Electrothermics

2.5. Generator model

2.5.1. Triode generator

The working frequency of radiofrequency inductive plasmas is higher than the bandwidths of transistor generators: we must then use triode generators. Figure 2.25 shows the schematics of a triode generator operating at 5 MHz and 32 kW. This generator consists of a triple-phased graduator, a transformer, a diode rectifier, a feed back circuit, and the adaptation circuit.

Figure 2.25. Triode generator circuit at 5 MHz

The graduator, transformer, rectifier, and filter part of this generator are meant to deliver a continuous voltage U, applied at the oscillatory anode. From this voltage, the generator is modeled. This hypothesis of a continuous voltage is the only one made, with no other simplifying hypotheses.

2.5.2. Modeling the HF generator in the steady state

To study the generator’s transient state, we can use the state variables method [ERN 94, PLO 96]. For the generator shown in Figure 2.25, the state equations are nonlinear. We must then use the Runge-Kutta method to solve the system of equations. However, the model requires many hours before converging. The computation time is too high, and coupling this simulation with the torch’s simulation can only be done for some operating points. The model also has problems with convergence at rest (i.e. without plasma).

Furthermore, while the state variables method allows us to know the generator’s ...