Alfvén Mach number

The Alfvén Mach number (also known as the Alfvén number, Alfvénic Mach number, and magnetic Mach number; M_A or M_M) is a dimensionless quantity representing the ratio of the relative velocity of a fluid to the local Alfvén speed. It is used in plasma physics, where it is analogous to the Mach number but based on Alfvén waves rather than sound waves. Alfvén and Mach were physicists who studied shock waves.

Along with the sonic Mach number, the Alfvén Mach number is frequently used to characterize shock fronts^[1][2][3] and turbulence^[4][5] in magnetized plasmas.^[6][7] $${\displaystyle \mathrm {M_{A}} ={\frac {u}{u_{\mathrm {A} }}}}$$ where

• M_A is the Alfvén Mach number,
• u is the flow velocity, and
• u_A is the Alfvén speed.^[8]

When u < M_A, the flow is referred to as sub-Alfvénic; and when u > M_A, the flow is referred to as super-Alfvénic.^[2]

See also

• Plasma parameters
• Magnetic Reynolds number
• Lundquist number