Generalized theory of annularly bounded helicon waves
Abstract
The generalized dispersion relationship for annularly bounded helicon plasma is derived. The theory considers the effect of finite electron mass, which results in the plasma field described by superposition of classical helicon solution and the TrivelpieceGould (TG) wave. The solution is obtained for an insulating boundary. The solution shows that the wave structure is heavily affected by the presence of the TG wave, even when a strong axial magnetic field is applied. However, the electric field profile shows that a pair of external rf antennas can still be coupled to the strong radial electric field in the plasma to excite the wave. Moreover, the general solution permits an almost continuous spectrum of parallel wave numbers. The study of kf and n{sub 0}B{sub 0} diagrams shows that the linear relation obtained using classical theory holds everywhere except at low applied magnetic field strength.
 Authors:
 Department of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)
 Publication Date:
 OSTI Identifier:
 20974902
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 3; Other Information: DOI: 10.1063/1.2716663; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANTENNAS; BOUNDARY LAYERS; DIAGRAMS; DISPERSION RELATIONS; ELECTRIC FIELDS; ELECTRONS; HELICON WAVES; MAGNETIC FIELDS; PLASMA
Citation Formats
Yano, Masayuki, and Walker, Mitchell L. R. Generalized theory of annularly bounded helicon waves. United States: N. p., 2007.
Web. doi:10.1063/1.2716663.
Yano, Masayuki, & Walker, Mitchell L. R. Generalized theory of annularly bounded helicon waves. United States. doi:10.1063/1.2716663.
Yano, Masayuki, and Walker, Mitchell L. R. Thu .
"Generalized theory of annularly bounded helicon waves". United States.
doi:10.1063/1.2716663.
@article{osti_20974902,
title = {Generalized theory of annularly bounded helicon waves},
author = {Yano, Masayuki and Walker, Mitchell L. R.},
abstractNote = {The generalized dispersion relationship for annularly bounded helicon plasma is derived. The theory considers the effect of finite electron mass, which results in the plasma field described by superposition of classical helicon solution and the TrivelpieceGould (TG) wave. The solution is obtained for an insulating boundary. The solution shows that the wave structure is heavily affected by the presence of the TG wave, even when a strong axial magnetic field is applied. However, the electric field profile shows that a pair of external rf antennas can still be coupled to the strong radial electric field in the plasma to excite the wave. Moreover, the general solution permits an almost continuous spectrum of parallel wave numbers. The study of kf and n{sub 0}B{sub 0} diagrams shows that the linear relation obtained using classical theory holds everywhere except at low applied magnetic field strength.},
doi = {10.1063/1.2716663},
journal = {Physics of Plasmas},
number = 3,
volume = 14,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}

The general solution to the electrostatic and magnetic fields is derived with respect to the boundary conditions of a coaxial helicon plasma source. The electric field contours suggest that a simple antenna design can ionize the gas in a coaxial configuration. In addition, the power deposition as a function of excitation frequency is derived. The solution is validated by comparison with the standard cylindrical helicon plasma source. Further, a parametric study of source length, channel radius, channel width, and antenna excitation frequency are presented. This study suggests that it is possible to create a helicon plasma source with a coaxialmore »

Comment on 'Plasma ionization by annularly bounded helicon waves' [Phys. Plasmas 13, 063501 (2006)]
The neoclassical calculation of the helicon wave theory contains a fundamental flaw. Use is made of a proportional relationship between the magnetic field and its curl to derive the Helmholtz equation describing helicon wave propagation. However, by the fundamental theorem of Stokes, the curl of the magnetic field must be perpendicular to that portion of the field contributing to the local curl. Reexamination of the equations of motion indicates that only electromagnetic waves propagate through a stationary region of constant pressure in a fully ionized, neutral medium. 
Generalized theory of helicon waves. I. Normal modes
The theory of helicon waves is extended to include finite electron mass. This introduces an additional branch to the dispersion relation that is essentially an electron cyclotron or Trivelpiece{endash}Gould (TG) wave with a short radial wavelength. The effect of the TG wave is expected to be important only for low dc magnetic fields and long parallel wavelengths. The normal modes at low fields are mixtures of the TG wave and the usual helicon wave and depend on the nature of the boundaries. Computations show, however, that since the TG waves are damped near the surface of the plasma, the heliconmore »