Linearity and quadrupolarity of tetragonal and cylindrical penning traps of arbitrary length-to-width ratio

The two most popular Penning traps in use for Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry are tetragonal (i. e., orthorhombic with square cross section) and cylindrical. Here we compare tetragonal and cylindrical traps as a function of aspect (length-to-width) ratio and position within the trap, by comparing the numerically computed (from Simion 6.0) electric potential field of a given trap relative to each of three idealized potentials required for FT-ICR experiments: dipolar one-dimensional potential for alternating current (ac) excitation/detection of cyclotron motion, azimuthal two-dimensional quadrupolar potential for ac excitation for ion axialization, and axial three-dimensional quadrupolar potential for direct current axial confinement of ions. Our numerically computed results agree well with those previously derived analytically. The numerical approach provides a simpler and more accessible means for analyzing the aforementioned potentials. Moreover, the numerical approach (unlike the analytical approach) readily extends to traps of lower symmetry. Finally, even when analytical solutions are available, the numerical method presented here is complementary, since it provides a useful check on the validity of the derived equations.