In this article, we work with the basic equation for the fluid velocity in the case of a magnetoconducting fluid in two ways: (i) by Ampère’s law, (ii) taking into account the Maxwell correction. Considering an arbitrary direction between the wave vector and the magnetic field, an expression for the wave’s phase velocity is obtained. The phase velocity study implies three magnetohydrodynamic (MHD) wave modes when we neglect the displacement current. We compared the wave modes with each other, and we also compared the modes obtained with and without the displacement current. The comparison allows us to discuss the variations between these MHD modes in hypothetical cases when the Alfvén speed increases to values close to the speed of light. The article’s main objective is to show the importance of displacement current in the pure and fast MHD waves, in the particular case where the Alfvén speed is higher than the sound wave speed. We find that the displacement current has practically no influence on the value of the wave phase velocity when the Alfvén velocity increases for slow mode.
Keywords:
MHD waves; Alfven speed; Displacement current; Basic MHD equations
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