Plasma parameter

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:

:$Lambda\; =\; frac\; \{4pi\}\{3\}\; n\; lambda\_D^3$

where:"n" is the number density of particles,:λ_D is the Debye length.

Often the factor of $4pi/3$ is dropped. When the Debye length is given by $lambda\_D\; =\; sqrt\{frac\{epsilon\_0\; k\; T\_e\}\{n\_e\; q\_e^2$, the plasma parameter is given by [Miyamoto, K., Fundamentals of Plasma Physics and Controlled Fusion, (Iwanami, Tokyo, 1997)] :

:$Lambda\; =\; frac\{(epsilon\_0\; k\; T\_e)^\{3/2\{q\_e^3\; n\_e^\{1/2$

where: ε₀ is the permittivity of free space,: "k" is Boltzmann's constant,: "q"_"e" is the electron charge,: "T_e"is the electron temperature.

Confusingly, some authors define the plasma parameter as :

:$epsilon\_p\; =\; Lambda^\{-1\}$.

The ideal plasma approximation

One of the criteria which determine whether a collection of charged particles can rigorously be termed an ideal 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) [J.D. Callen, University of Wisconsin-Madison, Draft Material for Fundamentals of Plasma Physics book: Collective Plasma Phenomena [http://homepages.cae.wisc.edu/~callen/chap1.pdf PDF] ] . The equation of state of ideal plasma is that of ideal gas.

Plasma properties and Λ

The magnitude of Λ can be summarised below [See [http://farside.ph.utexas.edu/teaching/plasma/lectures/node8.html The plasma parameter] lecture notes from Richard Fitzpatrick] :

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 Inertial fusion experiments White dwarfs / neutron stars atmospheres	Ionospheric physics Magnetic fusion devices Space plasma physics Plasma ball

References