Wednesday, 27 July 2016

kinetic theory - How much do we know about the characteristic time for electron-ion recombination for a dense plasma?


As mentioned, how much do we know about the characteristic time for electron-ion recombination for a dense (noble gas) plasma (i.e. density of electrons at 1021cm3) at 10000K (i.e. at around 1eV)?


The dominant mechanism for electron-ion recombination at this temperature and density for a thermalised plasma seems to be three-body recombination (or dielectronic recombination). The mentioned process is the backward process as represented in the equation, X+eX+1+e+e, where X denotes the participating atom. The cross section of its inverse process, electron impact ionization, has been measured experimentally (probably at a low density of X), and the rate of this inverse process can be obtained from the cross section (i.e. $\approx ,where<\cdots>denotesathermalaverageovertheenergyoftheimpactingelectron,vthethermalvelocityoftheimpactingelectronand\sigma$ the cross section). It seems that the rate of three-body recombination can be obtained from the principle of detailed balance.


The problem is that the density effect of X has been ignored. It seems that we are extrapolating the cross sections at low densities of X to obtain the cross sections at high densities of X. Of course the obtained cross sections for Xenon for example, are about (PRA, 65, 042713, doi:10.1103/PhysRevA.65.042713) 1016cm2, which suggests a length 1010m. The average separation between the atoms seems to be greater than this value at 21×1021cm3, and so the density effect may be unimportant. Yet the argument is ad-hoc.


Is there any reason to believe that the electron-ion recombination time (or rate) will be significantly different from the one obtained using the above procedure? ("significantly" means the correct time will be several orders larger/smaller than the calculated time). Thanks.





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