The dispersion and attenuation of helicon waves in a uniform cylindrical plasma

Abstract

A systematic account is given of the derivation of the dispersion relation for helicon waves in a uniform cylindrical plasma bounded by a vacuum. By retaining finite resistivity in the equations, boundary conditions present no difficulties, since the wave magnetic field is continuous through the plasma-vacuum interface. Two unexpected results are found. First, the wave attenuation remains finite in the limit of vanishing resistivity. This is due to the energy dissipated at the interface by the surface currents required to match the plasma wave field to the vacuum wave field. Zero wave attenuation for zero resistivity is recovered if electron inertia is included. Secondly, it is found that waves with azimuthal numbers m of opposite sign propagate differently, but the sense of polarization at the axis of the cylinder is independent of the sign of m.The argument of the dispersion function is complex and numerical results were obtained using a computer. The method of programming is described, and results are given applicable to propagation in metals at low temperatures, or in a typical gas discharge plasma for the m = 0 and m = ± 1 modes.An example of the amplitude of the wave fields as a function of radius is given for the axisymmetric mode, and of amplitude and phase for the m = ± 1 modes.

Azimuthally symmetric pseudosurface and helicon wave propagation in an inductively coupled plasma at low magnetic field

“…This dispersion relation was first derived by Klozenberg et al 11 Both waves satisfy the Helmholtz equation,…”

“…Klozenberg et al 11 found an unexpected wave attenuation in a helicon wave study, for which the electrical resistivity term in the equations was not involved. They reported the surface current required at the boundary of the plasma needed to match the plasma wave field to the vacuum wave field.…”

Helicons in Unbounded Plasmas

“…For example helicon waves have a wavenumbers in azimuthal direction, radial direction and parallel direction along the ambient field B 0 . They have been studied in solid state plasmas [3] and in gaseous plasma columns [4] which opened up many applications [5,6]. In spite of a vast body of literature on helicons no measurements of magnetic field lines have been reported, partly because in-situ field line measurements are impossible in solid state plasmas or space plasmas.…”

Whistler waves with angular momentum in space and laboratory plasmas and their counterparts in free space

“…Some 50 years ago waves with similar properties were observed in magnetized solids [8]. Whistler modes were also excited in discharge plasmas produced in the laboratory [9]. The waves in bounded plasma columns were termed 'helicons' [10] and a new specialty of low temperature plasma applications evolved [11].…”