Comparison of equilibrium ion density distribution and trapping force in Penning, Paul, and combined ion traps

Starting from the classical Boltzmann distribution, we obtain the ion density distribution in the limit of either high temperature/low density (Coulomb interaction energy much less than ion kinetic energy) or low temperature/high density (kinetic energy much less than Coulomb interaction energy), and the trapping force for an ion cloud in Penning ion cyclotron resonance, Paul (quadrupole), and combined (Paul trap in a uniform axial static magnetic field) traps. At equilibrium (total angular momentum conserved), the ion cloud rotates at a constant frequency in Penning and combined traps. Ln a Penning trap, the maximum ion density is proportional to B-2/m (B is magnetic field and m is the mass of ions), whereas the maximum ion density in a Paul trap is proportional to (V-rf(2)/m Omega(2)r(0)(4)), with Mathieu equation axial q value < 0.4 to satisfy the pseudopotential approximation. Ion maximum densities in both Penning and Paul ion traps depend on the trapping field (magnetic or electric) and ion mass, but not on ion charge. Ln a Penning trap at maximum ion density (zero pressure), the radial (but not the axial) trapping potential is mass dependent, whereas both radial and axial potentials in a Paul trap at maximum ion density are mass dependent. (C) 1998 American Society for Mass Spectrometry.