What happens to the ions after excitation?
The ions at very high cyclotron radii will collide with background gas in the vacuum and their radii will exponentially decrease. It is in fact this exponential decay of the transient that is detected by the detection plates and then converted into a mass spectrum. Hence the Fourier Transformation does include this exponential decay term. If you want to know more about the theory of FT-ICR, please go to the Theory section, where I have put together a whole range of mathematical equations.