Tohru Hada

Nonlinear, dispersive, elliptically polarized Alfvén waves

The derivative nonlinear Schrodinger (DNLS) equation is derived by an efficient means that employs Lagrangian variables. An expression for the stationary wave solutions of the DNLS that contains vanishing and nonvanishing and modulated and nonmodulated boundary conditions as subcases is then obtained. The solitary wave solutions for elliptically polarized quasiparallel Alfven waves in the magnetohydrodynamic limit (nonvanishing, unmodulated boundary conditions) are obtained. These converge to the Korteweg–de Vries and the modified Korteweg–de Vries solitons obtained previously for oblique propagation, but are more general. It is shown there are no envelope solitary waves if the point at infinity is unstable to the modulational instability. The periodic solutions of the DNLS are charcterized.

Phase Coherence of MHD Waves in the Solar Wind

Large amplitude MHD waves are commonly found in the solar wind. Nonlinear interactions between the MHD waves are likely to produce finite correlation among the wave phases. For discussions of various transport processes of energetic particles, it is fundamentally important to determine whether the wave phases are randomly distributed (as assumed in quasi-linear theories) or they have a finite coherence. Using a method based on a surrogate data technique and a fractal analysis, we analyzed Geotail magnetic field data (provided by S. Kokubun and T. Nagai through DARTS at the Institute of Space and Astronautical Science) to evaluate the phase coherence among the MHD waves in the earths foreshock region. The correlation of wave phases does exist, indicating that the nonlinear interactions between the waves is in progress.

Chaos in driven Alfvén systems

The chaos in a one‐dimensional system, which would be nonlinear stationary Alfven waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schrodinger equation (DNLS), including resistive wave damping and a long‐wavelength monochromatic, circularly polarized driver. A Poincare map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and ‘‘strong’’ chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period‐doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.

Development of high-density helicon plasma sources and their applications

We report on the development of unique, high-density helicon plasma sources and describe their applications. Characterization of one of the largest helicon plasma sources yet constructed is made. Scalings of the particle production efficiency are derived from various plasma production devices in open literature and our own data from long and short cylinder devices, i.e., high and low values of the aspect ratio A (the ratio of the axial length to the diameter), considering the power balance in the framework of a simple diffusion model. A high plasma production efficiency is demonstrated, and we clarify the structures of the excited waves in the low A region down to 0.075 (the large device diameter of 73.8 cm with the axial length as short as 5.5 cm). We describe the application to plasma propulsion using a new concept that employs no electrodes. A very small diameter (2.5 cm) helicon plasma with 1013 cm−3 density is produced, and the preliminary results of electromagnetic plasma acceleration are briefly de...

Evolution of large amplitude Alfvén waves in the solar wind with β∼1

A new set of equations is obtained which describes evolution of finite amplitude, dispersive, elliptically polarized quasi-parallel Alfven waves, when the plasma and the wave amplitude satisfy the condition, |1-CS2/CA2| < δB/B0, where CA and Cs are the Alfven and the sound speed, respectively, and δB/B0 is the Alfven wave amplitude normalized to the background magnetic field. When this condition is satisfied, the sound wave as well as the right- and left-hand polarized Alfven waves are nearly all degenerated. The solar wind plasma is a typical medium for the obtained set of equations to apply, since the plasma β is high, and the solar wind Alfven waves have large amplitude. Modulational instability of a circularly polarized parallel Alfven wave is discussed.

Acceleration of charged particles by large amplitude MHD waves: Effect of wave spatial correlation

We discuss energy diffusion and acceleration of charged particles by large amplitude magnetohydrodynamic (MHD) waves by test particle simulations, paying particular attention to the effects of phase correlation of the waves. In quasi-linear theory, the wave phases are assumed to be random, but in reality, interaction between different wave modes may produce phase correlation. When the wave phases are strongly correlated, the waveform appears as spatially localized traveling wave packet. These wave packets can efficiently accelerate charged particles, as they are repeatedly mirror reflected by oppositely propagating wave packets: a process analogous to the Fermi acceleration.

Remarks on nonlinear relation among phases and frequencies in modulational instabilities of parallel propagating Alfvén waves

Abstract. Nonlinear relations among frequencies and phases in modulational instability of circularly polarized Alfven 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 Alfven 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 Schrodinger (DNLS) equation, which is a subset of the Hall-MHD system including the right- and left-hand polarized, nearly degenerate quasi-parallel Alfven 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 long time evolution of the Alfven 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.

Observations of linear and nonlinear processes in the foreshock wave evolution

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 right-hand 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.

Development of Electrodeless Plasma Thrusters With High-Density Helicon Plasma Sources

Helicon plasma sources are very useful in many aspects and are applicable to many fields across science and technology, as they can supply high-density (~1013 cm-3) plasmas with a broad range of external operating parameters. In this paper, developed, featured sources with various sizes are characterized along with discussions on their particle production efficiency. This paper aims to develop systems that can realize schemes with completely electrodeless plasma production and acceleration. This is expected to mitigate the existing problems of the finite lifetimes inherent in electric plasma propulsion tools. Experimental and theoretical approaches that implement such schemes are presented.

Kinetically modified parametric instabilities of circularly polarized Alfvén waves: Ion kinetic effects

Parametric instabilities of parallel propagating, circularly polarized, finite amplitude Alfven 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 Alfven 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 Alfven waves observed in the solar wind and in the earth’s foreshock region.