One‐Dimensional gcPIC‐ δf Simulation of Hooked Chorus Waves in the Earth’s Inner Magnetosphere

Chorus waves are coherent electromagnetic emissions in the inner magnetosphere, generally composed of a series of discrete and repetitive elements. These elements usually have rising frequency chirpings, which are occasionally mingled with one or several elements with a hooked spectrogram. In this letter, we perform a one-dimensional general curvilinear particle-in-cell (gcPIC)-delta f simulation of chorus waves excited by temperature anisotropic electrons in a dipole magnetic field, and identify one chorus element with a hooked spectrogram, which is embedded in several chorus elements with a rising frequency chirping. In the hooked chorus element, the frequency increases first, and then decreases. Interestingly, we find that there are clear electron holes in the electron velocity space, no matter whether the chorus element has a rising-tone or hooked-tone spectrogram. Our study presents an important clue for the theoretical analysis of the frequency chirping in the chorus waves. Plain Language Summary Chorus waves are intense electromagnetic emissions that occur naturally in the Earth's inner magnetosphere, which usually contain a series of discrete chirping elements. Via a one-dimensional (1-D) general curvilinear particle-in-cell (gcPIC)-delta f simulation in a dipole field, we have investigated the frequency chirping of chorus waves, excited by anisotropic electrons. After the waves leave away from the equator, their frequencies chirp, exhibiting as quasi-monochromatic emissions. Together with two rising-tone elements, there is one element with a hooked spectrogram, whose frequency first increases, and then decreases. This is consistent with the satellite observation of hooked-tone elements. In the nu(parallel to)-zeta plane, there are clear electron holes along with both rising-tone and hooked-tone chorus elements. Our study provides a novel idea for the theoretical work of chorus frequency chirping.