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.
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 ...
Get Electrothermics now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.