Why Is Sideband Mass Spectrometry Possible with Ions in a Penning Trap?

Many masses, particularly the masses of unstable nuclei, are measured with ions in Penning traps by determining the frequency of a driving force that most efficiently couples two of the three motions of trapped ions. A missing explanation of why such sideband mass spectroscopy works, contrary to simple estimates, begins with the established Brown-Gabrielse invariance theorem.