Knowledge of the fundamental limitations on a magnetic trap for neutral particles is of paramount interest to designers as it allows for the rapid assessment of the feasibility of specific trap requirements or the quality of a given design. In this paper, performance limitations are defined for convexity of magnetic trapping potential and bias field using a local approximation in the trapping center. As an example, the fundamental bounds are computed for current supporting regions in the form of a spherical shell, a cylindrical region, and a box. A Pareto-optimal set considering both objectives is found and compared with known designs of the baseball trap and Ioffe-Pritchard trap. The comparison reveals a significant gap in the performance of classical trap designs from fundamental limitations. This indicates a possibility of improved trap designs and modern techniques of shape synthesis are applied in order to prove their existence. The topologically optimized traps perform almost two times better as compared to conventional designs. Last, but not least, the developed framework might serve as a prototype for the formulation of fundamental limitations on plasma confinement in a wider sense.
Knowledge of the fundamental limitations on a magnetic trap for neutral particles is of paramount interest to designers as it allows for the rapid assessment of the feasibility of specific trap requirements or the quality of a given design. In this paper, performance limitations are defined for convexity of magnetic trapping potential and bias field using a local approximation in the trapping center. As an example, the fundamental bounds are computed for current supporting regions in the form of a spherical shell, a cylindrical region, and a box. A Pareto-optimal set considering both objectives is found and compared with known designs of the baseball trap and Ioffe-Pritchard trap. The comparison reveals a significant gap in the performance of classical trap designs from fundamental limitations. This indicates a possibility of improved trap designs and modern techniques of shape synthesis are applied in order to prove their existence. The topologically optimized traps perform almost two times better as compared to conventional designs. Last, but not least, the developed framework might serve as a prototype for the formulation of fundamental limitations on plasma confinement in a wider sense.
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.
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.
Magnetic trapping of laser-cooled neutral atoms has been demonstrated at NBS and is progressing in other laboratories. Confinement of any object requires exchanging kinetic for potential energy, and for neutral atoms, this necessarily derives from shifts of internal energy levels. This is implemented through the force experienced by the atomic magnetic moment in a carefully designed, highly inhomogeneous field. Since magnetic fields of convenient strength can shift atomic energy levels by only a few gigahertz (temperature ≌ 0.1 K), neutral atom traps are very shallow and must be loaded with very cold atoms. We present some motivations for using magnetic traps and then discuss the constraints and optimal configurations of various arrangements. For example, no trap can be isotropic. Next we discuss both the classical and quantum mechanical motions of trapped atoms. These motions are important for at least two reasons: First, several schemes under study for further cooling depend on knowing the position and velocity of the atoms, as well as the vector field at each point along the orbit. Second, magnetic traps depend on the atomic moment remaining aligned with the field as the atom orbits in the trap, and this precludes rapid motion through a low-field region.
We theoretically investigate properties of magnetostatic traps for cold atoms that are subject to externally applied uniform fields. We show that Ioffe-Pritchard traps and other stationary points of B are confined to a two-dimensional curved surface, or manifold M, defined by $\mathrm{det}(\ensuremath{\partial}{B}_{i}∕\ensuremath{\partial}{x}_{j})=0$. We describe how stationary points can be moved over the manifold by applying external uniform fields. The manifold also plays an important role in the behavior of points of zero field. Field zeroes occur in two distinct types, in separate regions of space divided by the manifold. Pairs of zeroes of opposite type can be created or annihilated on the manifold. Finally, we give examples of the manifold for cases of practical interest.
An ensemble of low-energy positrons injected into a supported magnetic dipole trap can remain trapped for more than a second. Trapping experiments with and without a positive magnet bias yield confinement times up to τ_{A}=(1.5±0.1) and τ_{B}=(0.28±0.04) s, respectively. Supported by single-particle simulations, we conclude that the dominant mechanism limiting the confinement in this trap is scattering off of neutrals, which can lead to both radial transport and parallel losses onto the magnet surface. These results provide encouragement for plans to confine an electron-positron plasma in a levitated dipole trap.