Plasma parameter: Difference between revisions

Revision as of 09:35, 31 July 2008

Revision as of 01:05, 25 March 2009

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The ''plasma parameter'' is a dimensionless number, denoted by capital Lambda, Λ,. which measuresOne definition of this parameter is given by the average number of electrons in a [[plasma (physics)|plasma]] contained within a [[Debye sphere]] (a sphere of radius the [[Debye length]]). in a [[plasma (physics)|plasma]] (but noteNote that the word parameter is usually used in plasma physics to refer to bulk plasma properties in general: see [[plasma parameters]]). ItIn this context, the plasma parameter is defined as:

:<math> \Lambda = \frac {4\pi}{3} n \lambda_D^3 </math>

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:λ_D is the [[Debye length]].

Often the factor of <math>4\pi/3</math> is dropped. When the Debye length is given by <math> \lambda_D = \sqrt{\frac{\epsilon_0 k T_e}{n_e q_e^2}}</math>, the plasma parameter is given by<ref>Miyamoto, K., Fundamentals of Plasma Physics and Controlled Fusion, (Iwanami, Tokyo, 1997)</ref>:

:<math> \Lambda = \frac{(\epsilon_0 k T_e)^{3/2}}{q_e^3 n_e^{1/2}} </math>

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:<math> \epsilon_p = \Lambda^{-1}\ </math>.

An alternative interpretation, and one more frequently encountered in scientific literature, defines Λ as the ratio of the maximum impact parameter to the classical distance of closest approach in [[Coulomb_collision |Coulomb scattering]]. In this case, the plasma parameter is given by<ref>Chen, F.F., Introduction to Plasma Physics and Controlled Fusion, (Springer, New York, 2006)</ref>:

:<math> \Lambda = 12\pi n \lambda_D^3 </math>

== The ideal plasma approximation ==