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This paper presents the derivation of a general wave dispersion relation for warm magnetized plasma under the two-fluid formalism. The discussion is quite general except for the assumption of low frequency and slow phase speed, for which the displacement current is negligible, under the implicit assumption that the plasma is sufficiently dense to satisfy the condition ωpe>ωce, where ωpe and ωce denote the plasma oscillation frequency and electron gyro frequency, respectively. The present discussion does not invoke charge neutrality associated with the fluctuations although it is implicitly satisfied. The resulting dispersion relation that includes the fluid thermal effects shows that there are three eigen modes, which include those corresponding to ideal MHD, namely, fast, slow, and kinetic Alfvén waves, as well as higher-frequency modes including the ion and electron cyclotron and lower-hybrid resonances. The fluid effects in the ideal MHD wave branches are influenced by the finite Larmor radius scales, and when the wave number in the cross field direction is comparable to these values, the fluid effects become significant. It is found that the Larmor radius should be interpreted in the sense as ion-acoustic gyro-radius instead of ion thermal gyro radius only. That is, it is found that the electrons also contribute to the non-ideal effect associated with the kinetic Alfvén wave. A comprehensive explanation of the polarization of each mode is also presented. The present findings indicate that the polarity may change its sign only for the kinetic Alfvén mode branch and that such a transition is based on the propagation angle. When such a change does take place, it is found that the kinetic Alfvén wave transits to an ion-acoustic mode. For each branch, it is also found that the electric field along the ambient magnetic field is purely transverse. 

It has become well-established that strong outer radiation belt enhancements are due to wave-driven electron energization by whistler-mode chorus waves. However, in this study, we examine strong MeV electron injections on 10 July 2019 and find substantial evidence that such injections may be a crucial contributor to outer radiation belt enhancement events. For such an examination, it is essential to precisely separate temporal flux changes from spatial variations observed as Van Allen Probes move along their orbits. Employing a new “hourly snapshot” analysis approach, we discover unprecedented details of electron flux evolutions that suggest that for this event, the outer belt enhancement was not continuous but instead intermittent, mostly composed of 4 large discrete injection-driven flux increases. The injections appear as sharp flux increases when observed near apogee. Otherwise, by comparing hourly snapshots for different times, we infer injections and infer temporally stable fluxes between injections, despite strong and continuous chorus emission. The fast and intermittent electron flux growth successively extending earthwards implies cumulative outer belt enhancement via a series of repetitive inward transport associated with injection-induced electric fields. 

Abstract The anomalous diffusion of resonant protons in parallel and perpendicular velocity space by kinetic Alfvén waves is discussed. The velocity diffusion coefficient is calculated by employing an autocorrelation function for proton trajectories. It is found that for protons resonant with the waves, the perpendicular diffusion coefficient decays away for a sufficiently long time, but parallel diffusion monotonically increases in time until it saturates at a certain level. This result indicates that a portion of resonant protons can undergo anomalous diffusion along the background magnetic field even if the intensity of the kinetic Alfvén wave is sufficiently low. The present findings imply that under suitable conditions, astrophysical charged-particle acceleration can take place in the parallel direction.