Electrothermics

3.5. Plasma stability in the transitory and sinusoidal states

3.5.1. Transitory state

Solving the general equation [3.11] in space and time allows us to obtain the stability criterion in the transient state and, more specifically, in the sinusoidal state. We assume that the phenomenon progresses from a stable initial state. The equation is then solved with an implicit method, in timesteps. The space discretization is done by the finite volume method as per the steady state:

[3.32]

where t is the timestep and T₀ is the value of the temperature in the previous time.

Figure 3.15 shows the evolution of the temperature of a plasma with a radius of 1 cm, for the minimum maintenance field value of 235 V/m and a field of 225 V/m, slightly less than the maintenance field. As expected, for fields under the maintenance field, the plasma extinguishes very quickly.

Figure 3.15. Evolution of the plasma’s maximum temperature

3.5.2. Sinusoidal state

The frequency of the inductor’s electric supply also impacts the plasma’s stability. Indeed, if the oscillations’ period is much larger than the plasma’s time constant, the electric field’s passage to zero can extinguish the plasma. Figure 3.16 shows ...