title: Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¼ÐµÑÐ¾Ð´Ð° ÑÐ°ÑÑÑÑÐ° Ð³ÑÐ°Ð½Ð¸ÑÑ Ð¿Ð»Ð°Ð·Ð¼Ñ Ð´Ð»Ñ ÑÑÑÐ°Ð½Ð¾Ð²ÐºÐ¸ ÑÐ¾ÐºÐ°Ð¼Ð°Ðº Â«ÐÐ»Ð¾Ð±ÑÑ-Ð2Â» Ð¤Ð¢Ð Ð¸Ð¼. Ð.Ð¤. ÐÐ¾ÑÑÐµ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Development of a mathematical method for calculating the plasma boundary for the &lt;&gt; tokamak of the Ioffe Institute
Creators: name: ÐÑÐ¸ÑÐ°ÐµÐ½ÐºÐ¾, ÐÐ¸ÐºÐ¸ÑÐ°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: Ð¿Ð»Ð°Ð·Ð¼Ð°
Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½ÑÐµ ÑÐ¸ÑÑÐµÐ¼Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÑ Ð°Ð»Ð³ÐµÐ±ÑÐ°Ð¸ÑÐµÑÐºÐ¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹
matlab
plasma
linear programming
interval system of algebraic equations

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¼ÐµÑÐ¾Ð´Ñ ÑÐ¾ÐºÐ¾Ð²ÑÑ ÐºÐ¾Ð»ÐµÑ Ð²Ð¾ÑÑÑÐ°Ð½Ð¾Ð²Ð»ÐµÐ½Ð¸Ñ Ð³ÑÐ°Ð½Ð¸ÑÑ Ð¿Ð»Ð°Ð·Ð¼Ñ. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1. &lt;&lt;ÐÑÑÐ¼Ð°Ñ&gt;&gt; Ð·Ð°Ð´Ð°ÑÐ° - Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ðµ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð»Ñ, ÑÐ¾Ð·Ð´Ð°Ð²Ð°ÐµÐ¼Ð¾Ð³Ð¾ ÑÐ¾Ð½ÐºÐ¸Ð¼Ð¸ ÑÐ¾ÐºÐ¾Ð²ÑÐ¼Ð¸ ÐºÐ¾Ð»ÑÑÐ°Ð¼Ð¸. 2. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° Ð·Ð½Ð°ÑÐ¸Ð¼ÑÑ ÑÐ¾Ð±ÑÑÐ²ÐµÐ½Ð½ÑÑ ÐºÐ¾Ð¼Ð¿Ð¾Ð½ÐµÐ½Ñ Ð¾Ñ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° Ð´Ð°ÑÑÐ¸ÐºÐ¾Ð² Ð¸ ÑÐ¾ÐºÐ¾Ð²ÑÑ ÐºÐ¾Ð»ÐµÑ. 3. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ &lt;&lt;Ð¾Ð±ÑÐ°ÑÐ½Ð¾Ð¹&gt;&gt; Ð·Ð°Ð´Ð°ÑÐ¸. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¾ Ð¿ÑÐµÐ´ÐµÐ»ÑÐ½Ð¾Ðµ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð¾ ÑÐ¾ÐºÐ¾Ð²ÑÑ ÐºÐ¾Ð»ÐµÑ Ð¸ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÑ Ð´Ð°ÑÑÐ¸ÐºÐ¾Ð² Ñ ÑÐ¾ÑÐºÐ¸ Ð·ÑÐµÐ½Ð¸Ñ Ð²Ð½ÐµÑÐµÐ½Ð¸Ñ Ð¿Ð¾Ð»ÐµÐ·Ð½Ð¾Ð¹ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ Ð² Ð¼Ð°ÑÑÐ¸ÑÑ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹. ÐÐ°Ð¼Ð¸ Ð¿ÑÐµÐ´Ð»Ð°Ð³Ð°ÐµÑÑÑ Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐ° Ð·Ð°Ð´Ð°ÑÐ¸ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð³Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ, ÑÑÐ¸ÑÑÐ²Ð°ÑÑÐ°Ñ Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÑ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ð¸Ð¹ Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÑ Ð´Ð°ÑÑÐ¸ÐºÐ¾Ð². ÐÑ ÑÑÐ°Ð²Ð½Ð¸Ð²Ð°ÐµÐ¼ ÑÑÐ¾Ñ Ð¿Ð¾Ð´ÑÐ¾Ð´ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÐ¼ÑÐ¼ Ð½Ð° Ð´Ð°Ð½Ð½ÑÐ¹ Ð¼Ð¾Ð¼ÐµÐ½Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ Ð½Ð°Ð¸Ð¼ÐµÐ½ÑÑÐ¸Ñ ÐºÐ²Ð°Ð´ÑÐ°ÑÐ¾Ð², Ð² ÐºÐ¾ÑÐ¾ÑÐ¾Ð¼ Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÑ Ð´Ð°ÑÑÐ¸ÐºÐ¾Ð² Ð½Ðµ ÑÑÑÐµÐ½Ð°. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÑÐµÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¼Ñ Ð¿ÑÐ¸ÑÐ¾Ð´Ð¸Ð¼ Ðº Ð²ÑÐ²Ð¾Ð´Ñ, ÑÑÐ¾ Ð¸Ð¼ÐµÐµÑ ÑÐ¼ÑÑÐ» Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°ÑÑ Ð¿ÑÐµÐ´Ð»Ð°Ð³Ð°ÐµÐ¼ÑÐ¹ Ð½Ð°Ð¼Ð¸ Ð¿Ð¾Ð´ÑÐ¾Ð´ Ð²Ð¼ÐµÑÑÐ¾ ÑÑÑÐµÑÑÐ²ÑÑÑÐµÐ³Ð¾. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¾Ð¿Ð¸ÑÐ°Ð½ Ð¼ÐµÑÐ¾Ð´ Ð²Ð¸Ð·ÑÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ ÑÐ¾ÐºÐ° Ð¿Ð»Ð°Ð·Ð¼Ñ, Ð·Ð°ÐºÐ»ÑÑÐ°ÑÑÐ¸Ð¹ÑÑ Ð² Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ð¸ ÑÐ»Ð»Ð¸Ð¿ÑÐ° Ð²Ð¾ÐºÑÑÐ³ ÑÐ¾ÐºÐ¾Ð²ÑÑ ÐºÐ¾Ð»ÐµÑ Ð¸ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½ ÑÐ¿Ð¾ÑÐ¾Ð± Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ Ð³ÑÐ°Ð½Ð¸ÑÑ Ð¿Ð»Ð°Ð·Ð¼Ñ. ÐÑÐ´ÐµÐ»ÑÐ½Ð¾ Ð¸Ð·ÑÑÐµÐ½Ð° ÑÐ°Ð·ÑÐµÑÐ¸Ð¼Ð¾ÑÑÑ Ð¸ Ð²Ð°ÑÐ¸Ð°Ð±ÐµÐ»ÑÐ½Ð¾ÑÑÑ &lt;&lt;Ð¾Ð±ÑÐ°ÑÐ½Ð¾Ð¹&gt;&gt; Ð·Ð°Ð´Ð°ÑÐ¸ Ð² Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐµ. Ð Ð°ÑÑÐ¼Ð¾ÑÑÐµÐ½ Ð¼ÐµÑÐ¾Ð´ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÐµÐ³ÑÐ»ÑÑÐ¸Ð·Ð°ÑÐ¸Ð¸ Ð´Ð»Ñ ÑÐ»ÑÑÑÐµÐ½Ð¸Ñ Ð¾Ð±ÑÑÐ»Ð¾Ð²Ð»ÐµÐ½Ð½Ð¾ÑÑÐ¸ ÑÐ¸ÑÑÐµÐ¼Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÑ Ð°Ð»Ð³ÐµÐ±ÑÐ°Ð¸ÑÐµÑÐºÐ¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹. Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½Ñ Ð´Ð»Ñ Ð²Ð¸Ð·ÑÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÑÐµÑÐµÐ½Ð¸Ð¹, Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¼ÐµÑÐ¾Ð´Ð° Ð½Ð°Ð¸Ð¼ÐµÐ½ÑÑÐ¸Ñ ÐºÐ²Ð°Ð´ÑÐ°ÑÐ¾Ð² Ð¸ ÑÐµÑÐµÐ½Ð¸Ñ Ð¿Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ð½Ð¾Ð¹ Ð½Ð°Ð¼Ð¸ Ð·Ð°Ð´Ð°ÑÐ¸ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð³Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÐ¸Ð¼Ð¿Ð»ÐµÐºÑ-Ð¼ÐµÑÐ¾Ð´Ð°.
description: The given work is devoted to the current filaments method for plasma boundary reconstruction. The research set the following goals: 1. &lt;&gt; problem - the calculation of the magnetic field produced by thin current rings. 2. The study of the dependence between the number of significant components and the number of magnetic probes and current filaments. 3. The study of the &lt;&gt; problem. The limit number of current rings and magnetic probes is determined in terms of useful information in the measurement matrix. We propose the linear programming problem, which takes into account an error of magnetic probes. We compare this approach with the least-squares method used nowadays, in which the probes error is not taken into account. As a result, we come to the conclusion that it makes sense to use our approach instead of the existing one. The paper describes a method for visualizing the plasma current, which consists in constructing an ellipse around the current rings and proposes a method for constructing the interval boundary of the plasma. Solvability and variability of the interval problem are researched. The method of interval regularization is considered to improve the conditionality of a system of linear algebraic equations. A tool has been developed for visualizing and comparing solutions obtained using the least squares method and solving the linear programming problem using the simplex method.