Hiroshi Tanaca

Cylindrical Ion Acoustic Soliton in Plasma with Negative Ion

Cylindrical ion acoustic solitons are investigated theoretically and numerically in a plasma with negative ion. In a theoretical part, we derive a cylindrical Korteweg-de Vries equation for an ion acoustic wave. The sign of nonlinear coefficient depends on the negative ion density. At the critical density of the negative ion where the nonlinearity of the Korteweg-de Vries equation vanishes, the ion acoustic wave is described by a cylindrical modified Korteweg-de Vries equation, and in the vicinity of the critical density, it is described by a combined cylindrical equation of the Korteweg-de Vries and modified Korteweg-de Vries types. The change of a soliton amplitude due to the geometrical effect is analytically obtained in two limiting cases when the geometrical effect is much stronger or weaker than the nonlinear and dispersive effects. In the numerical calculation, the theoretical prediction for the change of the soliton amplitude is verified.

Modulational Instability of Ion Wave in Plasma with Negative Ion

A modulational instability of an ion wave in a plasma composed of electron, positive ion and negative ion has been investigated theoretically. We derive a nonlinear Schrodinger equation for ion wave and examine the signs of nonlinear and dispersion coefficients. The dispersion coefficient is negative irrespective of the wavenumber. The sign of the nonlinear coefficient changes at a critical wavenumber k c , above which the coefficient becomes negative and the ion wave is modulationally unstable. The critical wavenumber k c depends strongly on the negative ion density. At the critical density of negative ion where the nonlinear coefficient of the Korteweg-de Vries equation for ion wave vanishes, the critical wavenumber k c is reduced to zero and the wave of any wavenumber is modulationally unstable.

Coupled Modes Approach to Non-Linear Dispersive Wave. I. Recurrence of Soliton

The K-dV equation is numerically solved by means of a mode coupling method for periodic waves launched at a certain boundary. The coupled modes equations for slowly varying complex amplitudes are first derived and are solved. The superposition of N modes yields almost periodic solutions in space which represent the recurrence of an initial state. The recurrence length is given explicitly as a function of a frequency and an initial amplitude at the boundary. The recurrence is, in general, imperfect and the waveform differs from each other at different recurrence points. The reason of the imperfect recurrence is discussed from the view points of wave-wave interaction and of soliton-soliton interaction.

Nonlinear evolution of double layers and electron vortices in an unstable plasma diode

Nonlinear evolution of a large-amplitude relaxation oscillation in an unstable plasma diode is investigated by a computer simulation using a particle model. The oscillation is closely related to double-layer dynamics accompanied by a negative potential dip on the low-potential tail. A vortex is formed in the electron velocity phase space during the potential evolution, which causes a topological rearrangement of the phase space in the high-potential plasma.

Response of ion acoustic waves to an impulse

Linear response of ion acoustic waves to an impulse has been numerically calculated using an exact dispersion relation. Two experiments have been simulated. Excellent agreement has been seen for a stable plasma, while for an unstable plasma, a positive frequency shift is observed.

Solitary Wave in Periodic Nonlinear Lattice

The behaviour of solitary wave has been studied numerically in periodic Toda lattice which has alternate Toda potentials with different parameters. In the numerical calculation, due to deviations from the ideal Toda lattice, the solitary wave decreases in propagation, trailing ripple oscillation behind it. Yet, the stability of the waves depends on the lattice parameters. A narrow solitary wave compared with the lattice constant can propagate stably in the periodic lattice under our special condition. The validity of the K-dV approximation is examined concerning the velocity and width of a small amplitude solitary wave. The duality of nonlinear lattice is also discussed.

Soliton in a Random System

Soliton propagation in a random medium has been numerically studied. As a model of the system, we consider a one-dimensional Toda lattice where two different mass particles are distributed randomly but the interaction potential is uniform. It is shown that the amplitude of a soliton decreases as n -1 ∼ n -1.2 ( n denotes the lattice point) in the course of propagation and that the damping is enhanced with soliton amplitude. The possibility of soliton damping with hysteresis is suggested.

Plasma Heating by Ion Wave Instability in Q-Machine

The heating of electrons and ions by the current driven ion wave instability was studied in a Q-machine. The heating occured when the ion wave sufficiently grew and steepened, i. e., in a certain turbulent state. The heating mechanism is not clear, but the heating by means of the ion wave was experimentally confirmed.

Dispersion of ion Landau damping of ion waves in plasma

The propagation of ion wave with frequency below 0.6 omega pi is studied experimentally. The Landau damping rate increases exponentially when the frequency of the ion wave approaches the ion plasma frequency omega pi, while its phase velocity decreases slightly. The results are compared with theory and good agreement is obtained.

A Method of Measurement of Plasma Conductivity. I. : Theoretical Approach

It is shown that the plasma conductivity can be evaluated from the change in magnetic flux in the plasma of an applied electromagnetic field. The evaluation requires no detailed knowledge of the electron collision frequency. This method, not being based on the usual conductor approximation will prove useful if a method of determining the magnetic flux change is established successfully.