Magnetohydrodynamic wave (MHD wave)

A magnetohydrodynamic wave is a linear disturbance of a conducting fluid and its magnetic field. A uniform ideal plasma supports an Alfvén mode and fast and slow magnetosonic modes.

An Alfvén wave is transverse and incompressible, with displacement perpendicular to both the background magnetic field and the wavevector. Its frequency is ${\omega }^2=(\mathbf{k}\cdot {\mathbf{v}}_A{)}^2$.

An Alfvén wing is a stationary Alfvénic disturbance attached to a conducting obstacle moving through a magnetized plasma. In a super-Alfvénic flow its boundaries follow downstream characteristics.

For a stationary cold-plasma disturbance with obstacle speed $u_0>u_A$, the characteristic slope is $m=\sqrt{u_0^2/u_A^2-1}$. It approaches $u_0/u_A$ in the strongly super-Alfvénic limit.

A magnetosonic wave is a compressive MHD mode polarized in the plane of the wavevector and background magnetic field.

The fast magnetosonic mode uses gas and magnetic pressure as reinforcing restoring forces and is the faster root of the magnetosonic dispersion relation.

The slow magnetosonic mode is the lower-frequency compressive root and is guided more strongly along the magnetic field.

The tube speed combines sound and Alfvén speeds according toIt is smaller than both constituent speeds.

An MHD interface wave propagates along a discontinuity and decays away from it. Continuity of normal displacement and total pressure determines its dispersion relation.