Effects of Parallel Wavelength on the Collisional Drift Instability

Abstract

An extensive investigation of the dependence of drift wave characteristics upon parallel wavelength in collisional potassium Q-machine plasmas is presented. Results are compared with a two-fluid slab-model theory which includes the effects of parallel resistivity and thermal conductivity for electrons and Larmor radius, collisional viscosity, and motion parallel to the magnetic field for ions. The general stability characteristics of the drift wave are confirmed: stability at low magnetic field (B/k⊥≲0.4 kG·cm) due to ion viscosity, stability at both long- and short-parallel wavelength (λ‖ ≳ 200 and λ‖≲100 cm, respectively) due to the combined effects of ion viscosity and parallel electron fluid expansion and stability of individual modes at high magnetic field (B/k⊥ ≈ 1 kG·cm, λ‖ ≈ 100 cm) due to ion parallel motion. Quantitative agreement between experiment and theory is demonstrated for the detailed parametric dependences of instability onset, complex frequency, and oscillation amplitude on parallel wavelength, magnetic field, and density.

Spectral properties of electrostatic drift wave turbulence in the laboratory and the ionosphere

“…Plasma currents can enhance the instability (Kadomtsev, 1965). The theoretic results for the linear instability (the resistive instabilities, in particular) of drift waves have been confirmed to good accuracy by a number of laboratory experiments (Hendel et al, 1968;Rowberg and Wong, 1970;Rogers and Chen, 1970;Schlitt and Hendel, 1972), mostly in Q machines (Motley, 1975;Pécseli, 2012). The fully developed saturated turbulent state of these instabilities is usually found to be nearly two-dimensional in the plane perpendicular to B.…”

“…Consequently the plasma conditions are not properly be called "strongly turbulent". The dispersion relations mentioned here differ from the frequency-wave-number proportionality implied by the use of the Taylor hypothesis (Shkarofsky, 1969;Hinze, 1975), or the "frozen turbulence approximation" to be discussed later.…”

“…For low observed frequencies it will generally not be correct to assume that the Doppler shift dominates. Limitations in the applicability of the Taylor hypothesis were discussed by Shkarofsky (1969). No universal criterion can be given for the applicability of the hypothesis, but some reasonably general models can be postulated stating the requirements to be U 2 u 2 and t 2 k 2 0 u 2 1 when applied to the autocorrelation function.…”

“…The Taylor hypothesis basically argues for the replacement r → U t in the detected correlation functions R c , stating that R c (r = 0, t) ≈ R c (r = U t, t = 0), or the equivalent ω → U · k replacement in the detected power spectra, where U is the detector velocity (Shkarofsky, 1969). A detected frequency in a power spectrum is interpreted in terms of the Doppler shift, ω ≈ k · U , for the case where the plasma is moving with a high velocity U past a detector, the tip of a Langmuir probe for instance.…”

“…Experiments in the laboratory and in space obtain frequency spectra which are subsequently interpreted as wave number spectra with reference to the Taylor hypothesis (or the frozen turbulence approximation) often used in studies of fluid and plasma turbulence (Shkarofsky, 1969). The Taylor hypothesis basically argues for the replacement r → U t in the detected correlation functions R c , stating that R c (r = 0, t) ≈ R c (r = U t, t = 0), or the equivalent ω → U · k replacement in the detected power spectra, where U is the detector velocity (Shkarofsky, 1969).…”