Source Coefficients

The source coefficients in the equations in the Electron Transport Theory section are determined by the plasma chemistry and are written using either rate or Townsend coefficients. Suppose that there are M reactions which contribute to the growth or decay of electron density and P inelastic electron-neutral collisions. In general, P >> M. In the case of rate coefficients, the electron source term is given by

where xj is the mole fraction of the target species for reaction j, kj is the rate coefficient for reaction j (SI unit: m3/s) and Nn is the total neutral number density (SI unit: 1/m3). When Townsend coefficients are used, the source term becomes

where αj is the Townsend coefficient for reaction j (SI unit: m2) and Γe is the electron flux as defined above (SI unit: 1/(m2·s)). Townsend coefficients can increase the stability of the numerical scheme when the electron flux is field driven as is the case with DC discharges.

The electron energy loss is obtained by summing the collisional energy loss over all reactions:

where Δεj is the energy loss from reaction j (SI unit: V). In the case of Townsend coefficients, the energy loss is given by

The energy loss due to inelastic collisions is the most important input parameter in the Drift Diffusion interface. If this is not correctly defined, severe numerical problems result.

The rate and Townsend coefficients kj and αj depend exponentially on the mean electron energy,

. When a Maxwellian EEDF is assumed, the rate and Townsend coefficients can be fitted with a function of the form:

The physics interface does not provide a way of calculating the rate or Townsend coefficients. The multiphysics interfaces for the most common types of reactor automatically compute the rate coefficients for each electron impact reaction based on plasma chemistry.