Базовий алгоритм апроксимації граничної траєкторії короткофокусного електронного пучка за допомогою коренево-поліноміальних функцій четвертого та п’ятого порядків

• Дата: 2023
• Автори: Melnyk, Igor, Pochynok, Alina
• Формат: Стаття
• Мова: English
• Опубліковано: The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2023
• Теми: апроксимація; інтерполяція; коренево-поліноміальна функція; яружна функція; метод найменших квадратів; нев’язка; похибка апроксимації; електронний пучок; електронно-променеві технології; approximation; interpolation; root-polynomial function; ravine function; least-square method; discrepancy; approximation error; electron beam; electron-beam technologies
• Онлайн доступ: http://journal.iasa.kpi.ua/article/view/290474
• Назва журналу: System research and information technologies

The new iterative method of approximating the boundary trajectory of a short-focus electron beam propagating in a free drift mode in a low-pressure ionized gas under the condition of compensation of the space charge of electrons is considered and discussed in the article. To solve the given approximation task, the root-polynomial functions of the fourth and fifth order were applied, the main features of which are the ravine character and the presence of one global minimum. As an initial approach to solving the approximation problem, the values of the polynomial coefficients are calculated by solving the interpolation problem. After this, the approximation task is solved iteratively. All necessary polynomial coefficients are calculated multiple times, taking into account the values of the function and its derivative at the reference points. The final values of polynomial coefficients of high-order root-polynomial functions are calculated using the dichotomy method. The article also provides examples of the applying fourth-order and fifth-order root-polynomial functions to approximate sets of numerical data that correspond to the description of ravine functions. The obtained theoretical results are interesting and important for the experts who study the physics of electron beams and design modern industrial electron beam technological equipment.