Turbulent cascade in vortex dynamics of magnetized pure electron plasmas

Abstract

Elementary processes in free-decaying two-dimensional (2D) turbulence are examined by extensive analyses of fine structures in the density distribution of a magnetized pure electron plasma that is linearly unstable with the initial ring-shaped profile, deforms nonlinearly into patches of vortices, and relaxes into a single-peaked stable distribution via successive mergers among the patches. The stochastic dynamics of the decreasing number of vortices in the real space correspond to the time evolution of energy spectra E(k) in the wave number (k) space that the energy transfers down to lower k while the upward-spreading tails of the spectra fit to the power-law (proportional k(-alpha)) with alpha > 3. The transfer rates, epsilon(k) and eta(k) in energy and enstrophy spaces, evaluated from the time-resolved k -spectra demonstrate characteristic features of the 2D turbulence, i.e., epsilon(k) is negative and deepest below the k(inj) corresponding to the size of the first-generated patches, and eta(k) increases from zero to a constant value at k > k(inj). By averaging the time-dependent spectra of E(k), epsilon(k), and eta(k), constructions are carried out for the spectra in a stationary turbulence that is sustained by the continuous generation of vortices due to the instability and dissipation at high k. The spectra are qualitatively consistent with the 2D turbulence theory with discrepancies including that alpha approximately 4.4 and that the enstrophy transfer rate is almost zero around k = k(inj) reflecting the contribution from the coherent vortices.