Experimental dynamics of a vortex within a vortex

Unprecedented confinement time of electron plasmas with a purely toroidal magnetic field in SMARTEX-C

Confinement time of electron plasmas trapped using a purely toroidal magnetic field has been found to exceed [Formula: see text] in a small aspect ratio ([Formula: see text], [Formula: see text] and a are device major and minor radius, respectively), partial torus. It improves upon the previously reported confinement time by nearly two orders of magnitude. Lifetime is estimated from the frequency scaling of the linear diocotron mode launched from sections of the wall, that are also used for mode diagnostics. Confinement improves as neutral pressures are reduced to [Formula: see text] in the presence of a steady state magnetic field of 200 Gauss ([Formula: see text] with droop [Formula: see text]) at [Formula: see text] electron injection energies. With reduced pressures the role of (ion driven) instability diminishes and loss mechanisms resulting from elastic electron-neutral (e-n) and the ubiquitous electron-electron (e-e) scattering seem to play an important role which suggests low electron temperatures. The contribution to electron population resulting from the ionization of background neutral gas at these temperatures and pressures are expected to be insignificant and is corroborated in our experiments.

A transformation between stationary point vortex equilibria

A new transformation between stationary point vortex equilibria in the unbounded plane is presented. Given a point vortex equilibrium involving only vortices with negative circulation normalized to -1 and vortices with positive circulations that are either integers or half-integers, the transformation produces a new equilibrium with a free complex parameter that appears as an integration constant. When iterated the transformation can produce infinite hierarchies of equilibria, or finite sequences that terminate after a finite number of iterations, each iteration generating equilibria with increasing numbers of point vortices and free parameters. In particular, starting from an isolated point vortex as a seed equilibrium, we recover two known infinite hierarchies of equilibria corresponding to the Adler-Moser polynomials and a class of polynomials found, using very different methods, by Loutsenko (Loutsenko 2004 J. Phys. A: Math. Gen. 37, 1309-1321 (doi:10.1088/0305-4470/37/4/017)). For the latter polynomials, the existence of such a transformation appears to be new. The new transformation, therefore, unifies a wide range of disparate results in the literature on point vortex equilibria.

A transformation between stationary point vortex equilibria

A new transformation between stationary point vortex equilibria in the unbounded plane is presented. Given a point vortex equilibrium involving only vortices with negative circulation normalized to -1 and vortices with positive circulations that are either integers or half-integers, the transformation produces a new equilibrium with a free complex parameter that appears as an integration constant. When iterated the transformation can produce infinite hierarchies of equilibria, or finite sequences that terminate after a finite number of iterations, each iteration generating equilibria with increasing numbers of point vortices and free parameters. In particular, starting from an isolated point vortex as a seed equilibrium, we recover two known infinite hierarchies of equilibria corresponding to the Adler-Moser polynomials and a class of polynomials found, using very different methods, by Loutsenko (Loutsenko 2004 J. Phys. A: Math. Gen. 37, 1309-1321 (doi:10.1088/0305-4470/37/4/017)). For the latter polynomials, the existence of such a transformation appears to be new. The new transformation, therefore, unifies a wide range of disparate results in the literature on point vortex equilibria.

Formation of a vortex crystal cell assisted by a background vorticity distribution

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.

Nonuniform non-neutral plasma in a trap

An analytical model for breathing oscillations in a nonuniform non-neutral plasma slab is developed. The plasma is relatively small and warm with the smallest dimension only of several Debye lengths. Nonuniformity in the equilibrium results in a frequency shift associated with pressure and boundary effects. The plasma size and temperature, being related to the frequency shift, can therefore be evaluated from frequency measurements. In particular, for small nonuniform plasmas the frequency of the breathing mode is twice that predicted by the cold fluid theory. Nonlinear oscillations are also considered and the pressure is shown to have an important effect on the dynamics. Analytical solutions for linear and nonlinear oscillations are obtained and compared with that from one-dimensional particle-in-cell simulations. Good agreement is found.

Measurements of viscosity in pure-electron plasmas

Measurements of the viscosity in quiescent magnetized pure-electron plasmas are up to 10(8) times larger than predicted by classical collisional theory. This strong viscosity is due to long-range " E x B drift collisions" between electrons separated by up to a Debye length. Recent theories of long-range collisions show order-of-magnitude agreement with the measurements, but do not give the observed dependence on the plasma column length. A simple empirical scaling law fits the length and magnetic field dependence surprisingly well.