Characterization of the 1st Mathieu stability regime in auto-ponderomotive Paul-trap-like electron guides

We demonstrate a detailed study of the 1st Mathieu stability region for an electrostatic auto-ponderomotive electron guide. Analog to a radio frequency-driven linear quadrupole mass filter, we find a roughly triangular stability region spanning the dimensionless a-q parameters in Mathieu space. In our experiments, we achieve stable guiding for a≤ 0.16 and 0.03 ≤q≤ 0.77. According to simulations, the pseudopotential trap depth was 0.44 eV, sufficient to confine guided electrons inside the trap radius of (290 ± 2) μm. Additionally, we detect an instability inside the guiding regime, which is due to parametric nonlinear excitation and matches well with simulation results. Our detailed study substantially improves the understanding of auto-ponderomotive guiding for charged particles. Most importantly, it shows that these electron guides, indeed, behave very similar to radio frequency Paul-trap-like quadrupole mass filters, thus might enable electron-optical elements such as electron beam splitters and electron resonators.