Electrothermics

3.3. Simplified analytical model for analysis and preliminary design

The first step in the analysis and design of a complex system is a preliminary step based on engineering techniques. For an inductive plasma transformer, we must put together a set of simplified analytical models regarding the electromagnetic, thermal, and flow equations. Combining these models gives an approximate prototype geometry, which is then refined with more precise numerical methods.

The analytical model used in this chapter is inspired by Eckert’s work [ECK 71]. This model extrapolates the maintenance and stability conditions from a cylindrical [EDE 65] to a toric plasma. To do this, Eckert imposes some hypotheses on the physical phenomena and system geometry. He also imposes that losses from radiation are negligible. This hypothesis results in fairly weak maintenance electric fields. For this reason, the model developed in this chapter takes radiation losses into account.

3.3.1. Hypotheses

Given the problem’s complexity, analytical study is only possible if based on some simplifying assumptions.

The first, well known, are to do with the inductive plasma:

– local thermodynamic equilibrium;

– negligible viscous dissipation;

– optically thin plasma;

– the Maxwell distribution of the particles’ velocities;

– plasma gas dominated by collisions.

Other hypotheses have to do with the physical phenomena and the geometry:

– annular plasma with a toric configuration (Figure 3.3);

– mean curvature plasma radius ...