荷電粒子系の運動の数値計算法

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The governing equations employed here are the Newton equation of motion for charged particles and the Maxwell equations for electromagnetic fields. In the case that the Newton equation inchludes only the dependent variables, velocity and position, and the independent variable, time, then convenient method such as Runge-Kutta-Gill can be applied to the numerical analysis. In reality, however, for motion of charged particles, the equation of motion includes other variables, electric field and magnetic field, as functions of time and position. Runge-Kutta-Gill method cannot be applied as the resrult. Usually, the Maxwell equations in forms of partial differential equations, are combined to solve electiric and magnetic fields. To solve partial differential equations numerically, at present there is no convenient method. Often numerical errors become bulky through the scheme to change differential equations to defference equations and through the boundary conditions. The aim of this paper is to develop the method as possible as exact to solve the system of Newton-Maxwell equations numerically. By using the scholar and vector potentials instead of electromagnetic fields, the Maxwell equations reduce to two d'Alembertian type equations, which has the exact solutions. The Newton equation of motion can be reformed as a pure ordinary differential equation, electromagnetic fields in it being substituted by exact solutions. In this process, a repetition approximation is employed to solve acceleration implicitly. After all, it is shown that numerical calculation for the system of Newton-Maxwell equations reduces to application of Runge-Kutta-Gill method. In principle, no error is included to solve electromagnetic fields in this method.
帝京平成大学の論文
2000-06-30

荷電粒子系の運動の数値計算法

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