Khan didn't know how to apply the Niqols' approach to the Wave spell. He knew the theory behind Liiza's ice, but each element required a different method or process to express its power.
The Niqols couldn't help Khan there since none of them had the same element, so he could only try to fuse the human training program to the Niqols' approach to mana. He knew that changing the nature of that energy required strong emotions. Still, he was also aware that the Wave spell needed specific images, something deeply connected to an idea of destruction.
Needless to say, Khan's greatest drive had always been his desperation, and his experiences on different planets had only strengthened it. His nightmares, Istrone, everything that had happened on Nitis, and his current predicament had turned that feeling into the most powerful fuel that his mind was able to produce.