Spectral analysis of forced turbulence in a non-neutral plasma

Abstract

The paper investigates the dynamics of magnetized non-neutral (electron) plasmas subjected to external electric field perturbations. A two-dimensional (2-D) particle-in-cell code is effectively exploited to model this system with a special attention to the role that non-axisymmetric, multipolar radio frequency (RF) drives applied to the cylindrical (circular) boundary play on the insurgence of azimuthal instabilities and the subsequent formation of coherent structures preventing the relaxation to a fully developed turbulent state, when the RF fields are chosen in the frequency range of the low-order fluid modes themselves. The isomorphism of such system with a 2-D inviscid incompressible fluid offers an insight into the details of forced 2-D fluid turbulence. The choice of different initial density (i.e. fluid vorticity) distributions allows for a selection of conditions where different levels of turbulence and intermittency are expected and a range of final states is achieved. Integral and spectral quantities of interest are computed along the flow using a multiresolution analysis based on a wavelet decomposition of both enstrophy and energy 2-D maps. The analysis of a variety of cases shows that the qualitative features of turbulent relaxation are similar in conditions of both free and forced evolution; at the same time, fine details of the flow beyond the self-similarity turbulence properties are highlighted in particular in the formation of structures and their timing, where the influence of the initial conditions and the effect of the external forcing can be distinguished.

Coherent structures and turbulence evolution in magnetized non-neutral plasmas

“…3. Despite the differences in the initial configuration and in the details of the first stage of the evolution, the coherent parts show almost the same time variations for all cases, in accordance with previous observations [54]. On the other hand, the effect of the different initial configurations can still be identified from the incoherent parts.…”

“…The initial configurations are a 3-turn clockwise (cw) spiral, a 4-turn cw spiral, a 3-turn counterclockwise (ccw) spiral and a 4-turn ccw spiral, respectively. The diocotron instability stage and the vortex merger events for these cases turn out to be quite different, but the effect of the drive is manifested through the generation of a square-shaped turbulent background in all cases, consistently with previous investigations [54]. The evolution of the total, coherent and incoherent enstrophy is shown in Fig.…”

“…Here, the conclusions of Refs. [51,52,53,54] are briefly reviewed, and results of new simulations and of the relevant statistical analysis are presented, that corroborate the previous findings. The attention is focused on the role on the late evolution of the system played by initial density fluctuations under the effect of a selected choice of multipolar RF drives, and by different initial conditions in the presence of a given external forcing.…”

“…[51,52] in the case of free evolution and in Refs. [53,54] in the case of forced turbulence, respectively. Both annular and spiral distributions are of experimental interest.…”

“…The analysis has been extended to higher multipoles and to spiral distributions in Ref. [54] with the aim to observe possible effects at the spatial scales of the involved unstable modes. These studies also present an experimental interest.…”