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 $\mathrm{H}/{\mathrm{H}}_2$ within the equations. This approach permits one to reduce the balance equation system to four equations in four unknowns, namely, the ${\mathrm{H}}^{+}$, ${\mathrm{H}}_2^{+}$, and ${\mathrm{H}}_3^{+}$ 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.

中文翻译：

---

利用半经验零维方法从质子源中的等离子体参数估算射束特征

束强度，质子分数和束发射率代表质子源提取的束的最重要特征。束参数与从中提取束的等离子体的参数密切相关。致力于紧凑型离子源的等离子体诊断技术的最新改进，尤其是光发射光谱学的发展，使得在离子源操作期间，等离子体参数的测量变得更加可靠。本文介绍了一种能够从质子源中的等离子体参数估算射束强度和离子分数的零维方法。该模型基于氢等离子体中平衡方程组的简化解，该方程包括电子密度，电子温度和相对中性相对丰度比$\mathrm{H}/{\mathrm{H}}_2$在等式中。这种方法允许将平衡方程组简化为四个未知数中的四个方程，即${\mathrm{H}}^{+}$， ${\mathrm{H}}_2^{+}$和 ${\mathrm{H}}_3^{+}$密度和封闭时间。平衡方程组通过自制数字代码求解。该模型已在质子源为欧洲散裂源（PS-ESS）生成的光束中应用，该光束在卡塔尼亚的Nazionali del Sud实验室的Izituto Nazionale di Fisica Nucleare试运行期间。通过这种方法估算的提取电流和离子分数已与PS-ESS束诊断获得的实验结果进行了比较。通过这种方法估算的质子约束时间已与基于扩散模型的理论模型的结果进行了比较。比较表明，该模型已经实现了令人惊讶的估计能力。本文讨论了零维方法的主要特征及其主要优点和局限性。