Alfvén speed

The Alfvén speed (named after the Swedish physicist and Nobel Prize winner Hannes Olof Gösta Alfvén ) is the speed of the Alfvén wave in plasma physics . In addition to the slow and fast magneto-sonic wave plays the Alfven wave a crucial role in MHD - Jets and MHD accretion influences.

Similar to water or air, one imagines plasma as a structure capable of vibrating and disrupting, in which ionized gas particles can vibrate around their starting position and thus propagate a wave. From the approach that kinetic and magnetic energy densities are equal:

${\displaystyle {\frac {1}{2}}\cdot \rho \cdot v^{2}={\frac {1}{2}}\cdot {\frac {B^{2}}{\mu _{0}}}}$

With

• ${\displaystyle \rho }$the density in the system
• B the magnetic field in the plasma
• ${\displaystyle \mu _{0}}$the magnetic field constant

the Alfvén velocity for an ideal ( viscosity and electrical conductivity ) incompressible MHD plasma as a uniform distribution solution results in: ${\displaystyle \mu =0}$ ${\displaystyle \sigma =\infty }$

${\displaystyle v=c_{A}={\frac {|{\vec {B}}|}{\sqrt {\mu _{0}\cdot \rho }}}}$

The printout shows that the Alfvén velocity not only increases linearly with the magnetic field, but also with decreasing mass density.