I can see why Bedini might think there is some radient energy after looking at the pulse on the scope. There is an faint aura around it. It probably has something to do with the cemf spike, but it's there before, after, above and below.
I think I've gone about as far with this version as I can go. I've got a few ideas on fine tuning the pulse, now that I have some working experience with it, but the platform will have to be modified.
For instance, Bedini's system operates on repelling the magnet from the center of the core. His iron core attracts the magnet to the center. But the iron core also attracts the magnet back as it moves past the center, so he has to use weak magnets. On the permogator, with the air core, the repelling field is on when the magnet approaches the center of the core, so it isn't being attracted; rather the field is retarding its progress but since the field is weak the momentum carries it through. But with no iron to pull it back on the other side, a strong magnet gets a strong kick out of the weak core. It's a trade off. I can't say which works better in this configuration.
With the air core, I can see there may be some more options to manipulate the coil field timing and to use even stronger magnets and their momentum. But I'll probably have to build a new platform to test it.
I think the trigger wave can be advanced so that it occurs entirely before the magnet reaches the center of the core by pulling the trigger circuit out and putting it in another coil. Keep in mind, that the strong reaction involves the center of the magnet and the center of the core where the density is strongest. If the polarity of the circuit is set to attract, then there will be a strong attraction of the magnet to the center of the core with a final kick right where the density is great and then the attraction can be stopped by chopping the current just before it reaches dead center, letting the magnet coast across the center, so as not to retard. Then it seems like another switch could be set up on another coil/transistor combo to discharge a capacitor in the repelling direction as the magnet is carried beyond the center. That would give it two strong kicks, each close to and on either side of the dense fields and with no retarding effect at all, using the same input power. It should jump the output power quite a bit.