Mitsuo Kono

Spontaneous excitation of magnetic fields and collapse dynamics in a Langmuir plasma

We discuss various aspects of the spontaneous generation of magnetic fields in a Langmuir plasma. We first of all show that the correct general expression for the ponderomotive force leads to the solenoidal current responsible for the magnetic-field generation. We derive the ponderomotive-force expression and also the magnetic-field generation equations from a two-time-scale two-fluid description. We also use a kinetic approach to derive the magnetic-field generation equations. We discuss the stability of monochromatic Langmuir waves and show that they are subject to both the ordinary modulational instability and to a magneto-modulational instability. We show that the coupled nonlinear equations describing the electric field strength amplitude, the plasma density, and the self-generated magnetic field can, under certain conditions, be reduced to a generalized cubic nonlinear Schrodinger equation. We finally show, by using a virial theorem, that the self-generated magnetic field does not stabilize the wave collapse.

Modon formation in the nonlinear development of the collisional drift wave instability

Nonlinear evolution of the collisional drift wave instability has been investigated by means of numerical simulations based on a model equation derived from a two‐fluid approximation. This approximation is reduced to the Hasegawa–Mima equation when the collision and viscosity are neglected. A crucial feature is that coherent structures are formed from a turbulent state. A scenario for a path to the self‐organized motion through the turbulent motion has been found as follows. The initial exponential growth of a linear instability is followed by a parametric instability that excites many modes. At the same time, the wave breaks up into small vortices. The inverse cascade of the wave energy then sets in and small vortices fuse into larger ones. A large modon is formed at the final stage of evolution.

Soliton and Nonlinear Explosion Modes in an Ion-Beam Plasma System

Nonlinear wave evolutions are studied both numerically and analytically in an ion-beam plasma system. In the linearly stable case solitons associated with linear eigen modes inherent in the system are shown to be mutually independent K-dV solitons so long as their amplitudes are smaller than a certain critical value. In the case of supercritical amplitudes, nonlinear explosion modes are found, whose analytical solution is obtained near the critical point.

Bifurcations and chaos in a current-carrying ion sheath

Cascading bifurcations to chaos are investigated experimentally and theoretically in a current‐carrying stable plasma. A dc plasma current is required to produce an electron‐depleted thick sheath on a grid, which obeys the Child–Langmuir law of space‐charge‐limited current in a diode. Bifurcation cascade and chaotic behavior are exhibited when an external periodic oscillation is applied to the grid, and are in good agreement for the first time with a theory, which describes ion dynamics in the Child–Langmuir sheath and is represented by the differential equation with three independent variables. A fractal dimension predicted by the theory is verified by the experiment.

Instability of Coherent Ion Acoustic Wave in a Phonon Gas

The ion-acoustic wave propagation in a field of randomly excited low-frequency waves (phonon gas) is investigated, by obtaining the linear response function of plasmas in a turbulent phonon state. The turbulent phonons have an influence on the propagation of the coherent wave, to lead a decreased phase velocity. The coherent wave becomes unstable due to the resonant coupling with the beat wave of turbulent phonons. As the result of the instability, the coherent wave with long wavelength piles up in a plasma with turbulent phonons. The results qualitatively agree with the recent experiment.

Chaotic behavior driven by an external periodic oscillation in a current‐carrying unstable ion sheath

A quasiperiodic route to chaos is investigated experimentally and theoretically in a current‐carrying unstable ion sheath. A quasiperiodic regime with two frequencies is realized by a coherent instability and an external periodic oscillation. Chaos appears directly from the quasiperiodic regime when the amplitude of the external oscillation is increased, making nonlinear effects more important. A correlation dimension and the largest Lyapunov exponent, obtained experimentally in the chaotic regime, confirm that the observed chaos is deterministic and the attractor is strange. A period‐doubling route to chaos is also observed after the instability is quenched with the external oscillation by increasing the amplitude of the external oscillation further. These experimental results are in fair agreement with a theory that describes ion dynamics in the ion sheath.

A theory of bifurcations and chaos observed in an ion sheath

A theory of cascading bifurcations to chaos observed in a current‐carrying ion sheath [Komori et al., Bull. Am. Phys. Soc. 36, 2408 (1991)] is developed. The ion sheath on both sides of a grid forms a potential well in which ions oscillate to give a primary motion, being subject to cascading bifurcations to chaos when an external oscillation field is applied to the grid. A model equation is derived to describe ion dynamics in the ion sheath which obeys the Child–Langmuir law for a large potential drop. The numerical solutions are shown to recover the observations.

A route to turbulence in nonlinear development of an ion beam-plasma instability

Nonlinear evolution of the ion beam–plasma instability has been investigated by means of numerical simulations based on a hybrid code. A scenario on a path to the onset of turbulence has been found as follows. The initial exponential growth of the linear instability is saturated by beam trapping, which causes, in turn, amplitude oscillation. The more highly driven harmonics initiate the stochastic instability of the trapped particles. The trapped beam particles begin to wander from one potential wave trough to another and spread in phase space. A transition to turbulence is found to occur through subharmonic excitations because of a parametric decay instability.

Electromagnetic vortices in streaming pair plasmas

Two coupled nonlinear equations for a perturbed electromagnetic field in an electron–positron streaming plasma which is placed in a nonuniform magnetic field are derived and solved analytically, yielding stationary solutions in the form of vortices consisting of monopolar and quadrupolar parts. It is shown that vortices are created in and carried by a specific given linear shear flow profile and a given nonuniformity of the magnetic shear.

Cascading Bifurcations to Chaos in a Current-Carrying Ion Sheath

A theory is developed to explain cascading bifurcations to chaos observed in a current-carrying ion sheath. The basic equation is derived to describe ion dynamics in an ion sheath which obeys the Child-Langmuir law for a large potential drop and is numerically solved to show the same bifurcation sequences as those in the experiments.