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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 {4\pi}{3} n \lambda_D^3


n is the number density of particles,
λD 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}}


ε0 is the permittivity of free space,
k is Boltzmann's constant,
qe is the electron charge,
Teis the electron temperature.

The natural logarithm of the plasma parameter, lnΛ, is the Coulomb Logarithm.

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]:

DescriptionPlasma parameter magnitude
CouplingStrongly coupled plasmaWeakly coupled plasma
Debye sphereSparsely populatedDensely populated
Electrostatic influenceAlmost continuouslyOccasional
Typical characteristicCold and denseHot and diffuse
ExamplesSolid-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


  1. ^ Miyamoto, K., Fundamentals of Plasma Physics and Controlled Fusion, (Iwanami, Tokyo, 1997)
  2. ^ J.D. Callen, University of Wisconsin-Madison, Draft Material for Fundamentals of Plasma Physics book: Collective Plasma Phenomena PDF
  3. ^ See The plasma parameter lecture notes from Richard Fitzpatrick
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Plasma_parameter". A list of authors is available in Wikipedia.
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