For the first time, the dispersion relation for turbulence magnetic field fluctuations in the solar wind is determined directly on small scales of the order of the electron inertial length, using four-point magnetometer observations from the Magnetospheric Multiscale mission. The data are analyzed using the high-resolution adaptive wave telescope technique. Small-scale solar wind turbulence is primarily composed of highly obliquely propagating waves, with dispersion consistent with that of the whistler mode.
Chorus waves are usually generated outside the plasmapause in the equatorial region of the magnetosphere. The discrete characteristics of chorus elements are quantified by the three parameters: lasting time, frequency bandwidth, and repetition period. A systematic study in the lasting time and frequency bandwidth in terms of background plasma and magnetic fields has not been performed in the past. Here we use burst mode waveform data from the Time History of Events and Macroscale Interaction during Substorms (THEMIS) probes and the random forest method of machine learning and Pearson's correlation analysis to investigate which background plasma and magnetic field parameter is dominant over the lasting time and frequency bandwidth. We find that the temperature is the most important parameter that controls the lasting time. The lasting time is shorter when this temperature is higher. We also find that the normalized bandwidth by the local electron cyclotron frequency is controlled by the number density of energetic electrons. The normalized bandwidth is wider when this number density is larger. These results can be well explained by the threshold and optimum wave amplitudes for the nonlinear generation of chorus waves (Omura & Nunn, 2011, https://doi.org/10.1029/2010JA016280). The findings derived from this analysis can be used to serve as a guideline for a deep understanding of the generation mechanism of chorus elements and help choose input for a modeling of wave‐particle interactions in the radiation belts.
Abstract. Nonlinear relations among frequencies and phases in modulational instability of circularly polarized Alfvén waves are discussed, within the context of one dimensional, dissipation-less, unforced fluid system. We show that generation of phase coherence is a natural consequence of the modulational instability of Alfvén waves. Furthermore, we quantitatively evaluate intensity of wave-wave interaction by using bi-coherence, and also by computing energy flow among wave modes, and demonstrate that the energy flow is directly related to the phase coherence generation. We first discuss the modulational instability within the derivative nonlinear Schrödinger (DNLS) equation, which is a subset of the Hall-MHD system including the right-and left-hand polarized, nearly degenerate quasi-parallel Alfvén waves. The dominant nonlinear process within this model is the four wave interaction, in which a quartet of waves in resonance can exchange energy. By numerically time integrating the DNLS equation with periodic boundary conditions, and by evaluating relative phase among the quartet of waves, we show that the phase coherence is generated when the waves exchange energy among the quartet of waves. As a result, coherent structures (solitons) appear in the real space, while in the phase space of the wave frequency and the wave number, the wave power is seen to be distributed around a straight line. The slope of the line corresponds to the propagation speed of the coherent structures. Numerical time integration of the Hall-MHD system with periodic boundary conditions reveals that, wave power of transverse modes and that of longitudinal modes are aligned with a single straight line in the dispersion relation phase space, suggesting that efficient exchange of energy among transverse and longitudinal wave modes is realized in the Hall-MHD. Generation of the longitudinal wave modes violates the assumptions employed in deriving the DNLS such as the quasi-static approximation, and thus Correspondence to: Y. Nariyuki (nariyuki@esst.kyushu-u.ac.jp) long time evolution of the Alfvén modulational instability in the DNLS and in the Hall-MHD models differs significantly, even though the initial plasma and parent wave parameters are chosen in such a way that the modulational instability is the most dominant instability among various parametric instabilities. One of the most important features which only appears in the Hall-MHD model is the generation of sound waves driven by ponderomotive density fluctuations. We discuss relationship between the dispersion relation, energy exchange among wave modes, and coherence of phases in the waveforms in the real space. Some relevant future issues are discussed as well.
Parametric instabilities of parallel propagating, circularly polarized finite amplitude Alfvén waves in a uniform background plasma is studied, within a framework of one-dimensional Vlasov description for ions and massless electron fluid, so that kinetic perturbations in the longitudinal direction (ion Landau damping) are included. The present formulation also includes the Hall effect. The obtained results agree well with relevant analysis in the past, suggesting that kinetic effects in the longitudinal direction play essential roles in the parametric instabilities of Alfvén waves when the kinetic effects react "passively". Furthermore, existence of the kinetic parametric instabilities is confirmed for the regime with small wave number daughter waves. Growth rates of these instabilities are sensitive to ion temperature. The formulation and results demonstrated here can be applied to Alfvén waves observed in the solar wind and in the earth's foreshock region. (accepted to Physics of Plasmas)
Abstract. Waves in the foreshock region are studied on the basis of a hypothesis that the linear process first excites the waves and further wave-wave nonlinearities distribute scatter the energy of the primary waves into a number of daughter waves. To examine this wave evolution scenario, the dispersion relations, the wave number spectra of the magnetic field energy, and the dimensionless cross helicity are determined from the observations made by the four Cluster spacecraft. The results confirm that the linear process is the ion/ion righthand resonant instability, but the wave-wave interactions are not clearly identified. We discuss various reasons why the test for the wave-wave nonlinearities fails, and conclude that the higher order statistics would provide a direct evidence for the wave coupling phenomena.
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