I'm not sure I buy into that photon ignition explanation, but the way to test it would be to entirely block the path to the upper stage with a clean clear Pyrex glass slide, and test the upper stage ignition probability.
This may be like arguing how many angels can dance on the head of a pin, but so be it,
I think the plexiglass test would fail. I was thinking of an opposite test, a mesh screen that would allow gas to go through but not particles.
Logically I think it makes more sense than particle theory especially when you consider long gap staging.
I’ve done over 6 feet with a 24mm D motor on a test stand, although it failed in flight. I’ve don’t over 50 inches in flight, both successful.
Ducting and venting is essential in long gap staging whichever theory you want to use. You have to get a concentrated bonus of hot gas and/or particles from the booster to the sustainer nozzle.
There is no way to vent THROUGH the nozzle, it’s essentially a deep bowl with no outlet, so the best you can do is vent just below the nozzle out the side (or all sides, I leave a gap of about 1/8” between the upper end of the extended booster motor tube and the butt of the sustainer motor.
So all the gas and particles make it TO the nozzle, but the particles are going to go out the sides (could inertia drive a particle into the nozzle? Yes, but at 6 feet it would have to be well aimed, have enough mass to deviate from the flow stream which is going out the sides, and enough fire to light the powder. It just seems a bit unlikely that a flaming particle will follow the stream all the up the length of the extended motor mount tube and then suddenly deviate due to inertia fortuitously into a closed space.)
BUT, now imaging a ball or stream of flaming hot gas that reaches up to but NOT into the nozzle. This burning gas is emitting a sphere of outwardly streaming hot photons in all directions. While the jet stream affects the flow of the gas, it does NOT affect the directions of the photons emitted BY the gas. If I can get that ball to just below the nozzle, the concentration of photons is hopefully sufficient to light the powder, even if it is spread roughly spherically around the gas cloud.
Ducting and venting do two things in long gap staging.
First, you have a dead space of air temperature gas between the motors that, if allowed to compress, may blow the stages apart before the gas/particles arrive.
Second, the combination guides the gas/particle cloud to the opening of the nozzle.