Up: Main body of lecture 30: Plasma propulsion
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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
where
is the Dirac delta function.
- For
, the exponential can be expanded to give
- The Debye length has been introduced.
- The spherically symmetric solution is
John F Santarius
Fri Apr 19 23:02:29 CDT 1996