Tatsuki Ogino

Modified Nonlinear Schrödinger Equation for Alfvén Waves Propagating along the Magnetic Field in Cold Plasmas

The basic nonlinear equation which describes the Alfven waves, with small but finite amplitude propagating along the magnetic field in cold plasmas, is derived modifying the reductive perturbation method proposed by Taniuti and Wei. Then as a result, the nonlinear dispersion relation is obtained through a procedure which clarifies the physical meaning. Furthermore, the modified nonlinear Schrodinger equation which describes the modulated Alfven wave more correctly than the previous works is proposed. An example of the nonlinear phenomena is shown by the numerical calculations of the initial value problem, using our basic equation for the Alfven waves.

Modulational Instability and Envelope-Solitons for Nonlinear Alfvén Waves Propagating along the Magnetic Field in Plasmas

The modulational instability and envelope-solitons are analyzed for the Alfven waves propagating along the static magnetic field in cold collisionless plasmas, using the modified nonlinear Schrodinger equation previously derived by the authors. The modulational instability occurs in the left-hand circularly polarized Alfven wave (left Alfven wave) for a small amplitude but does not for an amplitude larger than the critical value. On the other hand, the instability never occurs in the right-hand circularly polarized Alfven wave (right Alfven wave). When the modulational instability does not occur, the rarefactive and compressive envelope-solitons exist in the left Alfven wave and the two types of the rarefactive envelope-solitons exist in the right Alfven wave.

Computer Simulation and Analysis for the Spherical and Cylindrical Ion-Acoustic Solitons

The behavior of the spherical and cylindrical ion-acoustic solitons are studied by the computer simulation using a fluid model as well as the theoretical analysis. The simulated results agree well with those obtained by approximately solving the modified Boussinesq equation. A small residue of the high or low density is formed for the inward or outward propagation, respectively, after the spherical and cylindrical ion-acoustic solitons propagate. Moreover, the electron plasma and ion-acoustic waves are emitted from the solitons as they propagate inwards or outwards. The amplitude of the soliton such as the ion density does not grow infinitely for the finite ion temperature even when the soliton concentrates at the center. This is because the half width of the maximum amplitude is limitted by the ion Debye length.

A Perturbation Method and Its Application to Obliquely Propagating Nonlinear Alfvén Wave

A procedure to the coordinate stretching and the perturbation expansion for the reductive perturbation method is proposed to analyze the nonlinear wave behaviors in dispersive medium. The method is applied to the nonlinear Alfven wave propagating in an oblique direction to the static magnetic field in cold plasmas. Although the wave is described by a linear equation for some physical quantities, the nonlinearity appears in the relation among the other quantities for considerably large amplitude. These outstanding features are much different from other waves in plasmas.

Nonlinear Evolution of the Resistive MHD Modes in a Toroidal Plasma

The nonlinear stabilities of resistive MHD modes are investigated in a tokamak configuration by a three dimensional MHD simulation based on a rectangular column model under the fixed boundary condition. The m =1 internal resistive kink mode is excited for the central safety factor, q 0 < 1, resulting in a sawtooth oscillation of temperature. Only the m =2 mode is excited for q 0 < 2 and a small resistivity. On the other hand, the several modes of (- m : n )=(2:1), (1:1) and (3:2) appear for q 0 < 2 and a little large resistivity depending on the q -configuration through the variation of toroidal current. The (3:2) mode plays an important role on the mode coupling between the (1:1) and (2:1) modes. As the result, the (2:1) mode finally determines the stability and stable configurations of plasma are formed with the condition of \(q \gtrsim 2\).

Computer Simulation for the Fast Magnetosonic Solitons

A computer simulation for the fast magneto-sonic soliton (FMS soliton) propagating across the external magnetic field is studied under the periodic boundary condition using the fluid model. A theor...

Computer Simulation for the Ion-Acoustic Solitons Propagating in both Directions

The temporal behaviors of the finite amplitude ion-acoustic waves propagating in both directions are simulated by a fluid model. In the simulation, several ion-acoustic solitons propagating in both directions emerge and nonlinearly interact one another at the collisions. At the head-on collision, the combined amplitudes of the density and velocity differ from the simple sum of the amplitude of the two solitons. Moreover, the phase shifts cannot be predicted from the Boussinesq equation but agree with those by a reductive perturbation method. The system including the solitons propagating in both directions becomes a turbulent state more quickly than that including only the solitons propagating in unidirection.

Nonlinear Evolution of the Kink Ballooning Mode in a Toroidal Plasma

The nature of nonlinear evolution of the kink ballooning mode for the aspect ratio, R / a =2 and the parameter dependence on the critical β have been investigated by a three dimensional MHD simulation based on a rectangular torus model. Consequently, it turns out that ballooning modes form large convective cells concentrated in regions of unfavourable curvature of the magnetic field line for a high-β plasma. Moreover, a stable equilibrium is found with up 5% average β value by adjusting the vertical magnetic field and the diamagnetic effect.

Modulational Instability of Electron Plasma and Ion Plasma Waves

Through application of the reductive perturbation method to the fluid equations for electrons and ions, a nonlinear Schrodinger equation is derived. For the electron plasma wave, the assumption of the uniform background of ions is not used. Then exact properties of the equation are obtained for all wave numbers, including a modulationally unstable region predicted by Zakharov, For the ion-acoustic mode, the assumptions of the Boltzmann distribution for electrons and of cold ions are not used. Then a modulationally unstable region for the ion plasma wave exists for wavelengths shorter than the electron Debye length, and the growth rate of the instability is appreciably large even at low ion temperatures.

Computer Simulation of Modulational Instability for the Electron Plasma Wave

Modulational instabilities for the electron plasma wave are studied by computer simulation based on the fluid equations for the electron and ion. The growth rate and frequency shift given by the simulation are in agreement with the theoretical predictions by Fried et al. in the wavenumber regions for both koγ-1/2 and ko\lesssimγ-1/2, where ko and γ are the normalized carrier wavenumber and mass ratio respectively. Although an envelope soliton is produced at the saturation state of the instability, a coupled soliton is not observed. The tails of ion density are excited, whenever the half width of the soliton is a little less than 10λDe, where λDe is the electron Debye length. Therefore, such a width, often observed in laboratory experiments, is explained by the generation of the tails.