Is the compressibility positive or negative in a strongly-coupled dusty plasma?

In dusty plasmas, dust particles are often strongly coupled with a large Coulomb coupling parameter $\Gamma$, while the electrons and ions that share the same volume are weakly coupled. In most substances, compressibility $\beta$ must be positive; otherwise there would be an explosive instability. In a multicomponent plasma, however, one could entertain the idea that $\beta$ for a single strongly coupled component could be negative, provided that the restoring force from charge separation overwhelms the destabilizing effect. Indeed, the compressibility for a strongly-coupled dust component is assumed to be negative in three theories we identified in the literature for dust acoustic waves. These theories use a multi-fluid model, with an OCP (one component plasma) or Yukawa-OCP approach for the dust fluid. We performed dusty plasma experiments designed to determine the value of the inverse compressibility $\beta^{-1}$, and in particular its sign. We fit an experimentally measured dispersion relation to theory, with $\beta^{-1}$ as a free parameter, taking into account the systematic errors in the experiment and model. We find that $\beta^{-1}$ is either positive, or it has a negligibly small negative value, which is not in agreement with the assumptions of the OCP-based theories.