Turbulent Cascade in Vortex Dynamics of Magnetized Pure Electron Plasmas

Elementary processes of two-dimensional (2D) turbulence has been examined by extensive analyses of fine-scale structures in the density distribution of a magnetized pure electron plasma that evolves from an unstable initial state to a single-peaked stable distribution through successive mergers of vortex patches. The observed vortex dynamics in the real space corresponds to the spectral dynamics analyzed in the wave-number (k) space. Along with the merging process among patches, the energy spectrum E(k) broadens upward and its shape shows a power-law scaling k-α with α>3 in a wide wave-number region above kinj corresponding to the size of the first generated patches. From the energy and enstrophy transfer rate evaluated from the time-resolved spectra, it has been observed that the enstrophy cascades at a constant transfer rate in the region k>3kinj, while the energy is transferred downward at k<kinj. This spectral dynamics is qualitatively consistent with the theoretical picture of 2D turbulence with discrepancies that the power index of E(k) is larger than the theoretical prediction of α = 3 and the enstrophy transfer rate is almost zero around kinj reflecting the effect of coherent vortices.