A helium discharge in a low-pressure plasma-processing chamber has electron…

PHYSICS · Multi-part · Fermi University Physics · Plasma Physics · Kinetic theory, collisions and transport · Kinetic theory, collisions and transport

Plasma Physics, Ch Transport across and along the field: ambipolar, classical, neoclassical and anomalous

Problem

A helium discharge in a low-pressure plasma-processing chamber has electron temperature Te=3.0 eVT_e = 3.0\,\mathrm{eV} and ion temperature Ti=0.040 eVT_i = 0.040\,\mathrm{eV}. Measurements of ion mobility and collision frequency give an ion diffusion coefficient Di=0.020 m2 s−1D_i = 0.020\,\mathrm{m^2\,s^{-1}}. Near the wall the density falls off with gradient scale length Ln=5.0 cmL_n = 5.0\,\mathrm{cm}. Assume ambipolar diffusion with the electron mobility much larger than the ion mobility, so Da≈Di(1+Te/Ti)D_a \approx D_i(1 + T_e/T_i), and that the ambipolar field is E≈Te/(eLn)E \approx T_e/(eL_n). ((a)) Find the ambipolar diffusion coefficient DaD_a. ((b)) Find the magnitude of the ambipolar electric field needed to hold the electrons back.

Browse the problem library