Power law spectra and intermittent fluctuations due to uncorrelated Lorentzian pulses

TL;DR

This paper presents a stochastic model explaining how superimposed uncorrelated Lorentzian pulses generate various spectral behaviors, including power laws, and characterizes their intermittency and statistical properties relevant to plasma fluctuations.

Contribution

It introduces a model linking pulse duration distributions to spectral shapes, revealing how intermittency and power law spectra emerge from uncorrelated Lorentzian pulses.

Findings

Constant pulse duration yields exponential spectra.

Distributed pulse durations produce power law spectra.

Fluctuations exhibit intrinsic intermittency with high kurtosis.

Abstract

A stochastic model for intermittent fluctuations due to a super-position of uncorrelated Lorentzian pulses is presented. For constant pulse duration, this is shown to result in an exponential power spectral density for the stationary process. A random distribution of pulse durations modifies the frequency spectrum and several examples are shown to result in power law spectra. The distribution of pulse durations does not influence the characteristic function and thus neither the moments nor the probability density function for the random variable. It is demonstrated that the fluctuations are intrinsically intermittent through a large excess kurtosis moment in the limit of weak pulse overlap. These results allow to estimate the basic properties of fluctuations from measurement data and describe the diversity of frequency spectra reported from measurements in magnetized plasmas.