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The type 99 20mm cannon was available, and in in use by the IJN, from 1939 onward and used on such types as the A6M.Although not a great destructive power with Ki-43 2x12.7mm it is possible to damage a plane so much it was a written off as a wreck. There are many accounts I read of allied bombers making it back in shot up planes planes and injured or dead crewmen.
The Ki-61 started with German U-Boat imported 20mm MG/151 cannon in 10/1943, so there was no JAAF cannon for available for Ki-43 anyhow!
Using hindsight the Japanese best option would have been a big wing Ki-44 or Ki-84 "junior" using the same engine as the Ki-44.
ahh yes its like a big sub-machine gun?The type 99 could not be synchronized......)