Rigid and differential plasma crystal rotation induced by magnetic fields

TLDR

Plasma crystals in an RF discharge sheath rotate when exposed to a vertical magnetic field. The study develops a simple analytical model to explain how plasma crystal rotation depends on confining potential and discharge conditions, and proposes further quantitative refinement. The model incorporates electrostatic, ion drag, neutral drag, and interparticle forces, reconstructs the confining potential for rigid-body rotation, and uses radial rotation data to estimate shear stresses, elastic modulus, and viscosity. Experiments reveal rigid-body and sheared rotations, with direction reversal at high voltage, and the critical shear stress for melting yields estimates of the crystal’s elastic modulus and elastic viscosity contribution.

Abstract

Observations show that plasma crystals, suspended in the sheath of a radio-frequency discharge, rotate under the influence of a vertical magnetic field. Depending on the discharge conditions, two different cases are observed: a rigid-body rotation (all the particles move with a constant angular velocity) and sheared rotation (the angular velocity of particles has a radial distribution). When the discharge voltage is increased sufficiently, the particles may even reverse their direction of motion. A simple analytical model is used to explain qualitatively the mechanism of the observed particle motion and its dependence on the confining potential and discharge conditions. The model takes into account electrostatic, ion drag, neutral drag, and effective interparticle interaction forces. For the special case of rigid-body rotation, the confining potential is reconstructed. Using data for the radial dependence of particle rotation velocity, the shear stresses are estimated. The critical shear stress at which shear-induced melting occurs is used to roughly estimate the shear elastic modulus of the plasma crystal. The latter is also used to estimate the viscosity contribution due to elasticity in the plasma liquid. Further development is suggested in order to quantitatively implement these ideas.