Potential formulation of the dispersion relation for a uniform, magnetized plasma with stationary ions in terms of a vector phasor

TL;DR

This paper reexamines the helicon dispersion relation in a uniform, magnetized plasma using potential formulation, addressing nonlinear effects and expressing solutions via a vector phasor for all frequencies.

Contribution

It introduces a potential-based derivation of the helicon dispersion relation, including nonlinear self-coupling effects and a comprehensive solution in terms of a vector phasor.

Findings

Propagation occurs mainly at low conductivity and below cyclotron frequency.

Solution behavior depends on conductivity to magnetic field ratio.

Significant propagation is limited by skin depth and wavelength ratio.

Abstract

The derivation of the helicon dispersion relation for a uniform plasma with stationary ions subject to a constant background magnetic field is reexamined in terms of the potential formulation of electrodynamics. Under the same conditions considered by the standard derivation, the nonlinear self-coupling between the perturbed electron flow and the potential it generates is addressed. The plane wave solution for general propagation vector is determined for all frequencies and expressed in terms of a vector phasor. The behavior of the solution as described in vacuum units depends upon the ratio of conductivity to the magnitude of the background field. Only at low conductivity and below the cyclotron frequency can significant propagation occur as determined by the ratio of skin depth to wavelength.