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Wavelet analysis is applied to examine two-dimensional (2D) structures of pure electron plasma density distribution observed in a free-decaying turbulent stage starting from an unstable distribution. In contrast to the traditional Fourier analysis, the simultaneous resolution of the structures in terms of the physical coordinates and length scales (or wave numbers) allows us to discriminate instrumental dot noises without generating spurious high wave-number components that tend to distort the energy and enstrophy spectra. With this analysis at each time segment, the following features are clearly observed: Intermittency in the structures of electron density distribution, that is equivalent to the 2D vorticity distribution, is clearly demonstrated in terms of the scale-resolved kurtosis. The upward cascade of the enstrophy in the wave-number space is associated with the development of vortex filamentation in the physical space. Controlled discrimination of the coherent component in terms of the wavelet coefficients of the observed density distribution indicates significant contribution of persisting coherent vortices in steepening the energy spectra of the 2D turbulence far above the theoretically predicted power law of k(-3).

Systematic examinations are carried out experimentally about the contribution of background vorticity distributions (BGVD's) to the spontaneous formation and decay of ordered arrays (vortex crystals) composed of strong vortices (clumps) by using a pure-electron plasma. It is found that the BGVD level needs to be higher for an increasing number of clumps to form vortex crystals and that the number of the clumps constituting the crystal decreases in time as proportional to gamma lnt in contrast to proportional to t (-xi) with xi approximately 1 as accepted well in turbulence models. The decay rate gamma increases with the BGVD level. The observed configurations of the clumps cover the theoretically predicted catalogue of vortex arrays in superfluid helium, suggesting a possible relaxation path of the crystal states.

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.

Dynamics of two-sign point vortices in two-dimensional circular boundary is examined by numerical simulations with MDGRAPE-2. The vortex system is characterized by the inverse temperature beta as determined from the density of states of the microcanonical ensemble of numerically generated 10(7) states. The massive simulation shows that different configurations appear in the time-asymptotic state depending on the sign of beta. Condensation of the same-sign vortices is observed when beta<0, while the both-sign vortices tend to be uniformly neutralized when beta>0. During the condensation, a part of the vortices gains energy to form clumps (patches), and the other part of the vortices loses energy to keep the total energy constant and mixes with vortices of the other sign. This observation demonstrates a characteristic feature of negative beta states that the system energy concentrates into the clumps of the same-sign vortices.

A vortex crystal is a quasistationary, symmetric array of intense vortices (clumps). A low level of background vorticity is experimentally observed to assist three clumps in forming an equilateral triangle starting from initial positions on a linear array. The triangle constitutes a unit cell of a crystal in a many-vortex system. The background vortex curbs the orbital motion of the clumps with unequal strengths to arrest them at the vertices of an equilateral triangle by wrapping them with different sized belts of depleted vorticity (ring holes). We characterize the contributions of a low-level background vorticity distribution on the formation of ordered states of clumps in light of the experimental results and existing theories.

Dynamics of a point vortex in interaction with a broad profile of background vorticity is studied experimentally by using an electron plasma. The observed motion of the vortex compares favorably with a recently proposed theoretical model [D. A. Schecter and D. H. E. Dubin, Phys. Rev. Lett. 83, 2191 (1999)]. Perturbations in the background distribution in the wake of the spiral orbit of the vortex amount to several tens of percent and are considered to be a major reason for deviations of the observation from the linear theoretical model.

A small rail gun with a barium electrode can be operated at higher than one shot per second to produce more than 2x10(16) barium ions with energy 10-20 eV. The operation of the gun takes advantage of the external magnetic field for cross-field plasma injection into a trap. Up to 7 kG of the magnetic field examined, the gun performance improves with the increased magnetic field strength.