How does the fractal tree index work when moving data to disk?

I study fractal tree indexes, such as those found in TokuDB . I am passionate about the strategy that he uses to write fast by writing to the processor cache most of the time and rarely writing slow RAM memory. However, the index of the fractal tree must ultimately make large writes to RAM, and then the giant writes to disk, and then completely writes completely to disk. I'm embarrassed here. Can this fractal tree metric do this efficiently? More efficiently, say, can a B-tree update a disk in updating the worst case scenario? In addition, what is the effect of gigantic overwriting on disk when looking for time for this data? And, conversely, what effect does a few searches on this data do during a gigantic rewriting?

As a context for answering this you should know:

• Everything I learned about fractal tree indices I learned in this slide presentation
• I do not have a good mental model for the spinning machine's hard drive.
• When I say “giant rewrite”, basically what happens is that you have two sorted arrays of the same length (size 2^largeNumber), and you write them into one array (size 2^(largeNumber+1)), which is sorted.