We discuss an extension of the velocity Verlet method that accurately approximates the kinetic-energy-conserving charged particle motion that comes from magnetic forcing. For a uniform magnetic field, the method is shown to conserve both particle kinetic energy and magnetic dipole moment better than midpoint Runge-Kutta. We then use the magnetic velocity Verlet method to generate trapped particle trajectories, both in a cylindrical magnetic mirror machine setup, and for dipolar fields like the earth's magnetic field. Finally, the method is used to compute an example of (single) mirror motion in the presence of a magnetic monopole field, where the trajectory can be described in closed form.

中文翻译：

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一种磁速度 Verlet 方法

我们讨论了速度 Verlet 方法的扩展，它可以准确地近似来自磁力的动能守恒带电粒子运动。对于均匀磁场，该方法比中点 Runge-Kutta 更能守恒粒子动能和磁偶极矩。然后，我们使用磁速度 Verlet 方法在圆柱形磁镜机设置和偶极场（如地球磁场）中生成捕获的粒子轨迹。最后，该方法用于计算存在磁单极子场的（单）镜运动的示例，其中轨迹可以用闭合形式描述。