A set of linear inhomogeneous time-dependent ordinary differential equations is derived to describe the dynamical interaction of the long-wavelength m = 1 instability with the stable oscillations to which it couples. The equations provide an algorithm for determining the plasma response to external feedback control fields. The method is based upon the new Scyllac ordering developed by Weitzner. The results agree with the steady-state equation of Ribe and Rosenbluth. The obtained m = 1 growth rates also agree with previous new-ordering results for a pure ℓ = 0 or ℓ = 2 system, but for a combined ℓ = 0 and ℓ = 2 system the equations have two distinct unstable eigenvalues corresponding to horizontal and vertical growth rates.
Investigation of oscillations and anomalous transport in a hydrogen hollow cathode discharge by a spatially three-dimensional two-fluid model