Abstract
Neutral particles can be guided and focused using electric field gradients that focus in one transverse direction and defocus in the other, alternating between the two directions. Such a guide is suitable for transporting particles that are attracted to strong electric fields, which cannot be guided using static fields. Particles are only transmitted if their initial positions and transverse speeds lie within the guide's phase-space acceptance. Nonlinear forces are always present in the guide and can severely reduce this acceptance. We consider the effects of the two most important nonlinear forces, a term in the force that is cubic in the off-axis displacement, and a nonlinear term which couples together the two transverse motions. We use approximate analytical techniques, along with numerical methods, to calculate the influence of these nonlinear forces on the particle trajectories and on the phase-space acceptance. The cubic term alters the focusing and defocusing powers, leading either to an increase or a decrease of the acceptance depending on its sign. We find an approximate analytical result for the phase-space acceptance including this cubic term. Using a perturbation method we show how the coupling term leads to slow changes in the amplitudes of the transverse oscillations. This term reduces the acceptance when it reduces the focusing power, but has little influence when it increases that power. It is not possible to eliminate both nonlinear terms, but one can be made small at the expense of the other. We show how to choose the guide parameters so that the acceptance is optimized.
Highlights
A neutral particle in an electric field gradient feels a force
An alternating gradient (AG) focusser is a series of lenses, each focussing in one transverse direction and defocussing in the other
In this paper we have shown how nonlinear forces alter the trajectories of neutral particles in an AG guide, and have shown how to calculate the phase space acceptance of guides with these nonlinear forces included
Summary
A neutral particle in an electric field gradient feels a force. The field polarizes the particle and, if it has a gradient, pulls on the induced dipole moment. It can be applied directly to other alternating gradient structures such as a storage ring for strong-field seeking molecules [15] or linear ac traps of the kind demonstrated for both molecules [16] and atoms [17]. The anharmonic forces present in AG guides and traps for neutral particles tend to be detrimental to the phase space acceptance, often reducing this by a factor of 10 or more. These nonlinearities reduce the quality of the images in an AG focussing system. We apply our analysis to some example AG guides for neutrals
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