# What exactly is a "Resonating Electromagnetic Wave"

The first thing to determine is exactly what is a "resonating electromagnetic wave" and how do we produce one?

The most basic oscillator is the RLC circuit where R stands for resistance, L stands for inductance and C stands for capacitance. Below is a diagram of a pure LC circuit.

First, the capacitor is assumed to have a charge, designated by the + and the - minus symbol. When the circuit is closed, then the current flows from the positive terminal of the capacitor, around the loop to the negative side of the capacitor. On the physical level, the electrons go from the negative terminal to the positive terminal and the "holes" go from the positive terminal to the negative. As the current passes through the inductor, a magnetic field is produced and at the instant when the charge on the capacitor reaches zero, the current in the inductor reaches it's maximum. The magnetic field is also at it's maximum in the inductor and as it starts to collapse, the current is sustained and the charge on the capacitor starts to accumulate on the opposite plates (the + and - now reverse). When the current has reached zero, the capacitor again has obtained it's maximum charge, although opposite, and then it starts to discharge and the current flows in the opposite direction. If there is little resistance, then the current will continue to flow back and forth repetitively and is called LC oscillation or an electromagnetic oscillation. Not only does the charge oscillate back and forth, but so does the energy which oscillates between being stored in the electric field of the capacitor and in the magnetic field of the inductor.

In more concrete terms, the resonant frequency, fo is found by fo= 1/2pi (1/LC)1/2. In other words, when the capacitor "reactance", Xc is equal to inductive "reactance", XL, then the impedance, R, is purely resistive (and assumed to be zero in the diagram above).

Reactance in an inductor describes the effect that an inductor has on a changing current. In other words, if the inductor L is large, then the allowed rate of change of the current is small. A good analogy is to compare the current to the acceleration in a vehicle, if there is a high L, then the car will accelerate like a loaded semi-trailer, very slowly, but if there is a low L, then it is like a Porsche and it can accelerate quickly. Even like a vehicle, when the semi is up to speed, say 110km/h, then it takes a long time to come to a stop, hundreds of meters, but a Porsche can stop in a much shorter distance. If the inductor is large then the current is not allowed to rapidly change and the reactance is proportional to the inductance and proportional to frequency.

Capacitive reactance works in a similar but opposite manner because where inductance is about keeping the current moving and blocking large changes, and capacitance is about stopping the current and letting large changes through. If you have a large value of capacitance, then the voltage on the plates builds to it's maximum slowly which means if the voltage is changing rapidly it will not be blocked. A useful analogy is like trying to ride a bike. If you are moving, then you are like the current and don't fall over. If you stop, then you will fall over and the current stops. High capacitance makes it easier to ride slower and not fall over (stop the current) and low capacitance means you have to pedal faster just to keep upright.

The difference is simple to remember by knowing that an inductor always works to make the voltage zero and current maximum and the capacitor works to make the current zero and the voltage maximum.

However, back to Alan's theories, the RLC circuit cannot be what was referred to for the reason that the electric and magnetic fields are separate, the first builds up in the capacitor and the second in the inductor. The circuit is worth studying because it can be used to drive a true resonating EM wave.

What we need is an electromagnetic wave but unlike an antenna which transmits it's energy away, we need it contained. Wave guides are the next logical solution, however when you think of a waveguide, typically you think small. However, from the drawings in Daniel's books, the cargo carrier has both elements we need, the transmitting elements and the ship itself as the wave guide.

In other words, when the EM wave is transmitted from the solid rings at the top and bottom (not hollow, therefore, they are not waveguides themselves), the EM wave bounces around the inside of the ship and can add upon themselves. With the right frequency, determined by the size of the ship's cavity and it's contents, it should be possible to build up a high power resonating EM wave. For our experiments, it isn't necessary to build an "oblate spheroid" to test with because our test apparatus doesn't have to fly through the air.

To understand waveguides we have to start with the basics and a search of the internet turned up a great source, chapter 11 of the "Naval Electricity and Electronics Training Series" from the United States Navy, which you can get for free.