SYM-H (black line) and AE (red line) indexes from 17:20 UT to 19:00 UT.The SYM-H index was around 9 nT and the AE index was about 150 nT.The geomagnetic activity was relatively quiet.The plasma density Ne should not change very much.The gray area indicates the period of 18:19:30-18:21:00 UT when the Arase satellite was located around the region: MLAT ∼ 37°, L ∼ 8 and Magnetic Local Time (MLT) ∼ 23.As shown in Figure