Plasma parameter: Difference between revisions

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The ''plasma parameter'' is a dimensionless number, denoted by capital Lambda, Λ. OneThe definition of thisplasma parameter is givenusually interpreted byto be the average numberargument of electronsthe inCoulomb alogarithm, [[plasmawhich (physics)|plasma]]is containedthe withinratio aof [[Debyethe sphere]]maximum (aimpact sphereparameter to the classical distance of radiusclosest theapproach in [[DebyeCoulomb_collision length|Coulomb scattering]]). NoteIn thatthis case, the wordplasma parameter is usuallygiven usedby<ref>Chen, inF.F., plasma physicsIntroduction to referPlasma toPhysics bulkand plasmaControlled propertiesFusion, in(Springer, general:New see [[plasma parameters]]. In this contextYork, the plasma parameter is defined as2006)</ref>:

:<math> \Lambda = \frac {412\pi}{3} n \lambda_D^3 </math>

where

:''n'' is the number density of particleselectrons,

:λ_D is the [[Debye length]].

This expression is typically valid for a plasma in which ion thermal velocities are much less than electron thermal velocities. A detailed discussion of the Coulomb logarithm is available in the ''NRL Plasma Formulary'', pages 34-35.

Note that the word parameter is usually used in plasma physics to refer to bulk plasma properties in general: see [[plasma parameters]].

An alternative 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]]).

This definition of the plasma parameter is more frequently (and appropriately) called the Debye number, and is denoted <math> N_D</math>. In this context, the plasma parameter is defined as

:<math> \LambdaN_D = 12\frac {4\pi}{3} n \lambda_D^3 </math>

Since these two definitions differ only by a factor of nine, they are frequently used interchangeably.

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

where

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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 ==

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) <ref>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]</ref>. The [[equation of state]] of each species in an ideal plasma is that of an [[ideal gas]].

== Plasma properties and Λ ==

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==References==

{{reflist}}

==External links==

[http://wwwppd.nrl.navy.mil/nrlformulary/NRL_FORMULARY_07.pdf NRL Plasma Formulary 2007 ed.]

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