Abstract

In the present work, a numerical modified Verlet scheme (MVS) is obtained. This scheme is intended to solve the equations of motion of charged particles immersed in an external stationary environment and a uniform magnetic field, for example, charged particles of a condensed substance in a buffer plasma (dusty plasma). The influence of the environment on the particle dynamics is described by the friction force. The particle dynamics are also affected by interparticle interaction and an external uniform magnetic field. To obtain the Verlet scheme (VS), the coordinates and velocities of the particles are decomposed into a Taylor series, taking into account the Lorentz force and the friction force. All Taylor series expansion terms that give the same order of accuracy are taken into account. In the obtained numerical scheme, the time step of modeling does not depend on the magnitude of the magnetic field but is determined only by the internal physical properties of the system under consideration, which is important when modeling an ensemble of charged particles taking electromagnetic fields into account. The paper solves a test problem for which particle trajectories obtained based on the conventional and modified VS for different values, both the friction parameter and the magnetic field parameter, are compared. Based on the analysis of the dependence of the maximum relative deviation of the coordinate on the time step, the time step is independent of the magnetic field in the Taylor expansion scheme, while in the inverse VS it is dependent.

中文翻译：

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考虑外部磁场和摩擦力的带电粒子系统物理性质研究模型

摘要

在当前的工作中，获得了数值修正的Verlet方案（MVS）。该方案旨在解决浸没在外部静止环境中的带电粒子和均匀磁场的运动方程，例如，缓冲等离子体（尘土等离子体）中冷凝物质的带电粒子。环境对粒子动力学的影响通过摩擦力来描述。粒子动力学还受到粒子间相互作用和外部均匀磁场的影响。为了获得Verlet方案（VS），考虑洛伦兹力和摩擦力，将粒子的坐标和速度分解为泰勒级数。所有给出相同精度顺序的泰勒级数展开项都应考虑在内。在获得的数值方案中，建模的时间步长不取决于磁场的大小，而仅取决于所考虑系统的内部物理特性，这在考虑电磁场的情况下对带电粒子的整体建模非常重要。本文解决了一个测试问题，该测试问题比较了基于常规和改进的VS针对不同值（摩擦参数和磁场参数）获得的粒子轨迹。基于对坐标的最大相对偏差与时间步长的相关性的分析，在泰勒展开方案中，时间步长与磁场无关，而在反向VS中，时间步长是相关的。