Self-Similarity Properties of the Probability Distribution Function of Turbulence-Induced Particle Fluxes at the Plasma Edge

Abstract

The probability distribution function of the turbulence-induced particle flux at the plasma edge has distinct functional forms over two distinct ranges of time scales. One range corresponds to the fluctuation time scales and the other one is the mesoscale range: time scales between the turbulence decorrelation and confinement time. In the second range, the probability distribution function is selfsimilar and essentially has only the outward flux tail. This structure reflects some of the mechanisms of the underlying turbulence. PACS numbers: 52.35.Ra, From the Langmuir probe measurements in low-power Ohmically heated or electron cyclotron heated plasma discharges and for several types of confinement devices, we have concluded that the electrostatic potential and density fluctuations at the plasma edge are self-similar over a broad range of time scales [1,2]. The selfsimilarity range is, in general, for time scales longer than the turbulence decorrelation times up to times of the order of confinement time, the mesoscale range. The upper bound of the self-similarity range is difficult to determine because of the lengths of time records available and the varying plasma conditions on these longer time scales. It was found that for fluctuation measurements within the plasma confinement region the self-similarity parameter [3] varies between H 0.62 and H 0.75, a relatively small range of variation given the diversity of plasma confinement devices considered.To find out whether these properties of the plasma fluctuations have any bearing on the dynamics of plasma transport, we must investigate the properties of their induced fluxes. The relative phase between density and potential fluctuations could be such that the induced particle flux does not share the self-similarity properties. The problem with studying fluxes is the scarcity of experimental measurements. Flux measurements for core plasmas are practically nonexistent. At the plasma edge, the turbulence-induced particle flux can be inferred from the simultaneous measurement of the density and potential fluctuations. By measuring the density fluctuations at one point in the plasma,ñ 1 ñ͑r 1 , u 1 , t͒, and the electrostatic plasma potential at two nearby positions, f 1 f 2 ͑r 1 , u 1 2 d, t͒ and f 2 f 3 ͑r 1 , u 1 1 d, t͒, the instantaneous turbulence-induced particle flux at this location can be calculated, G t ñẼ u ͞B ñ 1 ͑f 2 2 f 1 ͒͑͞2r 1 dB͒. Here, B is the magnetic field and E u is the poloidal electric field. Of course, what the Langmuir probe measures is the ion saturation current, I S~n p T e , and the floating potential, V f F 2 3T e . Therefore, the flux inferred from these measurements is not necessarily equal to the particle flux. However, measurements of the temperature fluctuations at the plasma edge in some confinement devices have shown that their relative phase is such that G t calculated from I S and V f is a good estimate of the particle flux [4,5].One of the main results of the present analysis is that the self-similarity of the electrostatic pot...

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