Electrothermics

3.4. Nonlinear model

In the case of the nonlinear system, the equation of conservation of energy in the steady state is of the form:

[3.25]

with boundary conditions:

[3.26]

[3.27]

Equation [3.25] can be solved using the finite volumes method:

[3.28]

where the quantities with the indices w, p, and e represent the values calculated at the left of the current point, those calculated at the current point, and those calculated at the right of the current point, respectively.

Assembling this equation by taking boundary conditions into account, [3.26] and [3.27] result in the following nonlinear equation:

[3.29]

This equation is solved using the iterative algorithm in Figure 3.11.

Figure 3.11. Nonlinear model algorithm

3.4.1. Nonlinear model results

For a given temperature, if we reduce the electric field, we reduce the power injected in the plasma, defined by the term (T)E_e². Decreasing ...