Waves Generated by Electron Beam in a Crater-Shaped Flux Rope

Understanding the nature and characteristics of high-frequency waves inside a flux rope may be important as the wave-particle interaction is important for charged-particle energization and the ensuing dissipation process. We analyze waves generated by an electron beam in a crater-shaped magnetic flux rope observed by MMS spacecraft on the dawnside tailward magnetopause. In this MMS observation, a depression of magnetic field, or a crater, of ∼100 km is located at the center of the magnetic flux rope of ∼650 km. There exist parallel and perpendicular electrostatic wave modes inside the depression of the magnetic field at the center of the flux rope, and they are distinguished by their locations and frequencies. The parallel mode exists at the center of the magnetic depression and its power spectrum peaks below Fce (electron cyclotron frequency). In contrast, the perpendicular mode exists in the outer region associated with the magnetic depression, and its power spectrum peaks near Fce . The linear analysis of kinetic instability using a generalized dispersion solver shows that the parallel mode can be generated by the electron beam of 5,000 km/s. They can thermalize electrons ≲100 eV effectively. However, the generation mechanism of the perpendicular mode is not clear yet, which requires further study.