The equivalent diameter of conical nozzle in Hagena scaling laws

Abstract

The cluster size is an important parameter in the study on the interaction of intense laser pulse with cluster jet produced by the gas adiabatic expansion through a nozzle into vacuum. The Hagena scaling law is usually used to estimate the average cluster size. However, there is the deviation of average cluster size from the prediction by the scaling law in the case that the conical nozzle is used at the high gas backing pressure. In this work, firstly the equivalent diameter of conical nozzle is re-calculated in detail, and then the relation between d(eq) and the radial dimension of the cluster jet is obtained. As an example, the images of Rayleigh scattering light by argon cluster jet at different backing pressures are recorded to investigate the dimensions of cluster jet. And then the corresponding theoretical dimensions based on the idealized straight streamline model in the scaling law are compared with the experimental dimensions. It is found that the experimental dimension is larger than the theoretical one, and is related to the gas backing pressure. This under-estimation of theoretical cluster jet dimension leads to the over-estimation of the equivalent diameter of conical nozzle which is responsible for the cluster size deviation in Hagena scaling laws.