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

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.

Remarks on the derivation and evaluation of the Stacey-Sigmar model for tokamak equilibrium

“…The homogeneous equations are satisfied identically in the potential formulation, while the inhomogeneous equations are constrained by continuity of the source ∂ µ J µ = 0 and the potential ∂ µ A µ = 0. One can easily show that even the most basic of derivations, such as that for the cold plasma dispersion relation 14 , when done in the field formulation without Gauss's law, are not consistent with results derived from the potential formulation of electrodynamics.…”