This article aims to understand the pitch angle distributions (PADs) of the charged particles in the Earth’s inner magnetosphere using test-particle simulations. The emphasis is on characterizing the variation in pitch angle of the charged particles trapped along the Earth’s magnetic field lines. These charged particles undergo gyration, bounce, and azimuthal drift motions in the Earth’s inner magnetosphere. They are trapped until their pitch angle falls into the loss-cone to get lost into the upper atmosphere. We have developed a three-dimensional test-particle simulation model in which the relativistic equation of motion is solved numerically to track these trapped particle’s trajectories. We have examined the pitch angle distributions of the electron, proton, and oxygen for the cases where adiabatic invariants are conserved and non-conserved. For this purpose, we have considered the particle’s trajectory in the latitudinal range of [$-40°,40°$] for one complete drift around the Earth. We found that when adiabatic invariants are conserved, the particles possess butterfly-type pitch angle distributions. Whereas, when adiabatic invariants are not conserved, the particle’s pitch angle distribution bunches toward the 90°-peaked distribution. The situation of non-conservation of adiabatic invariants demonstrated in the present simulation is arising due to larger gyro-radius (few Earth radii) over which the ambient magnetic field is not constant. We have noticed that in the static dipolar magnetic field, all three, 1st, 2nd, and partly 3rd adiabatic invariants are non-conserved when gyro-radius is larger. The information on the change in the pitch angle distribution pattern from butterfly-type to 90°-peak distribution will be useful to understand the pitch angle distributions observed by the recent spacecraft in the Earth’s radiation belts.

本文旨在使用测试粒子模拟来了解地球内部磁层中带电粒子的俯仰角分布 (PAD)。重点是表征沿地球磁场线捕获的带电粒子的俯仰角变化。这些带电粒子在地球内部磁层中经历旋转、反弹和方位角漂移运动。它们被困，直到它们的俯仰角落入损失锥体，从而迷失在高层大气中。我们开发了一个三维测试粒子模拟模型，其中相对论运动方程被数值求解以跟踪这些被捕获粒子的轨迹。对于绝热不变量守恒和不守恒的情况，我们已经检查了电子、质子和氧的俯仰角分布。$——40°,40°$] 绕地球一次完全漂移。我们发现，当绝热不变量守恒时，粒子具有蝶形俯仰角分布。而当绝热不变量不守恒时，粒子的俯仰角分布向 90° 峰值分布聚集。本模拟中证明的绝热不变量不守恒的情况是由于较大的陀螺半径（很少地球半径）引起的，在该半径上环境磁场不是恒定的。我们注意到，在静态偶极磁场中，当陀螺半径较大时，所有三个、第一、第二和部分第三绝热不变量都是不守恒的。