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

Abstract

Radiation 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. Key Points: • Using 2-D PIC simulations, the wave normal angle distribution of magnetosonic waves has been investigated • The wave normal angles are distributed over a narrow range (82°-89°) during the linear growth stage • The wave normal angles decrease with the increase of the ring velocity of the proton ring distribution SUN ET AL.Figure 6. (a) The power spectral density of δB ‖ /B 0 and (b) the wave normal angle as a function of frequency and time for the simulation in the dipole magnetic field. (c) The average wave normal angle <θ> versus the wave frequency ω.

Modeling the Propagation of Fast Magnetosonic Waves and Their Conversion to Electromagnetic Ion Cyclotron Waves at Low L Shells

“…Statistical investigation (Zou et al., 2019) shows that power‐weighted wave normal angles of MS waves at $$2.0< L< 6.0$$ are dominantly within $${87}^{{}^{\circ}}$$ to $${89}^{{}^{\circ}}$$ near the equatorial region ($$\vert {\lambda }_{1}\vert \le {5}^{{}^{\circ}}$$). Particle‐in‐cell simulation (Sun et al., 2020) finds that power‐weighted wave normal angles of MS waves range from $${82}^{{}^{\circ}}$$ to $${89}^{{}^{\circ}}$$ during the linear growth but increase to within $${84}^{{}^{\circ}}$$–$${89}^{{}^{\circ}}$$ during saturation. It is noteworthy that the small and intermediate population of the $${\theta }_{k1}$$ distribution will increase while the population of large $${\theta }_{k1}$$ will decrease if we adopt the wave normal angles from the above studies as the initial conditions of our ray tracing, suggesting the efficiency of the mode conversion presented in our full‐wave simulation should be higher.…”

“…After excitation, MS waves typically propagate in the whistler mode at the lower-frequency extensions with wave vectors nearly perpendicular to the magnetic field line (e.g., Boardsen et al, 2016;Gurnett, 1976;Laakso et al, 1990;Russell et al, 1970;Stix, 1992). Recent observations (Zou et al, 2019) and simulations (Sun et al, 2020) both show that the power-weighted wave normal angles of MS waves have distributions with peaks a few degrees away from 𝐴𝐴 90…”

Analytical Fast Magnetosonic Wave Model Based on Observations of Van Allen Probe

“…To be noted, the accuracy of this method depends in large part on the magnetic field intensity of plasma waves and the background magnetic field. For a precise research of MS wave normal angles, Sun et al (2020) have investigated the exact WNA distribution of MS waves using 2‐D PIC simulation. However, based the satellite observations, we have to ignore the errors brought by SVD method.…”

Particle‐in‐Cell Simulation of Rising‐Tone Magnetosonic Waves

“…The PIC simulation provides a powerful tool to study the interaction between waves and particles in the space plasma (Chen et al, 2016;Sun et al, 2019Sun et al, , 2020. In this paper, 1-D electromagnetic PIC simulations are used to investigate the excitation of rising-tone magnetosonic waves, which retain 3-D electromagnetic fields and particle velocities but only 1-D spatial variation in the x direction.…”