Plasma characteristics problem

[brad sue]

Hi,
Please I would like to have some hints on this problem (from plasma processing course):

a) Starting from Eq. (2.4.7) of the textbook, derive an equation for the Maxwell-Boltzmann distribution in terms of electron energy.

b) Calculate the rate of ionization of molecular chlorine as a function of mean electron energy using a Maxwellian EEDF and a Druyvesteyn EEDF. Plot the results for the energy range of 2-12 eV. (total cross ectiopn given in other document)

c) What fraction of electrons is capable of performing ionization of molecular chlorine for a Maxwellian EEDF with a mean energy of 3 eV ?

I just need to have some hints first (for question b and c )because, my background is not chemistry and I had to take an advance chemistry class. With some hints I will start working and come back with more work done.

So far I cannot find formula for ionization rate related to cross section.

Thank you

 

[Nino MMP]

!For part b), you need to calculate the ionization rate of molecular chlorine using both a Maxwellian EEDF and a Druyvesteyn EEDF. To do this, you will need to use the total cross section for ionization of molecular chlorine (given in the other document) to calculate the ionization rate at each energy level. The equation for the ionization rate is given by: Rate = σ(E) * n(E) * Vwhere σ(E) is the total cross section, n(E) is the electron density and V is the volume. In order to calculate n(E), you will need to use the Maxwell-Boltzmann distribution or the Druyvesteyn distribution, depending on which one you are using. Once you have calculated the ionization rate for each energy level, you can plot the results for the energy range of 2-12 eV. For part c), you can use the same equation for the ionization rate as in part b). All you need to do is to calculate the ionization rate for a Maxwellian EEDF with a mean energy of 3 eV. Then, you can calculate the fraction of electrons capable of performing ionization by dividing the ionization rate by the total number of electrons.