Dynamos produce power measured as a combination of voltage and current (watts.) When charging a battery the dynamo voltage must be above that of the battery for a current to flow, just as water will only flow from a higher pressure (which could just be height) to a lower.
Dynamos convert external power to electrical power. The field coil, when electric current flows through it, makes the outer iron frame into an electro-magnet. The iron armature completes the magnetic circuit, just like putting a nail across the end of a horseshoe magnet. The more current flowing in the field coil, the stronger the magnet until a maximum, dependent on the metal inside the coil, is reached.
If smoke or flames are coming out of the dynamo, this is a clear indication that it is faulty! Discontinue immediately and either replace or investigate… but the dynamo is probably beyond economic repair.
A simple dynamo check is to disconnect both field and power connections ensuring that they don’t short to surrounding metalwork in case there is also a regulator fault. The tractor is started at low speed (about 600 RPM), the voltage between power and ground measured (typically often 2 to 4 volts), then the field and power terminals linked. The voltage should rise (possibly to around 8 or 9 volts.)