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A stochastic model for intermittent fluctuations due to a super-position ofuncorrelated Lorentzian pulses is presented. For constant pulse duration, thisis shown to result in an exponential power spectral density for the stationaryprocess. A random distribution of pulse durations modifies the frequencyspectrum and several examples are shown to result in power law spectra. Thedistribution of pulse durations does not influence the characteristic functionand thus neither the moments nor the probability density function for therandom variable. It is demonstrated that the fluctuations are intrinsicallyintermittent through a large excess kurtosis moment in the limit of weak pulseoverlap. These results allow to estimate the basic properties of fluctuationsfrom measurement data and describe the diversity of frequency spectra reportedfrom measurements in magnetized plasmas.

Power law spectra and intermittent fluctuations due to uncorrelated Lorentzian pulses