Relationship between the durations of jumps in solar wind time series and the frequency of the spectral break

Several physically motivated examples of stochastic processes that exhibit discontinuous jumps at random times are used to show that if the discontinuous jumps are replaced by continuous or smooth transitions with an average duration Δ t , then the power spectral density of the process develops a high‐frequency spectral break at a frequency of order ω b = π /Δ t . Conversely, if the spectrum of the original process is altered by imposing a high‐frequency spectral break, as may be accomplished by filtering with a low‐pass filter of some kind, then the discontinuous jumps in the original signal are replaced by continuous jumps having a duration of magnitude Δ t = π / ω b , where ω b is the break frequency of the altered spectrum. These results suggest that for any stochastic process containing randomly occurring jumps in the time domain and a high‐frequency spectral break in the spectral domain with break frequency ω b , the average durations of the jumps are of order Δ t = π / ω b . This result is closely connected with the sampling theorem and the uncertainty principle for Fourier transform pairs and demonstrates that the physical processes responsible for the dissipation of solar wind turbulence also determine the thicknesses of the strongest current sheets in the solar wind.