中文摘要：

有短波长的修正的散 magnetohydrodynamic (MHD ) 波浪在从波浪把精力转变成粒子有一个重要角色。在这份报纸，基于二液体的模式，一个分散方程包括短波长的效果，并且它的准确答案被介绍。结果为三个理想的 MHD 模式的短波长的修正版本负责(即快，慢并且 Alfv

英文摘要：

Dispersive magnetohydrodynamic （MHD） waves with short-wavelength modification have an important role in transforming energy from waves into particles. In this paper, based on the two-fluid mode, a dispersion equation, including the short-wavelength effect, and its exact solution are presented. The outcome is responsible for the short-wavelength modification versions of the three ideal MHD modes （i.e. the fast, slow and Alfven）. The results show that the fast and Alfven modes are modified considerably by the shortwavelength effect mainly in the quasi-parallel and quasi-perpendicular propagation directions, respectively, while the slow mode can be affected by the short-wavelength effect in all propagation directions. On the other hand, the dispersive modification occurs primarily in the finite-β regime of 0.001 〈 β 〈 1 for the fast mode and in the high-β regime of 0.1 〈 β 〈 10 for the slow mode. For the Alfven mode, the dispersive modification occurs from the low-β regime ofβ〈 0.001 through the high-β regime of β〉 1.