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Hu'nan Shifan Daxue xuebao. Ziran kexue ban

The Field Structure of the Ioffe Trap

Zeng Gao-jian

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

Studies the field structure of the Ioffe trap and de scribed its features with both the exact expression and a multipole polynomial expansion that facilitates studies o f symmetry properties and classical or quantum orbits. As a discussion, we study the interaction potential energy between the neutral particle with magnetic mom ent μ and the idealized Ioffe trap and derive the classical motion equation of the neutral particle.

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Studies the field structure of the Ioffe trap and de scribed its features with both the exact expression and a multipole polynomial expansion that facilitates studies o f symmetry properties and classical or quantum orbits. As a discussion, we study the interaction potential energy between the neutral particle with magnetic mom ent μ and the idealized Ioffe trap and derive the classical motion equation of the neutral particle.
Recently, we developed a method for calculating the lifetime of a particle inside a magnetic trap with respect to spin flips, as a first step in our efforts to understand the quantum-mechanics of magnetic traps. The 1D toy model that was used in this study was physically unrealistic because the magnetic field was not curl-free. Here, we study, both classically and quantum-mechanically, the problem of a neutral particle with spin S, mass m and magnetic moment mu, moving in 3D in an inhomogeneous magnetic field corresponding to traps of the Ioffe-Pritchard, `clover-leaf' and `baseball' type. Defining by omega_p, omega_z and omega_r the precessional, the axial and the lateral vibrational frequencies, respectively, of the particle in the adiabatic potential, we find classically the region in the $(ømega_{r}% (omega_r -- omega_z) plane where the particle is trapped. Quantum-mechanically, we study the problem of a spin-one particle in the same field. Treating omega_r / omega_p and omega_z / omega_p as small parameters for the perturbation from the adiabatic Hamiltonian, we derive a closed-form expression for the transition rate 1/T_{esc} of the particle from its trapped ground-state. We find that in the extreme cases, the expression for 1/T_{esc} is dominated by the largest of the two frequencies omega_r and omega_z.
Recently, we developed a method for calculating the lifetime of a particle inside a magnetic trap with respect to spin flips, as a first step in our efforts to understand the quantum mechanics of magnetic traps. The one-dimensional toy model that was used in this study was physically unrealistic because the magnetic field was not curl free. Here, we study, both classically and quantum mechanically, the problem of a neutral particle with spin S, mass m, and magnetic moment μ, moving in three dimensions in an inhomogeneous magnetic field corresponding to traps of the Ioffe–Pritchard “clover-leaf” and “baseball” type. Defining by ωp, ωz, and ωr the precessional, the axial, and the lateral vibrational frequencies, respectively, of the particle in the adiabatic potential Veff =μ|B|, we find classically the region in the (ωr/ωp)−(ωz/ωp) plane where the particle is trapped. Quantum mechanically, we study the problem of a spin-one particle in the same field. Treating ωr/ωp and ωz/ωp as small parameters for the perturbation from the adiabatic Hamiltonian, we derive a closed-form expression for the transition rate 1/Tesc of the particle from its trapped ground state. In the extreme cases, the expression for 1/Tesc reduces to 4πωr exp(−2ωp/ωr) for ωp≫ωr≫ωz, to 82πωpωi exp(−2ωp/ωi) for ωp≫ωr=ωz≡ωi and to π/2 ωr(ωz/ωp)3/2exp(−2ωp/ωz) for ωp≫ωz≫ωr.
In view of the recent successful confinement of decelerated sodium atoms in a magnetostatic trap, it is of interest to evaluate possible trap-field configurations. Neutral atoms in a Zeeman sublevel whose energy increases with field can be confined by a field whose magnitude \ensuremath{\Vert}B\ensuremath{\Vert} increases with distance from the center. Because this same basic requirement applies also to traps for neutrons and for plasmas (in the guiding-center approximation), trap configurations developed previously for these purposes are of interest for neutral atoms. However, the desired properties differ considerably because of very different objectives and different behavior of very cold atoms as compared with hot plasmas. We characterize basic trap configurations using both the exact expressions for the field, and a multipole polynomial expansion that facilitates studies of symmetry properties and classical or quantum orbits. Polynomial terms for the field components are derived and coefficients obtained by comparison with Taylor-series expansions and by global fit. Contours of \ensuremath{\Vert}B\ensuremath{\Vert} for various trap configurations are also presented. Under certain restrictive conditions, \ensuremath{\Vert}B\ensuremath{\Vert}, and hence the effective potential, can be made isotropic to second order.
One proposed technique for trapping anti-atoms is to superimpose a Ioffe-Pritchard style magnetic-minimum neutral trap on a standard Penning trap used to trap the charged atomic constituents. Adding a magnetic multipole field in this way removes the azimuthal symmetry of the ideal Penning trap and introduces a new avenue for radial diffusion. Enhanced diffusion will lead to increased Joule heating of a non-neutral plasma, potentially adversely affecting the formation rate of anti-atoms and increasing the required trap depth. We present a model of this effect, along with an approach to minimizing it, with comparison to measurements from an intended anti-atom trap.