Debye length
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In plasma physics, the Debye length, named after the Dutch physical chemist Peter Debye, is the scale over which mobile charge carriers (e.g. electrons) screen out electric fields in plasmas and other conductors. In other words, the Debye length is the distance over which significant charge separation can occur. In space plasmas where the electron density is relatively low, the Debye length may reach macroscopic values, such as in the Magnetosphere, Solar wind, Interstellar medium and Intergalactic medium (see table):
| Plasma | Density ne(m3) |
Electron temperature T(K) |
Magnetic field B(T) |
Debye length λD(m) |
| Gas discharge | 1016 | 104 | -- | 10−4 |
| Tokamak | 1020 | 108 | 10 | 10−4 |
| Ionosphere | 1012 | 103 | 10−5 | 10−3 |
| Magnetosphere | 107 | 107 | 10−8 | 102 |
| Solar core | 1032 | 107 | -- | 10−11 |
| Solar wind | 106 | 105 | 10−9 | 10 |
| Interstellar medium | 105 | 104 | 10−10 | 10 |
| Intergalactic medium | 1 | 106 | -- | 105 |
http://www.pma.caltech.edu/Courses/ph136/yr2002/
Hannes Alfven pointed out that: "In a low density plasma, localized space charge regions may build up large potential drops over distances of the order of some tens of the Debye lengths. Such regions have been called electric double layers. An electric double layer is the simplest space charge distribution that gives a potential drop in the layer and a vanishing electric field on each side of the layer. In the laboratory, double layers have been studied for half a century, but their importance in cosmic plasmas has not been generally recognized.".
[edit] Debye length in a plasma
In a plasma, the Debye length is
where
- λD is the Debye length,
- ε0 is the permittivity of free space,
- k is Boltzmann's constant,
- qe is the charge on an electron,
- Te and Ti are the temperatures of the electrons and ions, respectively,
- ne is the density of electrons,
- nij'is the density of atomic specie i, with positive ionic charge jqe
The ion term is often dropped, giving
although this is only valid when the ions are much colder than the electrons.
[edit] Debye length in an electrolyte
In an electrolyte, the Debye length is
where
- I is the ionic strength of the electrolyte,
- ε0 is the permittivity of free space,
- εr is the dielectric constant,
- k is the Boltzmann's constant,
- T is the Temperature,
- NA is Avogadro's Number.
- e is the elementary charge,
or when mono-monovalent and symmetrical,
[edit] References
- Goldston & Rutherford (1997). Introduction to Plasma Physics. Institute of Physics Publishing, Philadelphia.
