Up: Main body of lecture 30: Plasma propulsion
Derivation of the Debye length
-
In the electrostatic approximation, consider a distribution of electrons
that is immersed in a uniform background of positive ions and is in thermal
equilibrium with a potential
.
The density distribution is then a Boltzmann distribution - Imagine a test particle of charge Ze placed at the origin. Poisson's equation is then
-
For
,
the exponential can be expanded to give - The Debye length has been introduced.
- The spherically symmetric solution is
where
is
the Dirac delta function.
John F Santarius
Fri Apr 19 23:02:29 CDT 1996