Power-law energy spectrum and orbital stochasticity

The power-law energy distributions are observed in space and fusion plasmas. The power law decay of the two-time velocity correlation function and the corresponding frequency spectrum of the correlation function are shown to be related to the power law distribution of the time interval of acceleration, which produces a power-law energy distribution. In particular, the two time correlation function, the distribution of acceleration duration, namely the distribution of the trapping time of the quasi-trapped orbits in the vicinity of the magnetic null such as the geomagnetic tail configurations are shown to produce a power law energy distribution function. The statistical property is applicable under conditions given here to the energy spectra of cosmic rays, electrons in laser-plasma interaction and the radio-frequency heated confined plasmas. 13 refs., 4 figs