Ambipolar diffusion
Under ambipolar diffusion refers to the coupled, rectified diffusion of positive and negative charge carriers in the rectified concentration gradient. It is a special case of diffusion in mixtures of free or quasi-free particles with electrically charged components and occurs in particular in plasmas .
The limitation to a stationary plasma model with electrons and simply positively charged ions is sufficient to explain the process . Their concentrations are accordingly or .
Due to the quasi-neutrality, these are approximately the same:
- .
From this it follows that the following also applies to the concentration gradients, which are necessary prerequisites for every diffusion:
- .
As a result, electrons and ions diffuse in the same direction. However, due to their lower mass and correspondingly higher thermal speed , electrons tend to equalize their concentration many times faster than the ions, so the diffusion coefficient applies
- .
This creates space charges and corresponding electric fields that slow the electrons and accelerate the ions. In steady state, both species diffuse with the same particle current density ,
- ,
so that no cargo is transported net.
Since the concentration gradients are also the same, there is a common diffusion coefficient, the ambipolar diffusion coefficient . To determine this, the diffusion is considered in only one direction, for example in the case of a spark in the radial direction :
- ,
where the mobilities of the particles are and are a common function of the electric field strength .
Inserting the common sizes and and eliminating results in
and after coefficient comparison with a general diffusion equation, the ambipolar diffusion coefficient
- .
literature
- Ulrich Stroth: Plasma Physics: Phenomena, Fundamentals, Applications . Vieweg 2011, ISBN 978-3-8348-1615-3 , limited preview in Google Book Search.