Nonlinear dynamics in an alternating gradient guide for neutral particles

Abstract

Neutral particles can be guided and focussed 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 focussing and defocussing 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 focussing 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.

Stark deceleration of CaF molecules in strong- and weak-field seeking states

“…Figure 2(c) shows the acceptance areas of the two decelerators in one of the two transverse directions. For the WF decelerator this is obtained by calculating the mean transverse spring constant [20], while for the AG decelerator it is found by using the Courant-Snyder formalism for AG focussing [24,29,30]. We find that the transverse acceptance areas are approximately the same for the two decelerators.…”

Ultracold molecules and ultracold chemistry

“…[96], and an analysis of how to optimise the transverse dynamics during AG guiding is provided in Ref. [97]. One of the advantages of producing decelerated ground state molecules is that these are not subject to energy releasing inelastic collisions, thus enhancing prospects for sympathetic cooling by elastic collision (see Section IV).…”

Preparation and Manipulation of Molecules for Fundamental Physics Tests

“…This theoretical model misses some largely undesirable effects that are present in reality. In the transverse directions, nonlinear forces are necessarily present and these reduce the transverse acceptance [57,62,63]. The linear part of the force changes sign between one lens and the next, leading to the dynamical stability discussed above, but the leading order non-linear terms in the transverse force do not change sign between the focussing and defocussing lenses and so tend to upset the dynamical stability.…”