Commensurate cyclotron and axial oscillations
= Commensurate cyclotron and axial oscillations
{title2=$\Omega_z/\Omega_c=p/q$}
A rational ratio of axial and <cyclotron frequencies> makes a nondegenerate combined orbit close after an integer number of turns. For ratio $p/q$ in lowest terms it closes after $q$ transverse periods and $p$ axial periods. An integer ratio is a sufficient special case. An irrational ratio instead gives <quasiperiodic motion> when both component amplitudes are nonzero.