Exponential Frequency Spectrum in Magnetized Plasmas

Measurements of a magnetized plasma with a controlled electron temperature gradient show the development of a broadband spectrum of density and temperature fluctuations having an exponential frequency dependence at frequencies below the ion cyclotron frequency. The origin of the exponential frequency behavior is traced to temporal pulses of Lorentzian shape. Similar exponential frequency spectra are also found in limiter-edge plasma turbulence associated with blob transport. This finding suggests a universal feature of magnetized plasma turbulence leading to nondiffusive, cross-field transport, namely, the presence of Lorentzian shaped pulses.

Figure 1

(a) Power spectra of $I_{\mathrm{sat}}$ fluctuations (black trace) at $r=3\mathrm{mm}$ from the filament center displaying both an exponential character and strong coherent modes. The red or dark gray curve is a numerical simulation of an ensemble of randomly distributed Lorentzian pulses, dashed blue lines are the same exponential fit to the data. (b) Time evolution of single-shot ion saturation current (black curve) and filtered signal (red curve) showing pulses.

Figure 2

Unfiltered ion saturation current highlighting a single pulse. Inset: Comparison of measured pulse (black curve) to a model Lorentzian pulse (red dashed trace).

Figure 3

Time evolution of power spectra of ion saturation current showing transition from coherent mode regime ($t-t_{\mathrm{beam}}\le 5.5\mathrm{ms}$) to broadband fluctuations displaying an exponential spectrum. Frequency is displayed on the left axis in terms of both absolute (black) and normalized (red or dark gray) units. The white trace near the top is a single-shot ion saturation current showing Lorentzian pulses when the exponential spectrum develops.

Figure 4

Power spectra of ion saturation current in limiter-edge experiment display exponential behavior in frequency at different radial positions.

Figure 5

Ion saturation current (solid black curve) and Lorentzian fit (dashed red curve) from the limiter-edge experiment.