An oscillating system typically has two states that store energy in different ways. For example a pendulum stores energy as either gravitational potential energy or kinetic energy, an LC oscillator stores energy either as charge in the capacitor or flux in the inductor. Resonance occurs when the frequency of a driving source matches the natural frequency of the oscillating system.
So in order to know how to build the resonating reactor Director proposes we need to know what two energy storing states the reactor or its contents would/could oscillate between? We would also need to calculate (or perhaps measure) the natural frequency in order to drive it at resonance.
There is some merit in the idea because at resonance a) the amplitude of oscillation is a maximum and b) the oscillator draws the maximum power from the driver. Eg it becomes easier to inject energy into the system.
Edit: I should add that the system should naturally "want" to trade energy between the two states. For example a pendulum naturally wants to accelerate when released with GPE. In a parallel connected LC oscillator a voltage on the capacitor causes an increase in current in the inductor.
There's a great deal of literature to comb through that discuss how the properties of circuits attached to a plasma tube in the negative resistance regime will effect the ion acoustic oscillations. This is good news. What's also good news is that if you have any electrical discharge that you are capable of keeping in the negative resistance regime (instead of letting the current rise to the point a true arc discharge with positive resistance is established) you will create a macro-EVO and ion acoustic oscillations. Then you can tune it to enhance these oscillations by changing the parameters of the circuit.