Stability of ion confinement for a novel mass spectrometer of infinite mass range

We study the ions dynamics inside an Electrostatic Ion Beam Trap (EIBT) and show that the stability of the trapping is ruled by Hill's equation. This unexpectedly demonstrates that an EIBT, in the reference frame of the ions, works very similar to a quadrupole trap. The parallelism between these two kinds of traps is illustrated by comparing experimental and theoretical stability diagrams of the EIBT. The main difference with respect to quadrupole traps is that the stability depends only on the ratio of the acceleration and trapping electrostatic potentials, not on the mass nor the charge of the ions. All kinds of ions can be trapped simultaneously and since parametric resonances are proportional to the square root of the charge/mass ratio the EIBT can be used as a mass spectrometer of infinite mass range