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

Abstract

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.

Kinetic theory of point vortex systems from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy

“…The system considered by Chavanis is closely related to the system of non-neutral plasmas in the Malmberg trap [18,19,20,21,22,23,24]. The dynamics of the non-neutral plasma in the Malmberg trap is described by the 2D Euler equation in a circular domain, using the guiding center approximation.…”

“…Thus, if we are interested in non-neutral plasma in the experimental situation, as an idealized model, we should consider a point vortex system in a circular domain. From experiments on non-neutral plasmas, many interesting properties of vortex dynamics of the 2D Euler equation are now known [18,19,20,21,22,23,24]: (1) Diocotron instability (i.e., in other words, Kelvin-Helmholtz instability), (2) Violent relaxation, (3) Slow decay, (4) Vortex crystals, and (5) Merger of vortices. As a theoretical aspect, recently the slow decay was numerically analyzed using the point vortex system [30,31,32].…”

Numerical Simulation of Vortex Crystals and Merging inN-Point Vortex Systems with Circular Boundary

“…In the experiment by Sanpei et al, 15 it is found that three clumps are accelerated to form an equilateral triangular configuration by interaction with continuous low-level background vorticity distribution. Since three clumps make a unit cell of vortex crystals, it is regarded that this process is a fundamental process of forming vortex crystals.…”

“…(10)(11)(12)(13)(14)(15) that the plots on the Poincaré section are lying on the circle of which radius is 1/2 and at the origin. When the value of E changes from E r slightly for the same value of I, the region of the plots becomes concentric rings as Fig.2 …”

“…In the recent experiment, 15 it is observed that three clumps arrayed on a straight line form an equilateral triangular lattice under certain conditions of the background. When the…”