Injection radius in a Penning trap

Hello! When an ion is injected in a Penning trap, how well is its initial radius know? I understand that usually people use cooling mechanism to reduce that radius as much as needed, but I was wondering in the beginning, before the cooling starts, how small is the radius of the ion and how well is it know? Thank you!

Not sure I understand the question. It isn't known until it's measured. Typically the initial position of an ion depends on how it's loaded to the trap. I am sure the probability distribution for loading an ion would be very different in the ALPHA experiment compared to the electron g-2 measurement (for example).

The most general answer I can give is that the expectation value of the radial position of the ion is determined by the velocity distribution of the ions being loaded and trapping potential (if loading axially) or the strength of the magnetic field (if loading radially).