title: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¸Ð½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ñ Ð·Ð°ÑÑÐ¶ÐµÐ½Ð½ÑÑ ÑÐ°ÑÑÐ¸Ñ Ð² ÑÐ»ÐµÐºÑÑÐ¾Ð¼Ð°Ð³Ð½Ð¸ÑÐ½ÑÑ Ð¿Ð¾Ð»ÑÑ ÑÐ»Ð¾Ð¶Ð½Ð¾Ð¹ ÐºÐ¾Ð½ÑÐ¸Ð³ÑÑÐ°ÑÐ¸Ð¸
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: The study of methods for the numerical integration of the equations of motion of charged particles in electromagnetic fields of complex configuration
Creators: name: Ð§Ð¸ÑÐ¾Ð½Ð¾Ð²Ð°, ÐÐ½Ð°ÑÑÐ°ÑÐ¸Ñ
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: ÑÐ»ÐµÐºÑÑÐ¾Ð¼Ð°Ð³Ð½Ð¸ÑÐ½Ð¾Ðµ Ð¿Ð¾Ð»Ðµ
Ð¼ÐµÑÐ¾Ð´ Ð ÑÐ½Ð³Ðµ-ÐÑÑÑÑ 4 Ð¿Ð¾ÑÑÐ´ÐºÐ°
Ð¸Ð½ÑÐµÐ³ÑÐ°ÑÐ¾Ñ ÐÐ¾ÑÐ¸ÑÐ°
ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ
Ð´Ð²Ð¸Ð¶ÐµÐ½Ð¸Ðµ ÑÐ°ÑÑÐ¸Ñ
Ð»Ð¾Ð²ÑÑÐºÐ° ÐÐµÐ½Ð½Ð¸Ð½Ð³Ð°
ÑÐ½ÐµÑÐ³Ð¸Ñ
ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½Ð¾Ðµ Ð¿Ð¾Ð»Ðµ
Ð¿Ð¾Ð»Ðµ Ñ Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²ÐµÐ½Ð½ÑÐ¼Ð¸ Ð³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ°Ð¼Ð¸
electromagnetic field
Runge-Kutta method of 4 orders
Boris integrator
stability
particle motion
Penning trap
energy
stationary field
field with spatial gradients

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description: This paper presents methods for modeling particle motion in electromagnetic fields of complex configuration. The analysis of two methods for solving the problem: 1. Runge-Kutta method 4 orders. 2. Boris integrator. The 4-order Runge-Kutta method was chosen as a classical method for solving such problems, the Boris integrator as a specialized and not widely known method. The analysis of the solution of the problem using the above methods in conditions for which an exact analytical solution is known. Among them are problems with a stationary electromagnetic field, the solution of which was evaluated from the point of view of correspondence between the calculation of the analytically calculated trajectory and the execution time. A model of the Penning trap was chosen as a problem with an electromagnetic field with spatial gradients. For this problem, the correspondence of the trajectories of motion was evaluated, and the change in the particle energy was also estimated. As a result, the analysis was performed according to the following criteria: 1. Correspondence of the trajectory of movement by analytical calculation. 2. Time to complete the calculations. 3. Stability. 4. Evaluation of a solution from a physical point of view. A comparison of the considered methods for each of the listed characteristics is performed. Based on the analysis result, it was concluded that the Boris integrator is more suitable for solving the task.