Effect of initial conditions on electron–plasma turbulence: a multiresolution analysis

Abstract

The transverse dynamics of a pure electron plasma confined in a Penning–Malmberg trap is investigated, taking advantage of two-dimensional particle-in-cell numerical simulations. The evolution of the electron plasma turbulence is studied by means of a wavelet-based multiresolution analysis. In particular, a modified recursive denoising algorithm is developed to separate coherent and incoherent (not necessarily homogeneous) components of the flow. A set of simulations have been carried out changing systematically the radii of an initial annular density distribution of the electrons. The results of the multiresolution analysis indicate that the initial density configuration may have a considerable effect on the evolution of turbulence. Even very small initial density fluctuations can lead to quite different final states, especially in the presence of multiple active diocotron modes characterized by similar growth rates.

Coherent structures and turbulence evolution in magnetized non-neutral plasmas

“…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.…”

“…In particular, in the case of the free evolution of annular initial distributions a relation between the initial parameters of the ring and the time required to achieve a state of fully-developed turbulence has been evidenced [51]. These studies highlighted also the strong influence on the subsequent plasma evolution of density fluctuations introduced by the random number generator used to define the initial particle distribution.…”

“…In order to identify the parameters playing a major role in the early dynamics of the system, the results of numerical simulations of the 2D electron plasma dynamics starting from particular classes of initial conditions (specifically, annular and spiral distributions) have been analyzed in Refs. [51,52] in the case of free evolution and in Refs. [53,54] in the case of forced turbulence, respectively.…”

“…, where H denotes the Heaviside step function, and r − and r + are the inner and outer radius of the ring, respectively, with r − /R w = 0.3724, r + /R w = 0.46. The following parameters are fixed in all simulations: n 0 = 10 7 cm −3 , R w = 2 cm, and B = 1 T [67,68,51]. In addition, the final time is 4 ms, and the time step is 10 −7 s.…”

“…Even when using the same electron trapping time and the same injection parameters, uncontrolled inhomogeneities are present also in the experiments due to small variations of the conditions of the electron source or of the residual gas pressure, so that, for instance, the formation of vortex crystals and/or the relevant number of vortices turn out to strongly depend on the initial conditions [45,10]. The irreproducibility of the final state has been linked to the presence of different unstable diocotron modes, characterized by similar growth rates but slightly different energy contents determined by the fine details of the initial particle distribution [51].…”