We develop a simple model for the kinematics of charged particles in regions of magnetic turbulence. We approximate the local magnetic field as smoothly varying in strength and direction, where adiabatic invariance prevails, or as presenting rapid changes in direction or ‘kinks’. Particles execute guiding centre gyromotion around a field line. However, in analogy to kinetic theory for collisional environments, when the particle undergoes a rapid change in direction by some angle $\unicode[STIX]{x1D703}$ , it would instantaneously transition to Larmor motion around the new field line. This mimics Brownian motion wherein we replace collisions with other particles by rapid transitions or ‘collisions’ with other field lines. Using standard methods drawn from Brownian motion, we follow the evolution of the parallel and perpendicular components of the velocity, namely $v_{\Vert }$ and $v_{\bot }$ , and rigorously show that kinetic energy isotropization necessarily emerges.

中文翻译：

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无碰撞环境中的带电粒子各向同性：湍流磁场作为随机游走的管道

我们为磁湍流区域中带电粒子的运动学开发了一个简单模型。我们将局部磁场近似为强度和方向平滑变化，绝热不变性占主导地位，或者呈现方向或“扭结”的快速变化。粒子围绕场线执行引导中心回转运动。然而，类似于碰撞环境的动力学理论，当粒子以某个角度快速改变方向时 $\unicode[STIX]{x1D703}$ ，它会立即转变为围绕新场线的拉莫尔运动。这模仿了布朗运动，其中我们通过快速跃迁或与其他场线的“碰撞”来代替与其他粒子的碰撞。使用从布朗运动中得出的标准方法，我们遵循速度的平行和垂直分量的演变，即 $v_{\垂直}$ 和 $v_{\bot }$ ，并严格表明动能各向同性必然出现。