Wave Normal Angle Distribution Research Articles

Propagation and Dispersion of Lightning-Generated Whistlers Measured From the Van Allen Probes

We study the propagation and attenuation of lightning-generated whistler (LGW) waves in near-Earth space (L ≤ 3) through the statistical study of three specific quantities extracted from data recorded by NASA’s Van Allen Probes mission, from 2012 to 2019: the LGW electric and magnetic power attenuation with respect to distance from a given lightning stroke, the LGW wave normal angle in space, and the frequency-integrated LGW refractive index. We find that LGW electric field wave power decays with distance mostly quadratically in space, with a power varying between -1 and -2, while the magnetic field wave power decays mostly linearly in space, with a power varying between 0 and -1. At night only, the electric wave power decays as a quadratic law and the magnetic power as a linear law, which is consistent with electric and magnetic ground measurements. Complexity of the dependence of the various quantities is maximal at the lowest L-shells (L < 1.5) and around noon, for which LGW are the rarest in Van Allen Probes measurements. In-space near-equatorial LGW wave normal angle statistics are shown for the first time with respect to magnetic local time (MLT), L-shell (L), geographic longitude, and season. A distribution of predominantly electrostatic waves is peaked at large wave normal angle. Conversely, the distribution of electromagnetic waves with large magnetic component and small electric component is peaked at small wave normal angle. Outside these limits, we show that, as the LGW electric power increases, the LGW wave normal angle increases. But, as the LGW magnetic power increases, the LGW wave normal angle distribution becomes peaked at small wave normal angle with a secondary peak at large wave normal angle. The LGW mean wave-normal angle computed over the whole data set is 41.6° with a ∼24° standard deviation. There is a strong MLT-dependence, with the wave normal angle smaller for daytime (34.4° on average at day and 46.7° at night). There is an absence of strong seasonal and continental dependences of the wave-normal angle. The statistics of the LGW refractive index show a mean LGW refractive index is 32 with a standard deviation of ∼26. There is a strong MLT-dependence, with larger refractive index for daytime 36) than for nighttime (28). Smaller refractive index is found during Northern hemisphere summer for L-shells above 1.8, which is inconsistent with Chapman ionization theory and consistent with the so-called winter/seasonal anomaly. Local minima of the mean refractive index are observed over the three continents. Cross-correlation of these wave parameters in fixed (MLT, L) bins shows that the wave normal angle and refractive index are anti-correlated; large (small) wave normal angles correspond with small (large) refractive indexes. High power attenuation during LGW propagation from the lightning source to the spacecraft is correlated with large refractive index and anti-correlated with small wave normal angle. Correlation and anti-correlation show a smooth and continuous path from one regime (i.e. large wave normal angle, small refractive index, low attenuation) to its opposite (i.e. small wave normal angle, large refractive index, large attenuation), supporting consistency of the results.

Evidence of Small Scale Plasma Irregularity Effects on Whistler Mode Chorus Propagation

AbstractThe impact of randomly distributed field‐aligned density irregularities on whistler‐mode wave propagation is investigated using full‐wave simulations and multipoint spacecraft observations. The irregularities are modeled as randomized density perturbations between 1% and 10% of the nominal background density value with scales of ∼10–60 km transverse and ∼50–500 km along the background magnetic field. The density irregularities affect whistler wave propagation and lead to spatial modulation of wave average power density accompanied by spreading of the wave normal angle distribution. Wave power variation is shown to statistically increase with the depth of density irregularities. The simulation results are in good agreement with the observed correlations of chorus power and variation of the plasma density from multipoint observations by the four Magnetosphere MultiScale spacecraft. The change in fundamental wave properties from scattering from these irregularities affects the efficiency of wave‐particle interactions in the radiation belts and needs to be incorporated into large‐scale energetic‐particle flux models.

Outer Radiation Belt Electron Lifetime Model Based on Combined Van Allen Probes and Cluster VLF Measurements

AbstractThe flux of energetic electrons in the outer radiation belt shows a high variability. The interactions of electrons with very low frequency (VLF) chorus waves play a significant role in controlling the flux variation of these particles. Quantifying the effects of these interactions is crucially important for accurately modeling the global dynamics of the outer radiation belt and to provide a comprehensive description of electron flux variations over a wide energy range (from the source population of 30 keV electrons up to the relativistic core population of the outer radiation belt). Here, we use a synthetic chorus wave model based on a combined database compiled from the Van Allen Probes and Cluster spacecraft VLF measurements to develop a comprehensive parametric model of electron lifetimes as a function of L‐shell, electron energy, and geomagnetic activity. The wave model takes into account the wave amplitude dependence on geomagnetic latitude, wave normal angle distribution, and variations of wave frequency with latitude. We provide general analytical formulas to estimate electron lifetimes as a function of L‐shell (for L = 3.0 to L = 6.5), electron energy (from 30 keV to 2 MeV), and geomagnetic activity parameterized by the AE index. The present model lifetimes are compared to previous studies and analytical results and also show a good agreement with measured lifetimes of 30 to 300 keV electrons at geosynchronous orbit.

Wave Normal Angle Distribution of Magnetosonic Waves in the Earth's Magnetosphere: 2‐D PIC Simulation

AbstractRadiation belt electrons can be accelerated and scattered by magnetosonic waves in the Earth's magnetosphere, and the scattering rate of electrons is sensitive to the wave normal angle. However, observationally it is difficult to identify the wave normal angle within a few degrees. In this study, using 2‐D particle‐in‐cell (PIC) simulations, we investigate the wave normal angle distribution of magnetosonic waves excited by ring distribution protons. Both the linear theory and simulations have shown that the wave normal angles are distributed over a narrow range (82°–89°) with a major peak at about 85° during the linear growth stage when the proton ring velocity is close to the Alfven speed. In addition, 2‐D PIC simulations further demonstrated that the waves tend to have larger wave normal angles (84°–89°) during the saturation stage since the waves with smaller wave normal angles are dissipated faster. It is also found that wave normal angles decrease with the increase of wave frequency. With the increase of the ring velocity of the proton ring distribution, the perpendicular wavenumber of excited magnetosonic waves decreases, which leads to the decrease of the wave normal angle. The simulation results provide a valuable insight to understand the property of magnetosonic waves, and the findings are useful for the global simulations of radiation belt dynamics.

Parametric Sensitivity of the Formation of Reversed Electron Energy Spectrum Caused by Plasmaspheric Hiss

AbstractScattering by plasmaspheric hiss is responsible for the newly reported reversed energy spectra with abundant high‐energy but fewer low‐energy electrons between hundreds of kiloelectronvolts and ~2 MeV in the inner magnetosphere. To deepen our understanding of the contributions of plasmaspheric hiss to the formation of reversed electron energy spectrum, we conduct a detailed theoretical parametric analysis through numerical simulations to explore the sensitivity of hiss‐induced reversed electron energy spectrum to ambient magnetic field, plasma density, and hiss wave distribution properties. Given L‐shell, variations of ambient plasma density and wave frequency spectrum contribute importantly to the formation of reversed electron energy spectrum, while variations of background magnetic field (which usually shows small changes in the plasmasphere) and wave normal angle distribution play a less effective role. Our study suggests that the reversed electron energy spectrum has important implications for unveiling the sophisticated energy‐dependent nature of wave‐particle interactions and energetic particle dynamics in geospace.

Validation and Analysis of Bounce Resonance Diffusion Coefficients

AbstractTheoretical bounce resonance diffusion coefficients for waves generated near the equatorial plane are analyzed theoretically and validated numerically using guiding‐center test particle simulations. A previous study demonstrated numerically the sensitivity of the diffusion coefficients to the peak wave normal angle and the maximum wave latitude for electrons in bounce resonance with equatorially confined magnetosonic waves. We demonstrate analytically that the sensitivity of the diffusion coefficients to the peak wave normal angle is due to the narrow width of the wave normal angle distribution of the particular wave model used by the previous study. We also show that there is no dependence on the maximum latitude if particle's mirroring points are located within the wave boundary. By analyzing the contribution of each harmonic resonance to the total diffusion coefficients, we show that the discontinuities of the diffusion coefficients as a function of the equatorial pitch angle (α0) occur when the contribution of a harmonic resonance goes to 0. Using a two‐dimensional pitch angle and energy diffusion simulation, we demonstrate that bounce resonance with magnetosonic waves can cause pitch angle scattering of equatorially mirroring electrons, leading to a smooth variation of flux with α0 for α0∼90∘. We conclude that bounce resonance with magnetosonic waves might be an important mechanism in pitch angle scattering and acceleration of electrons in the radiation belt.

Bounce resonance scattering of radiation belt electrons by H+ band EMIC waves

AbstractWe perform a detailed analysis of bounce‐resonant pitch angle scattering of radiation belt electrons due to electromagnetic ion cyclotron (EMIC) waves. It is found that EMIC waves can resonate with near‐equatorially mirroring electrons over a wide range of L shells and energies. H+ band EMIC waves efficiently scatter radiation belt electrons of energy >100 keV from near 90° pitch angles to lower pitch angles where the cyclotron resonance mechanism can take over to further diffuse electrons into the loss cone. Bounce‐resonant electron pitch angle scattering rates show a strong dependence on L shell, wave normal angle distribution, and wave spectral properties. We find distinct quantitative differences between EMIC wave‐induced bounce‐resonant and cyclotron‐resonant diffusion coefficients. Cyclotron‐resonant electron scattering by EMIC waves has been well studied and found to be a potentially crucial electron scattering mechanism. The new investigation here demonstrates that bounce‐resonant electron scattering may also be very important. We conclude that bounce resonance scattering by EMIC waves should be incorporated into future modeling efforts of radiation belt electron dynamics.

Scattering of relativistic and ultra-relativistic electrons by obliquely propagating Electromagnetic Ion Cyclotron waves

Electromagnetic Ion Cyclotron (EMIC) waves are transverse plasma waves that are generated in the Earth magnetosphere by ring current protons with temperature anisotropy in three different bands: below the H+, He+ and O+ ion gyrofrequencies. EMIC events are enhanced during the main phase of a geomagnetic storm when intensifications in the electric field result in enhanced injections of ions and are usually confined to high-density regions just inside the plasmapause or within drainage plumes. EMIC waves are capable of scattering radiation belt electrons and thus provide an important link between the intensification of the electric field, ion populations, and radiation belt electrons. Bounce-averaged diffusion coefficients computed with the assumption of parallel wave propagation are compared to the results of the code that uses the full cold plasma dispersion relation taking into account oblique propagation of waves and higher-order resonances. We study the sensitivity of the scattering rates to a number of included higher-order resonances, wave spectral distribution parameters, wave normal angle distribution parameters, ambient plasma density, and ion composition. Inaccuracies associated with the neglect of higher-order resonances and oblique propagation of waves are compared to potential errors introduced by uncertainties in the model input parameters.

Influence of wave normal angles on hiss‐electron interaction in Earth's slot region

AbstractWave‐particle interaction which occurs in the radiation belts is generally determined by variations in wave normal angles. Using the Gaussian wave normal angle ( ) distribution, we study the influence of peak wave normal angle ( ) on gyroresonance between plasmaspheric hiss waves and energetic electrons in the slot regions L = 2.5, 3.0, and 3.5. The bounce‐averaged diffusion coefficients are calculated for different Xm = 0,1,3,5, and then the phase space density (PSD) evolutions of energetic electrons driven by hiss waves are simulated over a continuous energy range 0.2–5 MeV. As Xm increases, diffusion coefficients basically decrease mainly from the medium to a critical pitch angle αc for Ek≤1.0 MeV but increase at lower pitch angles for Ek>1.0 MeV. Differences of diffusion coefficients between Xm = 0 and 1 are close but become substantial as Xm≥3. Hiss can cause substantial drops in electron PSDs for Ek≤0.5 MeV and Xm≤1 from the loss cone αL to αc. For Ek≥1.0 MeV, such PSD drops become much smaller and confined in the lower pitch angles close to αL for each Xm. In contrast, electron PSD increases for Ek≤1.0 MeV above αc at L = 2.5 and 3.0, probably because momentum diffusion coefficients increase steeply above αc. The current results demonstrate that gyroresonance between plasmaspheric hiss and energetic electrons in the slot region is strongly associated with variations of peak wave normal angles, which should be integrated into future global modeling of radiation belt dynamics.

Effect of chorus normal angle on dynamic evolution of radiation belt energetic electrons

Gyroresonance between chorus waves and radiation belt electrons is usually evaluated by using the Gaussian wave normal angle (X=tanθ) distribution. In this study, we examine the influence of peak wave normal angle (Xm=tanθm) on chorus-electron interaction in the heart of radiation belts L=4.5. By varying Xm=0,2,4,6, we calculate the bounce-averaged diffusion coefficients, and then simulate the phase space density (PSD) evolution of radiation belt energetic electrons induced by both dayside and nightside chorus waves. Numerical simulations show that diffusion coefficients move to the low pitch angle region and drop rapidly by a factor of ∼10 as Xm increases by 2 each time, consequently leading to the smaller amplitude and narrower pitch angle region in electron PSD evolution. The current results demonstrate that chorus-electron interaction in the outer radiation belt is largely dependent on peak wave normal angles.

Characteristics of the Poynting flux and wave normal vectors of whistler‐mode waves observed on THEMIS

The characteristics of the Poynting flux and wave normal vectors of whistler‐mode waves outside the plasmapause are investigated for the lower (0.1–0.5 fce) and upper bands (0.5–0.8 fce), where fce is the equatorial electron cyclotron frequency. To analyze the wave properties, we utilized high‐resolution waveform data from multiple THEMIS spacecraft in the near‐equatorial magnetosphere from June 2008 to November 2012. Full measurements of the wave electric and magnetic fields are used to calculate the Poynting fluxes and construct the wave normal vectors, which are then used to calculate the polar and azimuthal angles with respect to the background magnetic field. Statistical results show that the majority of whistler‐mode waves propagate away from the magnetic equator, suggesting that the major source region is very close to the equator. The lower band wave normal angle distribution shows a major peak close to the field line direction and a secondary peak near the resonance cone. In contrast, the wave normal distribution of upper band waves exhibits a broad distribution between 0° and 60° with the largest probability at ~0°. The azimuthal component of the wave normal vector predominantly points radially outward for both lower and upper band waves, but a tendency for azimuthal propagation is observed for lower band waves in the day and dusk sectors probably due to pronounced azimuthal density gradients in the afternoon sector. Our statistical results provide crucial information on the Poynting fluxes and wave normal vectors of whistler‐mode waves, which play a significant role in radiation belt electron dynamics.

Modeling the wave normal distribution of chorus waves

The propagation and attenuation characteristics of lower band and upper band chorus waves are investigated by ray tracing, and the evaluation of Landau damping based on an empirical suprathermal electron model derived from Time History of Events and Macroscale Interactions during Substorms (THEMIS) data. The rate of Landau damping is found to increase at larger L‐shell, for more oblique wave normal angles, and for higher geomagnetic activity. Damping is also larger on the nightside than on the dayside and is more pronounced in the upper band than in the lower band. These features can account for the statistical pattern of chorus waves observed away from the equatorial source region. A physical model of the wave normal angle distribution along a field line is presented, which provides insight on how the wave normal angle distribution varies as chorus waves propagate away from the equatorial source region. Our modeling shows that wave emissions at low latitudes (λ ≲ 30°) come predominately from the equatorial source at the same L‐shell and that their wave normal angles increase with increasing latitude due to wave refraction caused by magnetic gradients and curvature. However, at high latitudes (λ ≳ 30°), the wave normal angle distribution along a particular field line is affected by chorus waves that arrive from an equatorial source at lower L because of significant cross‐L propagation. As a consequence, the lower band wave normal angle tends to decrease with increasing latitudes, while the upper band wave normal angle can either increase or decrease depending on the equatorial source at lower L. The effect of cross‐L propagation might also explain why observed wave normal angle distribution tends to become more field‐aligned at high latitudes. Interestingly, the upper band chorus at such high latitudes originates from lower band waves originating near the equator at lower L. A global model of wave normal variation along a field line constructed in this study is not currently available from observations but is nonetheless critically important for evaluating bounce‐averaged diffusion coefficients for future radiation belt modeling.

Modeling the properties of plasmaspheric hiss: 1. Dependence on chorus wave emission

There is increasing evidence that plasmaspheric hiss is formed by the evolution of a portion of chorus waves that are excited in the plasmatrough and propagate into the plasmasphere. Comparison between the statistical spatial distributions of these two emissions in the morning sector during active times from THEMIS over ∼3 years shows that the two emissions have comparable peak intensities but are distinct in their spatial distributions. We present a modeling study of the hiss spectrum, based on ray tracing, by taking the observed chorus source region as an input in the magnetosphere, which contains cold and suprathermal electrons. Our modeling results show that we are able to reproduce the main features of typical hiss, including the frequency spectrum, wave normal angle and spatial distribution. However, the simulated hiss intensity is weaker (∼15 dB less) than the observed intensity, which suggests some modest internal amplification inside the plasmasphere. The responses of hiss to variations in the spatial distribution, wave normal angle distribution and frequency distribution of the source chorus are examined. We find that the majority of hiss formation is due to a small portion of chorus emission originating within ∼3 RE from the plasmapause, with wave normal directions pointing toward the Earth at an angle of 30°–60°, and over a frequency range of 0.1–0.3 fce. If the chorus power is made to increase closer to the plasmapause, the hiss intensity and the peak frequency also increases, which roughly mimics active geomagnetic conditions. Variations of the chorus source distribution do not significantly affect the wave normal angle distribution and frequency distribution of hiss, but does impact the absolute intensity of the resulting hiss.

Diffuse auroral scattering by whistler mode chorus waves: Dependence on wave normal angle distribution

[1] Using the statistical CRRES measurements of the electric field intensities of lower band chorus (LBC) and upper band chorus (UBC) around L = 6 under geomagnetically moderate conditions, we evaluate the variations in modeled magnetic field spectral intensity and the resultant changes in resonant scattering rates of plasma sheet electrons caused by different choices of the wave normal distribution. UBC scattering rates inferred from electric field measurements show a common trend of decreasing scattering with increasing peak wave normal angle, θm, for the plasma sheet electrons at all resonant pitch angles. This trend is mainly due to the lower power of magnetic field as derived from the electric field measurements for oblique waves. The LBC resonant diffusion inferred from electric field measurements shows a considerable increase in scattering rates with increasing θm for ∼1 keV electrons at all resonant pitch angles and for 3–30 keV electrons over certain ranges of pitch angles, which is contrary to the decrease in wave magnetic field amplitude and results mainly from the decrease in resonant energy and redistribution of the majority of wave power at large wave normal angles for increased peak wave normal angle. LBC-induced scattering rates of 3–10 keV electrons decrease with increasing θm at low pitch angles, consistent with the decrease in wave magnetic field amplitude when θm increases. Our investigation demonstrates that the knowledge of the wave normal distribution of LBC and UBC is essential for an accurate quantification of the net resonant scattering rates and loss timescales of the plasma sheet electrons for an improved global simulation of diffuse auroral precipitation and the evolution of plasma sheet electron pitch angle distribution if only measurements of wave electric field intensity are available. In contrast, the diffuse auroral scattering rates calculated from magnetic field measurements are much less sensitive to the assumption on wave normal angle distribution. While UBC scattering with constant magnetic field power is roughly insensitive to the assumed wave normal distribution, LBC scattering with constant magnetic field power becomes more dependent on the assumed wave normal angle distribution, especially for ∼1 keV electrons.

Resonant scattering of plasma sheet electrons leading to diffuse auroral precipitation: 2. Evaluation for whistler mode chorus waves

[1] Using the statistical wave power spectral profiles obtained from CRRES wave data within the 0000–0600 MLT sector under different levels of geomagnetic activity and a modeled latitudinal variation of wave normal angle distribution, we examine quantitatively the effects of lower band and upper band chorus on resonant diffusion of plasma sheet electrons for diffuse auroral precipitation in the inner magnetosphere. Whistler mode chorus-induced resonant scattering of plasma sheet electrons is geomagnetic activity dependent, varying from above the strong diffusion limit (timescale of an hour) during active times (AE* > 300 nT) with peak wave amplitudes of >50 pT to weak scattering (timescale of a day) during quiet conditions (AE* ∼2 keV) plasma sheet electrons in the inner magnetosphere. Efficient scattering by the combination of active time lower band and upper band chorus can cover a wide energy range from ∼100 eV to >100 keV and a broad interval of equatorial pitch angle, thereby accounting for the formation of observed electron pancake distribution. Decreased chorus scattering during less disturbed times can also modify the magnetic local time distribution of plasma sheet electrons. Compared to the effects of chorus waves, electron cyclotron harmonic wave-induced resonant diffusion coefficients are at least 1 order of magnitude smaller and are negligible under any geomagnetic condition, indicating that chorus waves act as the major contributor dominantly responsible for diffuse auroral precipitation in the inner magnetosphere. Chorus-driven momentum diffusion and mixed diffusion are also important. Lower band and upper band chorus can cause strong momentum diffusion of plasma sheet electrons in the energy ranges of ∼500 eV to ∼2 keV and ∼2 keV to ∼3 keV, respectively, which can significantly result in energization of the electrons and attenuation of the waves.

Importance of plasma injection events for energization of relativistic electrons in the Jovian magnetosphere

[1] Effects of density decrease in plasma injection regions and a latitude-dependent wave normal angle distribution on the energization of electrons by whistler mode waves at Jupiter are investigated. Previous work showed that whistler mode waves could enhance the fluxes of a few MeV electrons by an order of magnitude on a time scale of 30 days. However, density decrease in plasma injection regions and latitude dependence of the wave normal angle distribution of waves were not considered. Because this information is difficult to obtain from available observations, we perform a sensitivity study to demonstrate that the effect of density decrease on energization of electrons becomes important when the density inside injection regions is reduced to 25% of that outside. We also investigate the effect of a latitude-dependent wave normal angle distribution on energization of electrons using a ray tracing program and demonstrate that a realistic latitude-dependent wave normal angle distribution increases the rate of pitch angle diffusion near the loss cone, and thus enhances the loss rate, of 1–3 MeV electrons. However, the flux of 10 MeV electrons is not significantly affected. Results of the work are useful for understanding energization of MeV electrons at Jupiter, especially when combined with observations from future missions.

A parametric study on outer radiation belt electron evolution by superluminous R‐X mode waves

A parametric study is presented on the temporal evolution of the phase space density (PSD) of the outer radiation belt energetic electrons driven by the superluminous right‐hand extraordinary (R‐X) mode waves at the location L = 4.5. Bounce‐averaged diffusion rates in pitch angle and momentum are calculated by varying the peak wave frequency, the wave normal angle distribution, and the wave latitudinal distribution. Those diffusion rates are used as inputs to solve a 2‐D momentum‐pitch angle diffusion equation. In particular, three cases are considered: momentum diffusion rates alone, momentum +pitch angle diffusion rates, and momentum +pitch angle +cross diffusion rates. Numerical results show that at 24 h, electron PSDs can enhance substantially for 1 MeV energy at higher pitch angles. Momentum diffusion dominates the dynamic evolution of energetic electrons, whereas the contribution of pitch angle or cross‐diffusion rates is insignificant using the specified wave model. In addition, PSD evolutions are sensitively dependent on the assumed different wave normal angle distributions and tend to be located in lower pitch angles when wave normal angles move to smaller regions. Diffusion coefficients and PSD evolution are largely determined by the wave latitudinal distributions. High‐latitude R‐X mode waves primarily contribute to pitch angle scattering of energetic electrons, whereas equatorial (or lower latitude) R‐X mode waves yield efficient acceleration of electrons. This result supports the previous findings that superluminous R‐X mode waves potentially contribute to dramatic variation in the outer radiation belt electron dynamics under appropriate conditions.

Effect of electromagnetic ion cyclotron wave normal angle distribution on relativistic electron scattering in outer radiation belt

We present the equatorial and bounce‐averaged pitch angle diffusion coefficients for the scattering relativistic electrons by He+‐mode electromagnetic ion cyclotron waves. Both the model (prescribed) and self‐consistent distributions over the wave normal angle are considered. The main results of our calculation can be summarized as follows: First, in comparison with field‐aligned waves, intermediate and highly oblique waves decrease the bounce‐averaged scattering rate near the edge of the loss cone by up to orders of magnitude if the electron energy does not exceed a threshold (∼2–5 MeV) depending on specified plasma and/or wave parameters. Second, for greater electron energies, oblique waves operating the ∣n∣ > 1 resonances are more effective and provide the same bounce‐averaged diffusion rate near the edge of the loss cone as field‐aligned waves do.

Nonducted propagation of chorus emissions and their observation

Chorus emissions are one of the most intense electromagnetic waves of whistler mode observed in the Earth's magnetosphere. They are generated near the magnetic equator plane and consist of more or less regularly repeating rising (falling) tones. We focus on the propagation of this emission from the source region. Based on plasma density measurements and recent satellite observations, we consider that chorus emissions may in many cases propagate obliquely to magnetic field lines. We study the influence of initial wave normal angle distribution on the chorus propagation using the ray tracing method for different frequencies. Our special interest is the estimation of the ray bundle width. As for the initial dimension of the source, we use the published values: ∼100 km for the transverse dimension (with respect to magnetic field), and the longitudinal extent of ∼2000 km. We conclude that the merging of the ray bundles corresponding to different frequencies defines the frequency bandwidth of the emission that can be observed at a particular point. We estimate that the initial spread of ∼10° is sufficient so that the typical bandwidth ∼1 kHz could be observed. We also show that there may be regions, where ray bundle focuses for a specific frequency and a specific initial wave normal spread, leading thus to enhanced energy density at this frequency. In the experimental part, we show examples of the observation of nonducted propagating emission recorded on the MAGION 5 satellite.