Unit conversion problem for the electron thermal conductivity

Hello.



In CGS unit electron thermal conductivity for plasma is expressed as [itex]\frac{n_{e}T_{e}}{m_{e}\upsilon_{e}}\Gamma_{1}[/itex] [1] where [itex]\Gamma_{1}[/itex] is the dimensionless transport coefficient. [2]

You can also find similar expression in http://ift.tt/1mNmgbl



[itex]n_{e}[/itex]: electron number density in [itex]cm^{-3}[/itex].

[itex]T_{e}[/itex]: electron temperature in erg.

[itex]m_{e}[/itex]: electron mass in g (gram).

[itex]\upsilon_{e}[/itex]: electron-ion collision frequency.



Experimentally, SI unit is useful and I've tried to convert unit of the formula to Si unit of [itex]Wm^{-1}K^{-1}[/itex] but failed.



I directly replaced erg by [itex]gcm^{2}/s^{2}[/itex](= erg) and arranged dimensions in the formula. The results is [itex]cm^{-1}s^{-1}[/itex].



This appears far from what is supposed to be in SI unit.



Could you help me to figure out what I was wrong in conversion?



Thanks for reading this thread.



Reference

1. A. Esaulov, P. Sasorov, L. Soto, M. Zambra, and J. Sakai, "MHD simulation of a fast hollow cathode capillary discharge",
   
   Plasma Phys. Control. Fusion 43, 571 (2001).


2. E.M. Epperlein and M.G. Haines, "Plasma transport coefficients in a magnetic field by direct numerical solution of the Fokker-Pianck equation", Phys. Fluids 29, 1029 (1986).