Recoil protons from the β-decay of unpolarized neutrons are stored in a cryogenic ion trap formed by the superposition of an axisymmetric electrostatic field on a coaxial magnetic field, which varies uniformly in space between regions of high (∼4.30 T) and low (∼0.61 T) homogeneous field. Protons generated in the high field region are adiabatically focused onto a ‘mirror’ electrode in the low field region. The integrated energy spectrum is determined by counting the number of stored protons as a function of mirror potential. Violation of the exact adiabatic conditions is corrected for by carrying out alternate measurements at trapping times which differ by a factor of 2. The results: a0 = −0.1054 ± 0.0055, |λ| = 1.271 ± 0.018 are in agreement with previous measurements of these quantities.

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Motivated by recent developments in ion trap design and fabrication, we investigate the stability of ion motion in asymmetrical, planar versions of the classic Paul trap. The equations of motion of an ion in such a trap are generally coupled due to a nonzero relative angle θ between the principal axes of RF and DC fields, invalidating the assumptions behind the standard stability analysis for symmetric Paul traps. We obtain stability diagrams for the coupled system for various values of θ, generalizing the standard q-a stability diagrams. We use multi-scale perturbation theory to obtain approximate formulas for the boundaries of the primary stability region and obtain some of the stability boundaries independently by using the method of infinite determinants. We cross-check the consistency of the results of these methods.Our results show that while the primary stability region is quite robust to changes in θ, a secondary stability region is highly variable, joining the primary stability region at the special case of θ = 45• , which results in a significantly enlarged stability region for this particular angle.We conclude that while the stability diagrams for classical, symmetric Paul traps are not entirely accurate for asymmetric surface traps (or for other types of traps with a relative angle between the RF and DC axes), they are "safe" in the sense that operating conditions deemed stable according to standard stability plots are in fact stable for asymmetric traps, as well. By ignoring the coupling in the equations, one only underestimates the size of the primary stability region.

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