Charge and Debye length measurements in two-dimensional Debye clusters using thermal fluctuations

A two-dimensional Debye cluster is a system of $n$ identical particles confined in a two-dimensional parabolic well and interacting through a screened Coulomb force (i.e., a Debye-H\"uckel or Yukawa potential) with a Debye length $\lambda$. In the strong-coupling regime, the particles exhibit small-amplitude motions about their equilibrium positions. These thermal oscillations are projected onto the center-of-mass and breathing modes to determine resonance curves from which the natural mode frequencies are found. The ratio of the breathing frequency to the center-of-mass frequency is then compared with theory to determine the Debye length and the average particle charge. Experiments were performed for $n=3$ to 63 particles with $9~\mu\rm m$-diameter particles at a neutral argon pressure of 13.6 mtorr and for $\approx9$ W of rf power. The Debye length increases slightly and the absolute value of the charge decreases slightly as the number of particles increases.