Randy, I apologize for the long delay in replying, knee and foot surgeries have keep me a bit occupied. What I have found in researching is that there a lot of studies using gamma and x rays for pest control in the food industry. Most interesting to me was the Sterile Insect Technique which may work in controlling the Varroa mite, unfortunately testing would require a willing lab and government grants that are beyond the scope of most beekeepers ability to access. Below are two links that seem to have some fairly solid data on the subject. 
     http://www-naweb.iaea.org/nafa/ipc/crp/Biocontrol_final.pdf
https://www.iaea.org/About/Policy/GC/GC56/GC56InfDocuments/English/gc56inf-3-att1_en.pdf 

Cheers and good health 

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