Self ordering to imposed ordering of dust -- a continuous spatial phase transition experiment in MDPX

TL;DR

This work addresses how externally imposed boundary geometry interacts with magnetic-field-induced ion magnetization to alter dust ordering in a magnetized dusty plasma. Using the MDPX, the authors drive a 2D hexagonal Coulomb crystal into a 4-fold imposed ordering regime by ramping the magnetic field in the presence of a conducting mesh, and compare a uniform boundary case with an FTO-coated boundary. They quantify ordering via the pair-correlation function $g(r)$ and the characteristic spacing $\Delta_1$, relative to the mesh spacing $\delta = 1.67\,\mathrm{mm}$, identifying a transition near $B \approx 0.55$–$0.60\,\mathrm{T}$ corresponding to $H_{ion} > 0.67$. The FTO boundary suppresses imposed ordering, confirming the essential role of boundary-induced potential structures and aligning with ion-magnetization frameworks. Overall, the results demonstrate a controllable, continuous spatial phase transition in a dusty plasma and establish a measurable link between boundary conditions, mesh geometry, and ion magnetization effects.

Abstract

Previous experiments conducted in the Magnetized Dusty Plasma eXperiment (MDPX) revealed an intriguing phenomenon first referred to as imposed ordering. This occurs when micron-sized dust particles become aligned with the geometry of a conducting mesh placed above the dust (at a distance much larger than the plasma Debye length or the ion-neutral or electron-neutral mean free paths) in the presence of a strong magnetic field perpendicular to the mesh. In this work, results of a transition experiment are presented wherein starting from a classical two-dimensional Coulomb crystal with hexagonal symmetry in an unmagnetized plasma $(B = 0\,T)$, dust transitions to a state in which it flows along the geometry of a conducting mesh placed above it, mapping out the 4-fold symmetry of the boundary condition. It is hypothesized that beyond a certain magnetization, elongated electric potential structures emanating from the mesh drive the dust motion to reflect the mesh morphology, transitioning from a 6-fold self ordering to 4-fold imposed ordering. The various dust phases are quantified and a critical value of magnetic field is identified in the transition experiment indicating the onset of imposed ordering.

Figures (8)

• Figure 1: Experiment schematic: Dusty plasma is created in an octagonal vacuum chamber and the dust is viewed using laser sheet - camera sets. Schematic is representative and not to scale.
• Figure 2: A sectional schematic of the electrode(s) and dust along with the relevant dimensions. Schematic is representative and not to scale.
• Figure 3: A schematic showing how the FTO conducting glass is placed on the perforated sheet. Schematic is representative and not to scale.
• Figure 4: Dust behavior under the mesh at various magnetic fields. Each subpanel contains 500 image stacks (5 seconds) from the top ($x-y$) view and side ($x-z$) view. Next to the image stacks the time-averaged pair correlation functions are plotted. Error bars in the structure factors indicate small variations in time and a stability in the structure in time. $\Delta_1$ is the global maximum distance which represents the most probable inter-particle separation. (a) a two-dimensional hexagonal crystal with strong long-range ordering at $B=0\,T$; (b),(c) a rotating dust cloud with prominent motion parallel to the magnetic, with reduced long-range dust-dust correlations; (d) a state where there are weak signs of imposed ordering in the image stacks and little to no dust-dust correlations; (e),(f) imposed ordered dust phase where the image stacks as well as the structure factors show ordering that matches the mesh geometry.
• Figure 5: Image stacks of dust at magnetic fields $B>0.65\,T$. After significant particle loss for $B=0.65\,T$, more dust is added into the system and some of the particles get trapped for a long time in a 4-fold symmetry (as seen from the top image stacks), showing imposed ordering. The rest of the short lived cloud also exhibits periodicity along $\hat{x}$ that matches the mesh spacing.