I don’t know the exact process but I don’t think ammonium nitrate actually gets involved. The system I was looking at (Green Lightning) actually doesn’t make ammonia but rather liquid nitrogen fertilizer
Plasma to take N2 + O2 -> NO2 and NO gas
The NO and NO2 are dissolved in water to become HNO2 and HNO3, which then become NO2- and NO3- ions in the water.
It’s a low pH solution which stabilizes it and then you dilute right before application so that you don’t burn the crops.
That sounds like the Birkland-Eyde process. It's cool because it uses only electricity and air and seems to produce something from nothing, but it's not as efficient as Haber-Bosch.
That is the Birkeland-Eyde process, which was superceded by the Haber-Bosch process because it is much more energy effective.
As far as I understand, the reasons for using methane as the hydrogen source in industrial processes is because of costs and the difficulty in scaling electrolysis industrially.
I am curious what kind of plasma is used, as there are many ways to create plasma under various conditions, with very different efficiencies, selectivity, yield, etc.
Among the worst is the Birkeland-Eyde process, hot plasma by electric arcing, like it happens naturally during a thunderstorm. Even microwaving the air is more energy efficient. And amongst the most promising are transient non-equilibirum / cold plasma approaches using ns pulse generators.
Edit: So according to this video "Green Lightning" is indeed using the Birkeland-Eyde process. In other words, there is no way they even come close to their energy efficiency and yield claims. https://youtu.be/8TOnyAwJyvg?si=D9hat_XAfvuAAmpB&t=165