Deep Learning assisted microwave-plasma interaction based technique for plasma density estimation

TL;DR

This work develops a non-invasive, DL-assisted microwave-plasma interaction method to estimate two-dimensional electron density profiles in low-temperature plasmas from scattered microwave fields. A 2D FDTD Maxwell–fluid model generates synthetic data for symmetric and asymmetric density profiles, with masked and noisy E-field patterns to simulate dense/sparse sensing. A UNet-based neural network maps masked Erms to n_e, achieving high fidelity as measured by SSIM (~0.99–0.999) and low RMSLE/MAPE (often <0.1) across densities $n_e$ in the range $10^{16}$–$10^{19}$ m$^{-3}$, for both dense and sparse data. Phase-2 tests with asymmetric profiles show robust qualitative and quantitative recovery, though with modestly higher errors, indicating practical viability for real-time, non-invasive plasma diagnostics and potential extensions to more extreme plasmas and tokamak-like conditions.

Abstract

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.

Figures (13)

• Figure 1: The plot of the variation (a). $\omega _p/\omega$ vs. $n_e$ for fixed $\omega$(or f=500 MHz ) correspond to a microwave of f= 500 MHz, and an increasing plasma density profile $1e14-1e19$ m$^{-3}$, (b). the real component of the reflection coefficient( $\Gamma_r$) and transmission coefficient ( $T_r$) for collisional and non-collisional unmagnetized plasma is shown.
• Figure 2: Schematic representation for the category of problems that mostly exists for the EM-plasma interaction. The forward and inverse problem. The 2-D representation of plasma density and corresponding $E_{rms}$ obtained through the Maxwell-plasma fluid model (solution to forward problem) exists is shown, and no direct inverse mapping exists.
• Figure 3: (a). The schematic of a typical linear LTP device. (b). The schematic representation of a square computational domain, the length of the domain $L_{x}$ and $L_{y}$, is expressed in terms of the wavelength of the incident EM wave. The location coordinates $x_{0}$, $y_{0}$ is $0.5L_{x}$ and $0.5L_{y}$, respectively, where $L_x=L_y=1\lambda$, where $\lambda$ corresponds to the freq = 500 MHz. $r$: radius of the plasma and $n_{0}$: peak plasma density .
• Figure 4: Dense $E_{rms}$ data generation for ML training: (a) by removing the central part of the data and retaining the remaining, (b) addition of noise to the generated dense data, followed by removing the central part and retaining the remaining. (c1-c3): represents the 2-D as well as 1-D density profile, and corresponding, dense $E_{rms}$ data collected for both with and without noise (left to right). The color-bar maxima and minima correspond to $E_{rms}$. $D_{I}$: Initial data, $M_{D}$: Mask for dense data, $N$: Noise data
• Figure 5: Sparse $E_{rms}$ data generation for ML training: (a) by removing the central part of the data and retaining the sparse data using a concentric ring-based mask, (b) addition of noise to the generated dense data, followed by removing the central part and retaining the remaining. (c1-c3): represents the 2-D as well as 1-D density profile, and corresponding, dense $E_{rms}$ data collected for both with and without noise (left to right). The color-bar maxima and minima correspond to $E_{rms}$. $D_{I}$: Initial data, $M_{S}$: Mask for sparse data, $N$: Noise data