Ionised Air Battery: Can a Potential Difference Exist?

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Radioactive materials ionize the surrounding air, and carbon nanotubes, with their large surface area, may store the ionized charge. Wrapping carbon nanotubes around an insulated radioactive core raises the question of whether a potential difference could exist between the two. Managing charge effects near a radioactive core presents significant challenges. There have been attempts to convert radioactivity into electric power by using radiation to excite phosphors, which then drive solar cells. While the efficiency of this method is low, it is considered safe and robust.
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Radioactive material ionises the air around it.
Carbon nano tubes have an extremely large surface area, & could possibly "store" the ionised charge.
If a volume of carbon nano tubes is wrapped around a core of insulated radioactive material, can a potential difference exist between the wrapping & the core?
 
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Charge effects are challenging to manage, especially within a short radius of a radioactive core.
There have been efforts to harness radioactivity to create electric power directly by using the radiation to excite a phosphor. The emitted light then drives solar cells which produce electric power. The overall efficiency here is not high, but the setup is reasonably safe and robust.
 
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