Control of the Stokes frequency shift in a loop stimulated-Brillouin-scattering laser

Abstract

We examine in detail the theoretical underpinnings of previous successful applications of local molecular field (LMF) theory to charged systems. LMF theory generally accounts for the averaged effects of long-ranged components of the intermolecular interactions by using an effective or restructured external field. The derivation starts from the exact Yvon-Born Green hierarchy and shows that the approximation can be very accurate when the interactions averaged over are slowly varying at characteristic nearest-neighbor distances. Application of LMF theory to Coulomb interactions alone allows for great simplifications of the governing equations. LMF theory then reduces to a single equation for a restructured electrostatic potential that satisfies Poisson's equation defined with a smoothed charge density. Because of this charge smoothing by a Gaussian of width σ , this equation may be solved more simply than the detailed simulation geometry might suggest. Proper choice of the smoothing length σ plays a major role in ensuring the accuracy of this approximation. We examine the results of a basic confinement of water between corrugated walls and justify the simple LMF equation used in a previous publication. We further generalize these results to confinements that include fixed charges in order to demonstrate the broader impact of charge smoothing by σ . The slowly varying part of the restructured electrostatic potential will be more symmetric than the local details of confinements.