MadSci Network: Physics

Re: What equation is used to determine the resistivity of a plasma?

Date: Tue Aug 2 17:05:33 2005
Posted By: Kenneth Beck, Senior Research Scientist, Chemistry and Physics of Complex Systems, Pacific Northwest National Laboratory
Area of science: Physics
ID: 1117378612.Ph

Dear Jordan,

The conductivity for a material, such as a semiconductor, can be 
expressed as¡K

sigma = q*n*m  


m = u/Ea = electron mobility (cm^2/Vs)
n = electron charge
q = average number density
u = average electron velocity (cm/s)
Ea = applied electric field (V/cm)

The resistivity, R, as you probably know, is inversely proportional to 
the conductivity, sigma, such that...

R= L/(sigma*A)


L= length of the material (cm)
A= cross-sectional area of the material (cm^2)

In a collisionless plasma, the resistivity was previously believed to be 
due to particle scattering by unstable acoustic waves driven by applied 
electric and magnetic fields.  In fact, clumps of electrons and ions form 
apparently in these acoustically-driven plasmas.  These clumps act as if 
they were single particles ¡V ¡§macroparticles¡¨!  These macroparticles then 
collide and scatter from one another.  This adds a dynamic dragging 
factor to the conductivity of the plasma, so that¡K

sigma = q*n*uƒn/(-Edrag) =  q*n*uƒn/(E0) (units of cm^-1*ohm^-1)


E0= -Edrag(electron ¡§drag¡¨) (V/cm)

The calculation of the electron "drag" in an active plasma is a complex 
affair, beyond the mathematical tools you have been equipped with in 10-
12 grade.

Hope this help,

---* Dr. Ken Beck

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