This paper introduces a novel approach for determining the half-beam cone angle, a critical parameter in the preliminary design of Pierce electron guns, using an Artificial Neural Network (ANN) model. While traditional methods rely on iterative or noniterative calculations, often involving empirical factors, the proposed ANN model is trained and tested on experimental electron gun data. The study demonstrates that the ANN model significantly outperforms existing methods—Vaughan's iterative, Tiwary's noniterative, and Yang's modified noniterative methods—achieving a Mean Relative Error (MRE) of less than 5%. This establishes the ANN as a more reliable and accurate tool for efficient electron gun geometry estimation.
Summarizing the Determination of the Half-Beam Cone Angle for Pierce Electron Gun Design using an Artificial Neural Network
0:00 Introduction to Electron Guns: Electron beams are vital in diverse fields like metallurgy and microscopy, with the electron gun being a crucial component. Initial electron gun geometry is critical for efficient simulation and refinement, often based on Pierce's guidelines.
0:45 Existing Design Methods: Historically, electron gun design evolved from graphical methods to numerical computations. Current preliminary design relies on methods like Vaughan's iterative method and Tiwary's noniterative method (and Yang's modified version), which calculate parameters like the half-beam cone angle (alpha) from inputs like beam voltage, current, and beam waist radius.
1:15 Importance of Half-Beam Cone Angle: The half-beam cone angle is identified as a critically important parameter as it significantly influences the overall geometry of the electron gun.
1:40 Novel ANN Approach: The study proposes using an Artificial Neural Network (ANN), specifically a Multi-layer Perceptron (MLP) model, to predict the half-beam cone angle, aiming for a more accurate and efficient design process compared to traditional iterative and noniterative methods.
2:10 ANN Methodology: The MLP model uses perveance, beam waist radius, and convergence as input parameters. The network employs two hidden layers with 3 and 2 neurons respectively, trained for 5000 epochs using the Levenberg-Marquardt algorithm.
2:50 Data for Training and Testing: The ANN was trained and tested using 30 experimental data points from documented electron guns, covering a wide range of half-beam cone angles (9.80° to 70.00°) and perveance values (0.3 to 3.67 μP). The dataset was split into 23 for training and 7 for testing.
3:45 Strong Correlation and Low Error: The regression analysis shows a high Pearson correlation coefficient (0.997 for training, 0.990 for testing) between experimental and ANN-predicted values, indicating excellent precision. The Mean Square Error (MSE) significantly decreased during training, stabilizing quickly.
4:30 Superior Performance: The proposed ANN model demonstrates superior performance compared to Vaughan's iterative, Tiwary's noniterative, and Yang's modified noniterative methods. For test data, the ANN achieved a Mean Relative Error (MRE) of 3.74% and an RMSE of 2.09, significantly lower than the other methods (e.g., noniterative method had MRE of 27.93% and RMSE of 10.89).
5:10 Conclusion & Practicality: The ANN is confirmed as a reliable and accurate tool for predicting the half-beam cone angle in the preliminary design of Pierce electron guns. Its computational speed, despite being slightly slower than non-iterative methods, is justified by its substantially better performance.