Here the characteristic length is defined using the longitudinal frequency ω$_{x}$ . The dimensionless potential energy is then where U 0 is the characteristic potential energy. Equilibrium configurations { η$_{i}$, ξ$_{i}$ } of the model [Eq. (5)] depend on three parameters: n , κ and α $^{2}$. Here κ is the Debye shielding parameter and κ = 0 corresponds to an unshielded Coulomb interaction. The well anisotropy parameter is α $^{2}$. We assume ω$_{y}$ ≥ ω$_{x}$ or α 2 ≥ 1. Straight line configurations y$_{i}$ = η$_{i}$ = 0 then lie in the x (longitudinal) direction and are independent of α $^{2}$. An equilibrium configuration { ξ$_{i}$, η$_{i}$ } can be compared to an experimentally measured configuration { x$_{i}$, y$_{i}$ } by multiplying each coordinate by r 0 . Within the context of this model [Eq. (5)], abrupt 1D to 2D transitions [10, 16] are predicted to occur for critical values of the three parameters n , κ and α 2 due to a zigzag instability. This has been confirmed experimentally as n was varied by Melzer [11] and Sheridan and Wells [16]. Melzer [11] also observed a zigzag transition as the neutral gas pressure was changed, which presumably changed the plasma density and therefore both κ and α $^{2}$. Sheridan and Wells [16] confirmed that the zigzag transition caused by increasing n in small clusters behaves as a continuous phase transition between 1D and 2D states, where the cluster width near the transition obeys a power law. Using the model of Eq. (5), they also predicted [16] that the zigzag transition in small clusters exhibits power law behavior as either κ or α 2 is varied. Piacente, et al. [17] reached a similar conclusion from a computational study of unbounded Yukawa systems ( n → ∞ ) with a transverse parabolic well and longitudinal periodic boundaries. Structural transitions due to changes in κ or α 2 have not been characterized experimentally. In this work we investigate the transitions a Yukawa cluster (i.e., a small dusty plasma) undergoes as the well anisotropy α 2 is varied. We use a novel experimental method in which the physical geometry of the confining potential well is changed without disrupting the plasma discharge. The discharge parameters are nearly constant, so that the Debye shielding parameter κ is also nearly constant. The well anisotropy is accurately determined using measured center-of-mass frequencies for the dusty plasma. As predicted [16], the transverse 3 r$_{0}$ = ( 2 mω 2 x q 2 4 πϵ 0 ) 1 / 3 (4) U U 0 = n ∑ i =1 ( ξ 2 i + α $^{2}$η2 i ) + n ∑ i =1 n ∑ j>i e − κρ$_{ij}$ ρ$_{ij}$ , (5)