Landau length

The Landau length (according to Lew Dawidowitsch Landau ) indicates the distance at which the electrostatic potential energy of two charge carriers of a plasma is equal to the mean thermal energy . This is the typical minimum distance in butt processes . Although the electrostatic interaction has in principle an infinite range, very fast particles can approach each other closely before their orbit is strongly influenced.

By comparing the Landau length with other characteristic lengths , such as the mean free path and the Debye radius , important statements can be made about the state of the plasma. A plasma behaves like an ideal gas if the Landau length is small compared to the mean distance between the particles, because then the electromagnetic interaction in the equation of state can be neglected.

definition

The Landau length is defined as

{\ displaystyle \ lambda _ {\ mathrm {L}} = {\ frac {| q_ {1} \, q_ {2} |} {4 \ pi \, \ varepsilon \, k _ {\ mathrm {B}} T }}}

With

the amounts of the charges and the two particles ${\ displaystyle q_ {1}}$ ${\ displaystyle q_ {2}}$
the permittivity ${\ displaystyle \ varepsilon}$
the Boltzmann constant ${\ displaystyle k _ {\ mathrm {B}}}$
the temperature . ${\ displaystyle T}$

It results from equating the electrostatic potential energy

{\ displaystyle E_ {pot, elst} = {\ frac {| q_ {1} \, q_ {2} |} {4 \ pi \, \ varepsilon \, r}}}

with thermal energy

{\ displaystyle E_ {th} = k _ {\ mathrm {B}} T}

and solving for the distance between the two particles. ${\ displaystyle r}$

For example, for two electrons in a vacuum :

{\ displaystyle \ lambda _ {\ mathrm {L}} = {\ frac {e ^ {2}} {4 \ pi \, \ varepsilon _ {0} \, k _ {\ mathrm {B}} T}}}

With

Wilhelm H. Kegel: Plasma Physics: An Introduction . Springer, Berlin 1998, ISBN 3-540-63701-X .