|
|
| Line 1: |
Line 1: |
| {{expert|date=August 2012}}
| | Sculptor Gaye from Ingersoll, has hobbies and interests such as legos, free coins fifa 14 hack and crossword puzzles. Finds motivation through travel and just spent 4 days at Pisa.<br><br>My homepage: fifa 14 hack no survey ([https://www.youtube.com/watch?v=HSoNAvTIeEc click over here]) |
| {{citations|date=August 2012}}
| |
| | |
| In a [[Plasma (physics)|plasma]], the '''Boltzmann relation''' describes the [[number density]] of an [[isothermal]] [[charged particle]] [[fluid]] when the thermal and the electrostatic forces acting on the fluid have reached [[Mechanical equilibrium|equilibrium]].
| |
| | |
| In many situations, the electron density of a plasma is assumed to behave according to the Boltzmann relation, due to their small mass and high mobility.<ref name="Chen">{{cite book |title=Introduction to Plasma Physics and Controlled Fusion |last=Chen |first=Francis F. |year=2006 |publisher=Springer |edition=2nd |page=75 |isbn=978-0-306-41332-2}}</ref>
| |
| | |
| ==Equation==
| |
| | |
| If the local [[electrostatic potential]]s at two nearby locations are φ<sub>1</sub> and φ<sub>2</sub>, the Boltzmann relation for the electrons takes the form:
| |
| | |
| :<math>n_e (\phi_2) = n_e(\phi_1) e^{- (\phi_2-\phi_1)/k_B T_e}</math> | |
| | |
| where ''n''<sub>e</sub> is the electron [[number density]], ''T''<sub>e</sub> the [[temperature]] of the plasma, and ''k''<sub>B</sub> is [[Boltzmann constant]].
| |
| | |
| ==Derivation==
| |
| | |
| A simple derivation of the Boltzmann relation for the electrons can be obtained using the momentum fluid equation of the two-fluid model of [[plasma physics]] in absence of a [[magnetic field]]. When the electrons reach [[dynamic equilibrium]], the inertial and the collisional terms of the momentum equations are zero, and the only terms left in the equation are the pressure and electric terms. For an [[Isothermal flow|isothermal fluid]], the [[pressure]] force takes the form
| |
| :<math>F_{\rm fluid}=-k_BT_e\nabla n_e,</math>
| |
| while the electric term is
| |
| :<math>F_{\rm electric}=e n_e \nabla\phi </math>.
| |
| [[Integral|Integration]] leads to the expression given above.
| |
| | |
| In many problems of plasma physics, it is not useful to calculate the electric potential on the basis of the [[Poisson equation]] because the electron and ion densities are not known ''a priori'', and if they were, because of [[Plasma (physics)#Potentials|quasineutrality]] the net charge density is the small difference of two large quantities, the electron and ion charge densities. If the ion density is known and the assumptions hold sufficiently well, the electric potential can be calculated simply from the Boltzmann relation.
| |
| | |
| ==Inaccurate situations==
| |
| | |
| Discrepancies with the Boltzmann relation can occur, for example, when oscillations occur so fast that the electrons cannot find a new equilibrium (see e.g. [[plasma oscillation]]s) or when the electrons are prevented from moving by a magnetic field (see e.g. [[lower hybrid oscillation]]s).
| |
| | |
| ==See also==
| |
| *[[List of plasma (physics) articles]]
| |
| | |
| ==References==
| |
| *{{cite book
| |
| | last = Wesson
| |
| | first = John
| |
| | coauthors = et al.
| |
| | year = 2004
| |
| | title = Tokamaks
| |
| | publisher = Oxford University Press
| |
| | isbn = 0-19-850922-7
| |
| }}
| |
| {{Reflist}}
| |
| | |
| ==External links==
| |
| | |
| [[Category:Plasma physics]]
| |
| | |
| {{physics-stub}}
| |
Sculptor Gaye from Ingersoll, has hobbies and interests such as legos, free coins fifa 14 hack and crossword puzzles. Finds motivation through travel and just spent 4 days at Pisa.
My homepage: fifa 14 hack no survey (click over here)