In the Earth’s inner magnetosphere, there exist regions like plasmasphere, ring current, and radiation belts, where the population of charged particles trapped along the magnetic field lines is more. These particles keep performing gyration, bounce and drift motions until they enter the loss cone and get precipitated to the neutral atmosphere. Theoretically, the mirror point latitude of a particle performing bounce motion is decided only by its equatorial pitch angle. This theoretical manifestation is based on the conservation of the first adiabatic invariant, which assumes that the magnetic field varies slowly relative to the gyro-period and gyro-radius. However, the effects of gyro-motion cannot be neglected when gyro-period and gyro-radius are large. In such a scenario, the theoretically estimated mirror point latitudes of electrons are likely to be in agreement with the actual trajectories due to their small gyro-radius. Nevertheless, for protons and other heavier charged particles like oxygen, the gyro-radius is relatively large, and the actual latitude of the mirror point may not be the same as estimated from the theory. In this context, we have carried out test particle simulations and found that the L-shell, energy, and gyro-phase of the particles do affect their mirror points. Our simulations demonstrate that the existing theoretical expression sometimes overestimates or underestimates the magnetic mirror point latitude depending on the value of L-shell, energy and gyro-phase due to underlying guiding centre approximation. For heavier particles like proton and oxygen, the location of the mirror point obtained from the simulation deviates considerably (∼ 10°–16°) from their theoretical values when energy and L-shell of the particle are higher. Furthermore, the simulations show that the particles with lower equatorial pitch angles have their mirror points inside the high or mid-latitude ionosphere.

中文翻译：

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L壳层和地球磁层中带电粒子磁镜点的能量依赖性

在地球内部磁层中，存在等离子体层、环流和辐射带等区域，这些区域沿磁力线捕获的带电粒子数量较多。这些粒子不断进行旋转、反弹和漂移运动，直到它们进入损失锥并沉淀到中性大气中。理论上，执行弹跳运动的粒子的镜点纬度仅由其赤道俯仰角决定。这种理论表现是基于第一绝热不变量的守恒，它假设磁场相对于陀螺周期和陀螺半径变化缓慢。但是，当陀螺周期和陀螺半径较大时，不能忽略陀螺运动的影响。在这样的场景下，由于电子的陀螺半径很小，理论上估计的电子镜像点纬度很可能与实际轨迹一致。然而，对于质子和氧等其他较重的带电粒子，陀螺半径比较大，镜点的实际纬度可能与理论估计的不一样。在此背景下，我们进行了测试粒子模拟，发现粒子的 L 壳层、能量和陀螺相位确实会影响它们的镜像点。我们的模拟表明，由于潜在的引导中心近似，现有的理论表达式有时会高估或低估磁镜点纬度，这取决于 L 壳、能量和陀螺相位的值。对于质子和氧等较重的粒子，当粒子的能量和 L 壳层较高时，从模拟中获得的镜像点的位置与它们的理论值相差很大（约 10°–16°）。此外，模拟表明，具有较低赤道俯仰角的粒子的镜像点位于高纬度或中纬度电离层内。