**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 thenwhere 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

Fri Apr 19 23:02:29 CDT 1996