Determination of hydrogen cluster velocities and comparison with numerical calculations

TL;DR

This paper measures hydrogen cluster velocities in jet targets and develops a numerical model to accurately predict these velocities, aiding in the precise determination of target densities in storage ring experiments.

Contribution

It introduces a new method combining measurements and modeling to predict hydrogen cluster velocities with about 5% accuracy.

Findings

Measured hydrogen cluster velocities over a range of conditions.

Developed a numerical model based on van der Waals gas.

Achieved velocity predictions with approximately 5% accuracy.

Abstract

The use of powerful hydrogen cluster jet targets in storage ring experiments led to the need of precise data on the mean cluster velocity as function of the stagnation temperature and pressure for the determination of the volume density of the target beams. For this purpose a large data set of hydrogen cluster velocity distributions and mean velocities was measured at a high density hydrogen cluster jet target using a trumpet shaped nozzle. The measurements have been performed at pressures above and below the critical pressure and for a broad range of temperatures relevant for target operation, e.g., at storage ring experiments. The used experimental method is described which allows for the velocity measurement of single clusters using a time-of-flight technique. Since this method is rather time-consuming and these measurements are typically interfering negatively with storage ring experiments, a method for a precise calculation of these mean velocities was needed. For this, the determined mean cluster velocities are compared with model calculations based on an isentropic one-dimensional van der Waals gas. Based on the obtained data and the presented numerical calculations, a new method has been developed which allows to predict the mean cluster velocities with an accuracy of about 5%. For this two cut-off parameters defining positions inside the nozzle are introduced, which can be determined for a given nozzle by only two velocity measurements.