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RESEARCH PRODUCT

Subharmonic excitation of the eigenmodes of charged particles in a Penning trap

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When parametrically excited, a harmonic system reveals a nonlinear dynamical behaviour which is common to non-deterministic phenomena. The ion motion in a Penning trap -- which can be regarded as a system of harmonic oscillators -- offers the possibility to study anharmonic characteristics when perturbed by an external periodical driving force. In our experiment we excited an electron cloud stored in a Penning trap by applying an additional quadrupole r.f. field to the endcaps. We observed phenomena such as individual and center-of-mass oscillations of an electron cloud and fractional frequencies, so-called subharmonics, to the axial oscillation. The latter show a characteristic threshold behaviour. This phenomenon can be explained with the existence of a damping mechanism affecting the electron cloud; a minimum value of the excitation amplitude is required to overcome the damping. We could theoretically explain the observed phenomenon by numerically calculating the solutions of the damped differential Mathieu equation. This numerical analysis accounts for the fact that for a weak damping of the harmonic system we observed an even-odd-staggering of the the different orders of the subharmonics in the axial excitation spectrum.