This page is currently text only. I'm planning on finding some links and creating some images to help clarify the explanations. I'll probably put some equations in here as well.
Homopolar generators(HPGs) take mechanical energy and convert it into electrical energy. They consist of a large metal disk rotating in a magnetic field oriented along the axis of the disk. The motion of the conducting metal disk within the magnetic field generates a voltage. A sliding contact, or brush, on the axis and the circumference of the disk allows this voltage to generate a current through any given load. HPGs are capable of generating very high currents but only low voltages.
HPGs are based on the principle that any moving conductor in a magnetic field will generate a voltage which is proportional to the speed of the conductor, the strength of the field, and the length of the conductor. The simplest such conductor is a single wire moving in a direction that is both perpendicular to its length and the magnetic field. If you take this conductor and hold on end and allow it to swing around this end, the average speed is used to calculate the voltage. This speed is one-half the speed of the other end (or tip speed). You can add more and more of these wires until you have a solid metal disk. This spinning disk will generate a voltage difference between the center and the edge.
If you mount this disk on a shaft and place a sliding contact on the brush and another on the edge of the disk, you can use this voltage. If you connect a load (any electrical device) to these two contacts, you will draw a current. Once you start drawing a current, the disk will begin to slow down. This force is produced by the current in the disk moving through the magnetic field.
Any current flowing in a magnetic field will generate a force which is perpendicular to both the current and the field with a magnitude proportional to the current and the field. In an HPG, this force will act to slow the disk down. If you don't have an external motive force acting on the disk, it will eventually slow to a stop. If you take a heavy solid metal disk and spin it up to a very high speed and then hook it up to something, it will supply current until the force overcomes the inertia of the disk. This is a basic flywheel battery. Such flywheel batteries can have a very high energy density.
Because these generators can produce very high currents and are limited to low voltages, they are well suited to applications, such as railguns, which require such power. Unlike most chemical batteries, HPGs can discharge very fast without harming the device.