Suwon Cho

The effects of the density profile on the power absorption and the equilibrium density in helicon plasmas

Power absorption profiles are computed using numerical integration for radially non-uniform helicon plasmas with finite axial lengths. As in a uniform plasma, the Trivelpiece–Gould mode dominates the power absorption causing the surface deposition of the rf power. In addition to the surface heating, there is bulk electron heating for non-uniform plasmas, and the portion of this bulk heating increases with the degree of the inhomogeneity. It has been also found that the radial inhomogeneity of the plasma density results in the suppression of the m=−1 mode and reveals the axial resonance condition. Finally, the global power balance is considered to estimate average equilibrium densities, which are found to be in agreement with experimental values.

The field and power absorption profiles in helicon plasma resonators

Analytic expressions are presented for electromagnetic waves excited by Boswell and Nagoya III type antennae [F. F. Chen, J. Vac. Sci. Technol. A 10, 1389 (1992)] in a uniform plasma column, and profiles of the wave field and power absorption are calculated. The Trivelpiece‐Gould mode is found to be dominant causing the surface electron heating, while the linear dependence of the plasma density on the magnetic field is obeyed. In addition, the fast helicon wave approximation, with which the electron inertia is neglected, is examined in detail and its validity is discussed.

Self-consistent discharge characteristics of collisional helicon plasmas

The steady-state fluid equations and Maxwell’s equations are solved self-consistently in helicon plasmas. When the Trivelpiece-Gould mode dominates the power transfer, the density profile is relatively flat in the central region compared to the case where there is significant bulk heating by the helicon wave. It is shown that the density changes from a relatively flat to steep profile at a certain value of the magnetic field, and this is related to the mode coupling and decoupling of the helicon and Trivelpiece-Gould modes.

The role of the lower hybrid resonance in helicon plasmas

A numerical study is carried out to investigate the eigenmode characteristics of helicon plasmas near the lower hybrid resonance using the analytic solutions of the wave equation for uniform plasmas. It is shown that there are innumerable or a few isolated eigenmodes depending on the value of the wave frequency whether it is higher or not than that of the lower hybrid frequency. The plasma resistance is usually large with a sharp peak near the lower hybrid frequency, but it depends on the plasma density. Accordingly, the wave equation is solved self-consistently with the particle and power balance equations, and it is shown that there exists a threshold frequency for efficient ionization near the lower hybrid resonance. This may explain the existence of the optimum frequencies of helicon discharge which have been experimentally found to be near the lower hybrid frequencies.

Frequency dependence of the plasma density for helicon plasmas

Variations of plasma density are investigated as a function of frequency of rf power in a helicon plasma source. Abrupt, almost step-like changes in the plasma density are observed during the frequency scans under various conditions of the input rf power, the argon gas pressure, and the magnetic field. It is found that the transition frequencies shift to the lower value region as the input rf power and/or the argon gas pressure is increased, and to the higher value region as the magnetic field is increased. The observed density transitions are compared with semianalytical calculations based on the power balance relation and it has been shown that the results are in good agreement.

A self-consistent global model of neutral gas depletion in pulsed helicon plasmas

The time-dependent global model is employed to examine the temporal behavior of the electron density and temperature in helicon plasmas. The power absorption calculated from the solutions of the Maxwell equations is used in solving the power balance equation and a balance model for the neutral gas is considered to find its density self-consistently. The numerical results successfully explain neutral gas depletion and the occurrence of two distinct modes of pulsed helicon discharge, which have been observed experimentally.

The magnetic field and performance calculations for an electromagnetic pump of a liquid metal

For an annular-type electromagnetic pump of a liquid metal, the magnetic field is found in closed form by means of the Fourier transform method for two-dimensional field analysis based on an equivalent current sheet model, so that the terms contributing to the normal thrust and the end effect are analytically identified. Analytical solutions for the magnetic vector potentials are compared with numerical ones obtained from the finite difference equation, and they turn out to be in good agreement regardless of the assumption of infinite permeability used in the analytical approach. As a result of closed-form solutions, the electromagnetic body force exerted on a liquid metal flow and the efficiency of the pump are calculated without going through tedious time-consuming numerical work usually accompanied by troublesome convergence problems. The calculated results for estimating the influence of end effects on the performance of the electromagnetic pump clearly show that the end effects give rise to the obstructive force to the liquid metal flow at inlet and outlet ends of the pump. In addition, the efficiency is found to be lowered due to end effects, especially when the speed of the flow is high.

The resistance peak of helicon plasmas at low magnetic fields

The dispersion characteristics of the radial eigenmodes and resistive loading of helicon plasmas are studied to explain the occurrence of the density peak at low magnetic fields. The plasma resistance is usually found to be large for the eigenmodes near the magnetic field where the fast and slow waves are coupled and can be peaked at low magnetic fields depending on the antenna configuration. It is explained how reflection of the waves at an axial end causes the resistance peak at low magnetic fields for a single loop antenna and the Nagoya type III or helical antenna itself can give rise to the resistance peak regardless of reflection. Finally, the dependence of the resistance peak on the density and the wave frequency is examined to show that the general trend is consistent with experimental observations.

The dependence of the plasma density on the magnetic field and power absorption in helicon discharges

Abstract The plasma impedance is obtained using analytic solutions for wave fields excited by Nagoya type III or Boswell type antennae. Considering the power balance, possible explanations are suggested for the density jumps and for the linear dependence of the plasma density on the magnetic field observed in many helicon plasma sources.

Dispersion characteristics and field structure of surface waves in a warm inhomogeneous plasma column

The electron temperature and the radial inhomogeneity of the plasma density are considered in studying the characteristics of the surface electromagnetic wave in a plasma column. The Maxwell equations are combined with the fluid momentum equation to obtain the governing wave equations. For a uniform plasma the wave equations are analytically solved yielding the dispersion relation in a closed form and they are solved by the finite difference method after being converted to an operator eigenvalue equation for a nonuniform plasma. It is shown that the influence of the thermal electron motion is closely related to the density profile and the plasma column radius in addition to the electron temperature and collision frequency. Finally, the electric field structure is found to be quite different from the one obtained from the cold plasma theory.