Estimation of wave-number spectrum parameters from fixed probe-pair data

Abstract

Spectrum parameter estimation concerning a stationary and homogeneous random field is examined in terms of quantities obtainable from a pair of fixed probes. The estimators of the mean wave number and the wave-number spectral width are derived by relating wave-number spectral moments to spatial derivatives of the complex covariance of the field, the effect of finite probe size being taken into account. The estimate biases associated with the probe separation can be greatly reduced by employing an algorithm based on the polar-form representation of the complex covariance, while the variances of the estimates have a tendency to be enhanced with the decrease of the probe separation. An optimum range of the probe separation is theoretically determined.

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

“…The advantage of Taylor's hypothesis is that it requires only one probe for detection. More advanced methods that can estimate wave number spectra directly require two or more probes (Smith and Powers, 1973;Iwama et al, 1979;Beall et al, 1982). It might be instructive to show the result for a case where the turbulence is confined to a part of wave number space: assume we have S(k) = A|k| −α within a cone with an opening angle θ 0 as in Eq.…”

“…Summary figure from experimental studies of plasma density fluctuations in radio frequency (RF) discharges, obtaining dispersion relations against a noisy background (Iwama et al, 1979;Beall et al, 1982). For the conditions on the left it is feasible to obtain evidence of a dispersion relation.…”

“…Strong turbulence is found for cases where the linear dispersion relation is immaterial, and possible restrictions on triplet interactions are relaxed. In many studies of seemingly turbulent plasmas it is possible, by suitable chosen multiprobe diagnostic methods (Iwama et al, 1979;Beall et al, 1982), to determine a relation between frequency and wave vector experimentally. An illustrative example is shown in Fig.…”

A robust method for measurement of fluctuation parallel wavenumber in laboratory plasmas

“…A cylindrical reference frame is used in the following, where R is the major radius, z is the vertical coordinate with respect to the midplane and φ is the toroidal angle. it has to be long enough that the probes can be considered point-like with respect to their mutual distance, as also discussed in [18]. Second, it has to be short enough that the level of coherence in the range of frequencies of interest is sufficiently high, but yet the probes are not 'shielding' each other.…”

“…In addition, probes with finite size act as a high-pass filter in k-space [18], making the measurement untrustful for small values of k . It is therefore difficult to discriminate between a small but finite k associated with drift (including drift-interchange) waves in plasmas with small ion Larmor radius and a vanishing k associated with flute instabilities.…”