Semiempirical zero-dimensional approach for the estimation of beam features from plasma parameters in proton sources

Beam intensity, proton fraction, and beam emittance represent the most important characteristics of a beam extracted by a proton source. Beam parameters are strongly related to the parameters of the plasma from which the beam is extracted. The recent improvement of plasma diagnostics devoted to compact ion sources, and, in particular, the development of optical emission spectroscopy, allows an ever more reliable measurement of plasma parameters, also during source operations. In this paper, a zero-dimensional approach able to estimate the beam intensity and the ion fraction from plasma parameters in a proton source is introduced. The model is based on a simplified solution of the balance equation system in a hydrogen plasma achieved by including the electron density, the electron temperature, and the relative neutral abundance ratio H/H_{2} within the equations. This approach permits one to reduce the balance equation system to four equations in four unknowns, namely, the H^{+}, H_{2}^{+}, and H_{3}^{+} density and the confinement time. The balance equation system is solved by means of a homemade numerical code. The model has been applied to the beam generated by the Proton Source for the European Spallation Source (PS-ESS), during its commissioning at Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Sud in Catania. The extracted current and ion fraction estimated by this approach have been compared with the experimental results obtained by the PS-ESS beam diagnostics. The proton confinement time estimated by this approach has been compared with the results of a theoretical model based on a diffusion model. The comparison demonstrates that the model has achieved a surprising capability of estimation. The paper discusses the main characteristics of the zero-dimensional approach together with its main advantages and limits. The perspectives for further improvement of the model are also discussed