地球磁层辐射带区域的超低频波与相对论电子发生径向扩散作用，可以将被局地加速的电子快速地输运到其它区域，此外磁暴主相期间向外的径向扩散是磁暴期间相对论电子快速损失的主要机制。以往的径向扩散理论都是二维的，研究赤道平面90度投掷角电子与超低频波的漂移共振。然而由于超低频波性质在纬度方向上有很大不同，非90度投掷角的电子离开赤道后所感受到的超低频波强度会发生很大变化，因此现有的二维径向扩散理论在研究这一问题时存在较大误差。本项目将基于前期我们对超低频波和波粒相互作用研究中取得的成果，进一步研究超低频波对内磁层粒子的作用，特别是利用最新的卫星观测数据研究超低频波方位角波数和超低频波强度纬向分布在径向扩散中的作用，发展三维的投掷角相关的径向扩散理论，为更准确地量化辐射带电子加速提供理论基础和数据支持。

The interaction between ULF wave and radiation belt electrons can be described by radial diffusion, which can transports electrons to other region after local acceleration and dominate the loss of electron during the main phase of magnetic storms. The current theory of radial diffusion is based on a two-dimensional assumption, which studies only the electrons with 90 degree pitch angle mirroring at equator. However, it has been known that there are complicate and significant differences in the latitudinal distribution of ULF wave, thus the two-dimensional radial diffusion theory should be modified for non-90-degree pitch angle electrons. In this project we propose to use spacecraft observations to investigate the interaction between ULF wave and radiation belt electrons. Specifically, we strive to address the follow objectives: a) the effect of mode number of ULF wave in radial diffusion; b) the effect of latitudinal distribution of ULF wave in radiation belt. We propose to develop the three-dimensional pitch angle dependent radial diffusion theory in order to better quantify the variation of radiation belt electron acceleration.