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The Alfvén mode gyrokinetic equation in finite‐pressure magnetospheric plasma

The paper is concerned with the derivation of the Alfvén mode equation in finite‐pressure space plasma in gyrokinetic approach. The long plasma approximation is used, where the bounce frequency is much lower than both wave and drift frequencies. The only ultralow frequency mode in the long plasma approximation is the Alfvén‐ballooning compressional mode, which is described by the Alfvénic dispersion relation with some additional (ballooning) terms caused by the field line curvature and plasma pressure effects. Due to these effects the Alfvén mode acquires also considerable parallel magnetic field component. The long plasma approximation allowed us to consider the correspondence between the gyrokinetic and MHD approaches for the Alfvén mode equation. It is shown that in 0 < β ≪ 1 case, MHD approach gives correct Alfvén wave description, where β is plasma to magnetic pressure ratio.