Criterion for bulk behavior of a Yukawa disk

A Yukawa disk is a two-dimensional system of n particles interacting through a Yukawa potential (i.e., a screened Coulomb or Debye potential) with Debye length λ and confined in an isotropic parabolic well where the single-particle oscillation frequency is ω0. One example of a Yukawa disk is a two-dimensional complex (dusty) plasma. The emergence of bulk (macroscopic) behavior in a strongly coupled Yukawa disk is studied by considering the dependence of the normalized, squared breathing frequency ωbr2/ω02 (i.e., the bulk modulus) on n, λ, the disk radius R0, and the nearest-neighbor distance a. An analytical expression for ωbr2/ω02 is derived for the bulk limit, R0>>λ, with a/λ finite. In the plasma regime a < or approx. λ, so that each particle interacts with many other particles, ωbr2/ω02≅4 independent of a/λ. In the nearest-neighbor regime a > or approx. λ, short-range interactions dominate and ωbr2/ω02∼a/λ. Computational solutions of the model for n=100-3200 particles approach the theoretical bulk limit as n increases. Solutions with n=3200 and a/λ between 0.25 and 0.5 are found to give the best approximation to an unbounded plasma