Hirotada Abe

A binary collision model for plasma simulation with a particle code

Abstract A binary collision model by the Monte Carlo method is proposed for plasma simulations with particle codes. The model describes a collision integral of the Landau form. Collisional effects in spatially uniform plasmas are simulated, and the results are in good agreement with theoretical ones.

High‐energy tail formation by a monochromatic wave in the magnetized plasma

High‐energy tail formations due to the monochromatic wave in a magnetized plasma are studied numerically and analytically. By calculating the phase space trajectories of 10 000 particles, initially Maxwell‐velocity‐distributed, in the presence of a uniform magnetic field and a sinusoidal wave traveling closely in the perpendicular direction with the frequency of cyclotron harmonics, some properties of particle acceleration are clarified. The acceleration mechanism can be described by a modification of trapping theory and two types of stochastic acceleration. The behavior of the high‐energy tail formation depends on the magnitude of ω/Ω. For small ω/Ω (ω/Ω≲10), the cyclotron harmonics resonance is very important. The ratio of the perpendicular wavelength to the average Larmor radius and the wave amplitude play an important role in determining the ratio of tail to the bulk portion.

Propagation and plasma heating of the lower hybrid wave in the nonuniform density plasma

A particle simulation model which treats the wave excitation and propagation in nonuniform density by an external source is applied to the study of the behavior of lower hybrid wave heating. The observed values of the perpendicular wavenumber agree well with those calculated from the WKB approximation. In the case of the large wave amplitude, the following features are observed for the increase in the ion and electron kinetic energies. Ion perpendicular energy distributions are observed to have the components of the high energy tail. These phenomena are explained in terms of the mechanism of trapping and stochastic acceleration of a charged particle in the monochromatic and nearly perpendicular propagating wave with a frequency near cyclotron harmonic. A strong increase in the parallel kinetic energy of the electron is observed near the plasma surface. This is mainly due to the trapped electrons.

Computer simulation of nonlinear interaction between a cold beam and a weakly collisional plasma

The spatial growth of the instability and the nonlinear interaction between a small cold beam and a warm background plasma are examined by means of particle simulation. Up to the first maximum in the amplitude oscillation of the wave, quantitative measurements confirm the predictions based on the single wave model: the magnitude of the growth rate, monochromaticity of the unstable mode, the maximum wave amplitude, and the phase space orbits of the beam electrons. After the first maximum of the wave amplitude, the spatial dependence of the wave amplitude cannot be explained by the single wave model predictions and the wave power is anomalously overdamped by a factor of 0.1 smaller than the predicted value in the first minimum. The extended single wave model equations suggest that this anomalous phenomenon is caused by weak collisions of the order of ν/ωp∼10−3 within the background plasma.

Computational study on excitation, propagation, and two‐species‐ion‐plasma heating due to the ion‐Bernstein wave

External excitation, propagation, and ion heating for the ion‐Bernstein wave (IBW) are studied for the single‐ion and two‐ion species plasmas, using particle simulation. It is found that the value of ω/Ωi near the antenna position influences the excitation characteristics of the IBW. The wavelength and group velocity of the propagating IBW agree well with those calculated from the linear dispersion relation. Corresponding to the experiment done with the JIPP T‐II‐U device [Phys. Rev. Lett. 54, 2339, (1985)], the 3ΩD heating process in the plasma composed of deuterium‐like and hydrogen‐like ions is investigated. The wave energy is deposited into the bulk and tail of the deuterium‐like ions because of third harmonic cyclotron resonance and the bulk of the hydrogen‐like ions because of 3/2 ΩH cyclotron subharmonic resonance.The possibility is also discussed that the heating efficiency may not depend on the concentration of the deuterium‐like ion in the 3ΩD heating in the actual tokamak experiment.

Energy and momentum deposition in plasmas due to the lower hybrid wave by a finite source

Heating and current generation due to the lower hybrid wave are studied using particle simulation. In contrast with previous work, where only a single mode is treated, the main interest of this work is focused on the physical problems of a propagation cone consisting of many Fourier‐expanded modes. It is found that the trajectory of the propagation cone is well described up to the lower hybrid resonance layer using both the cold plasma approximation and the WKB method. An ion cross‐field drift due to the ponderomotive force is observed. A main discovery of this work is that the modes in the upper portion of the spectrum of the antenna play a key role in the creation of the ion high‐energy tail. This process cannot be explained by the linear theory and is called the cascade process judging from the time variation of the damping of each mode. The particle model is significantly improved using the elongated grid and the quadratic spatial interpolation. Applications of this model to simulations of other probl...

Electromagnetic particle simulation code PS2M for bounded plasmas with conducting walls

A computational method for solving boundary-value problems for the Maxwell equation in the particle simulation is developed and is emlcodied in a code PS2M, which is a new Particle Simulation code in 2.5 dimensions (2 space-dimensions and 3 velocity-dimensions) for electroMagnetic plasmas. This method is formulated by introducing a double representation of the δ functions which are expanded by two independent sets of eigen functions in a system. The validity of solutions of the boundary-value problems is proved by invoking the mathematical law of Greens functions. The high-order spline spatial interpolation was confirmed to be very useful in the simulation for electromagnetic plasmas, because its use removes the limit on the grid spacing, which has been severely limited of order of the Debye length in the conventional methods. This code, PS2M, has been used to study RF stabilization of the flute mode and ECRH.

Mode conversion and electron heating near the upper hybrid resonance frequency

Mode conversion near the upper‐hybrid resonance frequency and electron heating are studied using a one‐dimensional electromagnetic relativistic particle code. It is found that for a sufficiently small pump field E0, E20/4πnTe ≲0.01, electron heating is localized in a region near the electron cyclotron layer where the pump frequency is equal to the local electron gyrofrequency. For stronger pump fields, electron heating takes place more or less uniformly across a region between the upper‐hybrid resonance layer and the cyclotron layer. In addition, a significant fraction of electromagnetic energy associated with the pump is found to be reflected back into the vacuum from a region in the plasma near the upper‐hybrid resonance layer for both strong (E20/4πnTe ≊1) and weak pumps (E20/4πnTe ≪1).

Computer simulation of the linear and nonlinear propagation of electromagnetic waves in dielectric media.

We present a new computer simulation model developed to study the propagation of electromagnetic waves in a dielectric medium in the linear and nonlinear regimes. We construct the model by combining a microscopic model used in the semiclassical approximation for the dielectric media and the particle model developed for the plasma simulations. The model is then used for studying linear and nonlinear wave propagation in a dielectric medium such as an optical fiber. It is shown that the model may be useful for the study of nonlinear wave propagation and harmonic generation in nonlinear dielectric media.

Particle simulation on radio frequency stabilization of flute modes in a tandem mirror. I. Parallel antenna

A two‐ and one‐half‐dimensional electromagnetic particle code (PS2M) [H. Abe and S. Nakajima, J. Phys. Soc. Jpn. 53, xxx (1987)] is used to study how an electric field applied parallel to the magnetic field affects the radio frequency stabilization of flute modes in a tandem mirror plasma. The parallel electric field E∥ perturbs the electron velocity v∥ parallel to the magnetic field and also induces a perpendicular magnetic field perturbation B⊥. The unstable growth of the flute mode in the absence of such a radio frequency electric field is first studied as a basis for comparison. The ponderomotive force originating from the time‐averaged product 〈v∥B⊥〉 is then shown to stabilize the flute modes. The stabilizing wave power threshold, the frequency dependency, and the dependence on ∇‖E∥‖ all agree with the theoretical predictions.