I just finished playing the game "Star Wars the Force Unleashed" and this is where I get most of my points from. So Kyber crystals are a crystal right, they could not be used as fuel because of their melting point and the fact the death star runs of of beams of energy (possibly light) meaning it probably uses electricity. Kyber crystals refract light, that is why they are used in lightsabers. They take the raw energy and direct it making the blade of a lightsaber. In the game "Star Wars the Force Unleashed" it actually showed the inside of the death star and explained how it worked to you. Granted, it is a game and not the movie but it is official so it has some merit. In the game they said it used 64 "energy beams" split into 8 groups, each beam group having 8 smaller beams directed through each other creating one beam group (one of the 8 seen on the outside dish when firing), those beams then create the massive beam that destroys planets. While walking around you could see giant crystal structures (seen below) which they quoted as saying "They intensify and direct the beam"  

Also you broke through more crystal like walls that the beam passed through as seen below

Based on all of this I would say the kyber crystals are used to refract and make the death star beam stronger and more powerful. They use the term "fuel" loosely in the movie because they would have no way of truly knowing how it works without the plans.

I just finished playing the game "Star Wars the Force Unleashed" and this is where I get most of my points from. 

So Kyber crystals are a crystal right, they could not be used as fuel because of their melting point and the fact the death star runs of of beams of energy (possibly light) meaning it probably uses electricity. 

Kyber crystals refract light, that is why they are used in lightsabers. They take the raw energy and direct it making the blade of a lightsaber. 

In the game "Star Wars the Force Unleashed" it actually showed the inside of the death star and explained how it worked to you. Granted, it is a game and not the movie but it is official so it has some merit. In the game they said it used 64 "energy beams" split into 8 groups, each beam group having 8 smaller beams directed through each other creating one beam group (one of the 8 seen on the outside dish when firing), those beams then create the massive beam that destroys planets. 

While walking around you could see giant crystal structures (seen below) which they quoted as saying "They intensify and direct the beam" 

Also you broke through more crystal like walls that the beam passed through as seen below

Based on all of this I would say the kyber crystals are used to refract and make the death star beam stronger and more powerful. They use the term "fuel" loosely in the movie because they would have no way of truly knowing how it works without the plans.