The electron density is a key parameter to characterize any plasma. Most of the plasma applications and research in the area of low-temperature plasmas (LTPs) are based on the accurate estimations of plasma density and plasma temperature. The conventional methods for electron density measurements offer axial and radial profiles for any given linear LTP device. These methods have major disadvantages of operational range (not very wide), cumbersome instrumentation, and complicated data analysis procedures. The article proposes a Deep Learning (DL) assisted microwave-plasma interaction-based non-invasive strategy, which can be used as a new alternative approach to address some of the challenges associated with existing plasma density measurement techniques. The electric field pattern due to microwave scattering from plasma is utilized to estimate the density profile. The proof of concept is tested for a simulated training data set comprising a low-temperature, unmagnetized, collisional plasma. Different types of symmetric (Gaussian-shaped) and asymmetrical density profiles, in the range $10^{16}-10^{19}$ m$^{-3}$, addressing a range of experimental configurations have been considered in our study. Real-life experimental issues such as the presence of noise and the amount of measured data (dense vs sparse) have been taken into consideration while preparing the synthetic training data-sets. The DL-based technique has the capability to determine the electron density profile within the plasma. The performance of the proposed deep learning-based approach has been evaluated using three metrics- SSIM, RMSLE, and MAPE. The obtained results show promising performance in estimating the 2D radial profile of the density for the given linear plasma device and affirms the potential of the proposed ML-based approach in plasma diagnostics.

翻译：电子密度是表征等离子体的关键参数。低温等离子体（LTP）领域的大多数应用与研究都依赖于对等离子体密度与温度的精确估算。传统电子密度测量方法可提供给定线性LTP器件的轴向与径向分布，但这些方法存在工作范围有限、仪器复杂及数据分析流程繁琐等显著缺陷。本文提出一种基于深度学习（DL）辅助的微波-等离子体相互作用的非侵入式策略，可作为解决现有等离子体密度测量技术难题的新替代方案。通过利用等离子体对微波散射产生的电场模式来估算密度分布。概念验证基于包含低温、非磁化、碰撞等离子体的仿真训练数据集进行测试。研究考虑了对称（高斯型）与不对称密度分布（密度范围$10^{16}-10^{19}$ m$^{-3}$），覆盖多种实验配置。在构建合成训练数据集时，兼顾了真实实验场景中的噪声干扰及测量数据量（密集vs稀疏）问题。该DL技术具备测定等离子体电子密度分布的能力。采用结构相似性（SSIM）、均方根对数误差（RMSLE）与平均绝对百分比误差（MAPE）三个指标评估所提方法的性能。结果表明，该方法在估算给定线性等离子体器件的二维径向密度分布中展现出优异性能，验证了该机器学习方法在等离子体诊断中的巨大潜力。