Plasma parameter

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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:

$\Lambda = \frac {4\pi}{3} n \lambda_D^3$

where

n is the number density of particles,

λ_D is the Debye length.

Often the factor of $4π / 3$ 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^[1]:

$\Lambda = \frac{(\epsilon_0 k T_e)^{3/2}}{q_e^3 n_e^{1/2}}$

where

ε₀ is the permittivity of free space,

k is Boltzmann's constant,

q_e is the electron charge,

T_eis the electron temperature.

Confusingly, some authors define the plasma parameter as :

$\epsilon_p = \Lambda^{-1}\$ .

[edit] 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) ^[2]. The equation of state of ideal plasma is that of ideal gas.

[edit] Plasma properties and Λ

The magnitude of Λ can be summarised below ^[3]:

Description	Plasma parameter magnitude
Description	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

[edit] 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