For this answer, we're going to assume that the type of radiation to which you refer is Cherenkov radiation, which is a type of radiation emitted by a charged particle going through a dielectric medium at a speed that is greater than the speed of light in that medium.
(For clarification: "Charged particle" means particle with positive or negative electric charges; dielectric medium means something, such as a container of water, that does not conduct electricity, but takes on an electrically positive and an electrically negative pole when subjected to electric currents.)
The Oxford Dictionary of Physics gives a great analogy for Cherenkov radiation - it's like a sonic boom. A sonic boom is created when something travels in a medium faster than the speed of sound, say a plane traveling in air, and leaves a loud trailing boom. In the case of Cherenkov radiation, the charged particle or particle beam is the thing that travels, the dielectric medium is the "air", and the radiation is the "boom" left behind the traveling thing.
Most of the time, the radiation is very short-lived, so while it can be used to measure certain phenomena, its potential as a power source is very low, not to mention that in order to generate Cherenkov radiation, a large amount of energy needs to be used to send the charged particle or particle beam into a medium at such a high speed. Therefore, using Cherenkov radiation as a power source would be extremely energy-inefficient.
Hope this helps!
In theory yes- the first law from the field of thermodynamics says energy cannot be created or destroyed. It can, however, be converted from one form to another. This is what we currently due to generate power, since electric power is not something that really exists in a usable form in nature. Historically, we have taken chemical potential energy (in the form of fossil fuels), burned it to create thermal energy, used that thermal energy to turn a turbine that creates kinetic energy, and used magnets in that turbine convert the kinetic energy into electricity.
Tying back to your question specifically- the light from Cerenkov radiation occurs when a particle in a dielectric moves faster than light in the same medium (note- nothing will travel faster than the speed of light in a vacuum, but when traveling through a non-vacuum, such as a dielectric, light can be slowed down and a particle can travel faster). This phenomena emits light. Given this is a form of energy (particle motion and light), a process could be designed to convert it to a usable form of power for humans. Practically speaking however, I doubt it will be a feasible source of power, as generating and harvesting it would likely use more energy than you get from the process.
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