Ryohei Itatani

High-order spline interpolations in the particle simulation

Abstract In the conventional plasma simulation models using particles, in which the total momentum is conserved, the total energy is not conserved due to nonuniformity of space caused by the spatial grids. The grid spacing has been severely limited of order of the Debye length. It is found that the use of the high-order spline spatial interpolation removes this limit without a significant increase of the computation and complexity of the algorithm in the system that only the long-wavelength, collective phenomena are important. The theoretical analysis of the total energy is improved compared with the previous work and its scaling law is related to the so-called aliasing error explicitly. The coefficient η introduced previously is referred as the model index and is used again as a measure of the accuracy of the models for the energy conservation.

RF stabilization of high-density plasma in an axisymmetric mirror I: Identification and stabilization of flute mode

The low-frequency instability observed in an axisymmetric mirror is identified as a curvature-driven flute instability for a wide range of densities up to 1014cm−3. It is demonstrated that this flute instability is stabilized by the RF field which is coupled electromagnetically and applied only in the bad-curvature region. Radial plasma loss is significantly reduced by the stabilization. This method of stabilization is revealed to be effective for densities from 1010 to 1014cm−3, indicating the possibility of a purely axisymmetric tandem mirror.

Two‐dimensional modeling of electron cyclotron resonance plasma production

For the numerical simulation of electron cyclotron resonance plasma production, a two‐dimensional model that describes wave propagation and plasma transport is developed. The modeling code calculates profiles of electromagnetic wave fields, power absorption of electrons, and temporal evolution of plasma densities in a bounded, inhomogeneous, cylindrical system. The calculation of the plasma production in a mirror magnetic field shows that the plasma production property is very sensitive to the antenna location.

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.

Development and Plasma Characteristics Measurement of Planar-Type Magnetic Neutral Loop Discharge Etcher

A low-pressure and high-density plasma source, called a planar-type magnetic neutral loop discharge (NLD), has been developed for a single-wafer etching process, employing a pair of permanent magnet rings and a single-turn RF antenna on the quartz plate. First, the plasma characteristics of planar-type NLD were compared with those of a planar-type inductively coupled plasma (ICP) using the prototype etcher with a large magnetic neutral loop (MNL) of 230 mm diameter. The results of probe measurements in Ar plasmas have revealed that a planar-type NLD can be sustained at low pressures of 0.1–10 mTorr with higher plasma density and lower electron energy than a planar-type ICP. The depletion of high-energy electrons in NLD was revealed by the direct measurement of electron energy distribution function (EEDF) and optical emission spectroscopy. Next, for the purpose of uniform and large-diameter NLD generation, effects of magnetic field strength and the gap between an antenna and a wafer stage on the plasma uniformity have been investigated. By reducing the magnetic field strength that suppresses plasma diffusion, an ion current uniformity within ±2.5% and a high ion current density of 13 mA/cm2 was obtained over a 240 mm diameter in the downstream Ar plasma. As for C4F8+90%Ar plasmas, preferable gas phase chemistry of ion and neutral species for highly selective SiO2/Si etching was attained due to relatively low electron energy, and a uniformity within ±2% was also achieved over a diameter of 240 mm.

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.

Positional Instabilities in a Tokamak with a Resistive Shell

The investigation of positional instabilities, that is, vertical displacement and horizontal expansion of the plasma loop, is extended to a tokamak with a resistive shell. The shell current induced by a small displacement of the current-carrying plasma column produces a restoring force, which contributes to the stabilization. The quantitative analysis of the effect due to the shell shows that the finiteness of the minor radius of the plasma column reduces the effective skin time of the shell τs from the intrinsic one. Consequently it is shown that although the stability condition is not altered, a resistive shell restrains the growth rate of the instability to the order of τs-1, in a wider region than the stable one.

High density central cell plasma production and ion heating by helicon wave damping and its mode conversion into a slow Alfven wave

A new scheme of plasma production and ion heating in the central cell of the tandem mirror is demonstrated. Helicon mode plasma production in combination with two ion species plasma heating by mode conversion of a fast Alfven wave into a slow Alfven wave realizes ion heating of a high density plasma, and could remove the density limitation caused by the conventional scheme using slow ion cyclotron waves. The achieved value of products of electron density and average ion temperature is 9*1020 eV.m-3 for an RF power of 165 kW. Analysis of wave damping indicates that matching the radiation spectrum of the antenna with the damping spectrum results in efficient plasma production. The phased dual double-half-turn antenna is suitable for helicon wave spectrum control