Electrothermics

3.6. Advanced inductive plasma transformer model

The previous section was dedicated to the model and the sizing of the inductive plasma transformer using a simple model based on a preliminary one-dimensional (1D) study. This study has yielded interesting results regarding the maintenance conditions and the characteristics of annular plasma.

However, the 1D model cannot take into account variations in the electric field and temperature in the section and along the azimuthal axis of the torus containing the plasma. It also cannot model the different forms of magnetic circuits (i.e. circuits with one, two, or many arms).

To answer these questions, this section develops a more advanced study. This study, based on a 3D model, couples the mathematical models of electromagnetic and thermal phenomena. To simplify the model, we assumed a weak gas flow. The plasma is then static, and the flow equation becomes unnecessary. In a more precise study, and for a greater flow rate, we must introduce flow equations in the calculations and couple all the three physical phenomena.

3.6.1. Displacement current

In the study of electromagnetic problems in a conductive environment, we often ignore the displacement current J_d, which is very much smaller than the conduction term J_c. In the case of an inductive plasma, this is impossible. Indeed, the plasma’s temperature varies between about 1000 K at the quartz’ internal surface and 10,000 K at the center. The plasma’s electrical conductivity for both these ...