Plasma Parameter

and the distance of closest approach,

Recall that is the distance at which the Coulomb energy

(18) |

The significance of the ratio is readily understood. When this
ratio is small, charged particles are dominated by one another's electrostatic
influence more or less continuously, and their kinetic energies are small
compared to the interaction potential energies. Such plasmas are termed
*strongly coupled*. On the other hand, when the ratio is large,
strong electrostatic interactions between individual particles are
occasional and relatively rare events. A typical particle
is electrostatically influenced by all of the other particles within its
Debye sphere, but this interaction very rarely causes any sudden change in its motion.
Such plasmas are termed *weakly coupled*. It is possible to
describe a weakly coupled plasma using a standard Fokker-Planck equation
(*i.e.*, the same type of equation as is conventionally used to describe a
neutral gas).
Understanding the strongly coupled limit is far more difficult, and will not
be attempted in this course. Actually, a strongly coupled plasma has more in
common with a liquid than a conventional weakly coupled plasma.

Let us define the *plasma parameter*

It can be seen that the case , in which the Debye sphere is sparsely populated, corresponds to a strongly coupled plasma. Likewise, the case , in which the Debye sphere is densely populated, corresponds to a weakly coupled plasma. It can also be appreciated, from Eq. (20), that strongly coupled plasmas tend to be cold and dense, whereas weakly coupled plasmas are diffuse and hot. Examples of strongly coupled plasmas include solid-density laser ablation plasmas, the very ``cold'' (

In conclusion, characteristic *collective*
plasma behaviour is only observed on time-scales
longer than the plasma period, and on length-scales larger than the Debye length.
The statistical character of this behaviour is controlled by the plasma parameter.
Although , , and are the three most fundamental
plasma parameters, there are a number of other parameters which are worth
mentioning.