It’s usually a lot cheaper and safer to condense all that demand into a purpose-built facility where they can hire an engineer to look after all the generation, have centralized container storage, backup parts, etc.
None of that prevents putting the panels or windmills on farmer land, though. You could imagine some sort of “get a discount on ammonia if we can put a solar panel in your field” scheme. Or, even more simply, put up your own panels, sell the power back to the grid, use that money to buy fertilizer from the factory buying your power off the grid.
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.
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
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.
So this is pretty far outside of my area of expertise, but https://pmc.ncbi.nlm.nih.gov/articles/PMC8133363/ suggests that there may be an evolution of Birkeland-Eyde that isn’t nearly as bad as the original process was. I haven’t gone through this in detail and even if I had I probably don’t have the background to do it justice.