Compute the electron diffusion coefficient in m2s-1

Question

Q1. A particular experiment (no magnetic field present) involves an electric discharge through helium gas at a pressure and temperature of 1 Torr (133.2 Pa) and 298 K respectively. The discharge is contained in a long, slender tube, so that any diffusion of electrons can be assumed primarily radial, and any electric field driven motion is primarily axial, resulting in a current between the electrodes. A luminous region of this discharge, called the "positive column," contains electrons with a temperature of T_e = 2 eV. The electron-neutral collision cross section for 2 eV electrons in He is about 6πa_o², where a_o = 0.53⋅10^-8 cm is the radius of the first Bohr orbit of the hydrogen atom.

a) Compute the electron diffusion coefficient in m²s^-1 assuming that (σV), averaged over the electron velocity distribution, is just equal to σV_e, where V_e is the velocity the electrons would have if accelerated to a kinetic energy of 2 eV.

b) If the current density in the column is J = 2 kA/m² and the plasma density is 10¹⁶ m^-3, what is the electric field along the column?

Q2. A common plasma probe design involves the use of a small piece of exposed wire. For this problem, assume the probe geometry is a cylinder of diameter d = 2 mm and exposed length L = 5 mm. The probe collects plasma from the exposed sides and tip. The probe is immersed in a xenon plasma with electron temperature of 3.5 eV. The xenon ion mass is m_i = 2.18⋅10^-25 kg.

a) If the probe collects 1 mA of ion current, what is the plasma density?

b) Two characteristic sizes for this experiment are the probe radius (for the probe) and the Debye length (for the sheath). Based on these two characteristic sizes, do you think the sheath can be considered "thin" with respect to the probe? Justify your answer.

c) If the probe is at the plasma potential, what is the electron current collected?

d) If the probe is at the floating potential, what is the electron current collected?

e) If the probe is at the floating potential, what is the ion current collected?

Attachment:- Assignment File.rar