Debye Length - but where it is...

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Debye Length A parameter which is important when one considers plasma is the scale size within the plasma over which a particle "los which a particle "loses its identity". We call this scale size the Debye length. Below this scale size we see the individual particles (with a probing radar, for example), but above this the particles are seen as an interacting "whole" - a fluid or as wave motions in the plasma. Another way of looking at it is that the Debye length: is analogous to the free mean path above, so if we take a box this has a statistical variation in N e (the electron density) comparable to (N e -N + ), which is the more formal definition. Using the identity scale size argument, however,we can see how to get something approaching the derivation of the Debye length. (To do this properly takes more work than we need to put in here: we are just trying to get a feel for its meaning and rough size.) For an "unshielded" charge (or close to one in a plasma) the electric field falls off as:
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Unformatted text preview: but where it is "shielded" by other charges in a plasma we might expect there to be an exponential fall off with a scale size given by the Debye length: Taking a volume within that Debye length: This contains charge: And g/3C37-17c.gif"> And we have a potential energy here (at of: where Q is the charge contained in the volume, given above, hence the potential energy is: We can set take it that if this potential energy equals the kinetic energy of a particle passing this point that anything outside this distance can "escape" the central charge. Thus the point at which the potential energy balances the kinetic energy is a sort of "sphere of influence" of the central charge. The Kinetic energy of a particle is given by 3kT/2, so setting this equal to the p.e. above and rearranging, we have: This is the same as the "proper" equation for the Debye Length given above apart from a numerical factor....
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Debye Length - but where it is...

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