Yes, PMGs I recognize from my work with turbine engines... Another thing I don't get - why if the battery dies will the bike stop running? Doesn't a car keep going if the battery is dead once boosted? Is that because the alternator would be keeping it going in that scenario, vs a bike with a bad charging system?
PMGs are permanent magnet generators. They are always magnetized and only need rotation to create power.
Electromagnets are only magnetized when provided power. The SOHC4 has an electromagnet (field coil and rotor).
The ignition circuit needs power to make spark. A dead battery can't provide power for spark or energize the field coil. Therefore, no spark.
While a spinning alternator can provide enough power to self excite after jump starting, it has to provide more power than the bike is using. If you turn off non-essentials, and if the rotor is spinning fast enough, the motor will keep running. However, if rpm drops low enough to starve field coil and ignition, the bike will stop.
However, doing so has some risk involved. The battery absorbs and stabilizes the voltage output spikes from the alternator. Without it, the alternator can create voltage spikes far higher than with the battery present. These voltage spikes can harm or weaken the rectifier diodes. You can jump off some cliffs safely. You cannot jump off all cliffs safely.
There is no good reason to add stress to your electrical system unnecessarily.
But, people do foolish things and often get away with it. Doesn't prove there is no cost in all cases.
A car's alternator spins fast enough (pulley ratios) to provide all the power the car needs at idle RPM.
The SOHC4 alternator doesn't normally provide enough power for max consumption at idle, and draws from the battery to keep systems working.
Most people don't buy these bikes to sit around idling all day.
Cheers,