The plasma parameter is a dimensionless number, denoted by capital Lambda, Λ, which measures the average number of electrons contained within a Debye sphere (a sphere of radius the Debye length) in a plasma (but note that the word parameter is usually used in plasma physics to refer to bulk plasma properties in general: see plasma parameters). It is defined as:
where
- n is the number density of particles,
- λD is the Debye length.
Often the factor of is dropped. When the Debye length is given by , the plasma parameter is given by[1]:
where
- ε0 is the permittivity of free space,
- k is Boltzmann's constant,
- qe is the electron charge,
- Teis the electron temperature.
The plasma approximation
One of the criteria which determines whether a collection of charged particles can rigorously be termed a plasma is that Λ>>1. When this is the case, collective electrostatic interactions dominate over binary collisions, and the plasma particles can be treated as if they only interact with a smooth background field, rather than through pairwise interactions (collisions) [2].
Plasma properties and Λ
The magnitude of Λ can be summarised below [3]:
| Description | Plasma parameter magnitude | |
| Λ<<1 | Λ>>1 | |
| Coupling | Strongly coupled plasma | Weakly coupled plasma |
| Debye sphere | Sparsely populated | Densely populated |
| Electrostatic influence | Almost continuously | Occasional |
| Typical characteristic | Cold and dense | Hot and diffuse |
| Examples | Solid-density laser ablation plasmas Very "cold" "high pressure" arc discharge White dwarfs / neutron stars atmospheres Plasma ball | Ionospheric physics Astrophysical plasmas Nuclear fusion Space plasma physics |
References
- ^ Miyamoto, K., Fundamentals of Plasma Physics and Controlled Fusion, (Iwanami, Tokyo, 1997)
- ^ J.D. Callen, University of Wisconsin-Madison, Draft Material for Fundamentals of Plasma Physics book: Collective Plasma Phenomena PDF
- ^ See The plasma parameter lecture notes from Richard Fitzpatrick