Cascade process of two-dimensional turbulence observed in magnetized pure electron plasmas

Elementary dynamics of two-dimensional (2D) turbulence are examined experimentally by extensive analyses of fine-scale structures in the density distribution of a magnetized pure electron plasma. We observe the relaxation process of the electron plasma involving stochastic mergers of vortex patches generated by the instability in terms of a spatial pattern of vorticity, and compare with the theoretical picture of the 2D turbulence described in the wave-number (k) space. In the merging process among vortex patches, the energy spectrum shows a algebraic dependence of k−α above the kin j corresponding to the size of the first generated patches. The energy and enstrophy tranfer rate show the characteristic features of the cascade process predicted by the theory, i.e., in the fine-length scale of k > kin j the enstrophy cascades upward at a constant transfer rate, and in the region k < kin j the energy transfers down to lower k. Through time-averaging the evolution of the spectra, we derive the spectrum in the stationary turbulence sustained by the successive input of vortices due to the instability. The resultant spectrum is qualitatively consistent with the 2D turbulence theory, but also shows the discrepancies that the power index of the energy spectrum is larger than the theoretical prediction of α = 3 and that the enstrophy transfer rate is almost zero around k ≈ kin j reflecting the effect of coherent vortices.