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Physical Review Letters

Strongly Magnetized Antihydrogen and Its Field Ionization

D. Vrinceanu, Brian Granger, Robert E. Parrott, H. R. Sadeghpour, Lorenz S. Cederbaum, Areez Mody, Jerry Wei Heng Tan, G. Gabrielse

Published Mar 31, 2004• 37 citations
Publisher

Abstract

Internal orbits of experimentally analyzed antihydrogen (H) atoms depend as much on an external magnetic field as on the Coulomb force. A circular "guiding center atom" model is used to understand their field ionization. This useful model, assumed in the theory of three-body H recombination so far, ignores the important coupling between internal and center-of-mass motion. A conserved pseudomomentum, effective potential, saddle point analysis, and numerical simulation show where the simple model is valid and classify the features of the general case, including "giant dipole states."

DOI
10.1103/physrevlett.92.133402

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Internal orbits of experimentally analyzed antihydrogen (H) atoms depend as much on an external magnetic field as on the Coulomb force. A circular "guiding center atom" model is used to understand their field ionization. This useful model, assumed in the theory of three-body H recombination so far, ignores the important coupling between internal and center-of-mass motion. A conserved pseudomomentum, effective potential, saddle point analysis, and numerical simulation show where the simple model is valid and classify the features of the general case, including "giant dipole states."
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Using a classical Monte Carlo method, we have computed the three-body recombination (two free electrons and a proton scattering into one free electron and a hydrogen atom, $e+e+p\ensuremath{\rightarrow}\mathrm{H}+e$) in strong magnetic fields. The proton is fixed in space but the electrons are allowed their full, three-dimensional motion. We investigate recombination for temperatures and fields similar to those used in recent experiments that generated antihydrogen. The present rate is compared to that when the electrons' motion is given by the guiding center approximation, validating previous results at low temperature and demonstrating the breakdown of this approximation at higher temperature. Unlike the B=0B=0B=0 case, strong BBB gives preferential recombination to atoms with positive magnetic moment. Also, the canonical angular momentum in the field direction is often negative even when the magnetic moment is negative. Both results affect the trapping of antihydrogen using spatially dependent magnetic fields.
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The ApparaTus for High precision Experiment on Neutral Antimatter and antihydrogen TRAP collaborations have produced antihydrogen atoms by recombination in a cryogenic antiproton-positron plasma. This paper discusses the motion of the weakly bound atoms in the electric and magnetic field of the plasma and trap. The effective electric field in the moving frame of the atom polarizes the atom, and then gradients in the field exert a force on the atom. An approximate equation of motion for the atom center of mass is obtained by averaging over the rapid internal dynamics of the atom. The only remnant of the atom internal dynamics that enters this equation is the polarizability for the atom. This coefficient is evaluated for the weakly bound and strongly magnetized (guiding center drift) atoms understood to be produced in the antihydrogen experiments. Application of the approximate equation of motion shows that the atoms can be trapped radially in the large space charge field near the edge of the positron column. Also, an example is presented for which there is full three-dimensional trapping, not just radial trapping. Even untrapped atoms follow curved trajectories, and such trajectories are discussed for the important class of atoms that reach a field ionization diagnostic. Finally, the critical field for ionization is determined as an upper bound on the range of applicability of the theory.
We have studied the motion of antihydrogen atoms in electric and magnetic fields of arbitrary orientation. Our aim was to find an exact model of external (centre-of-charge) and internal dynamics which would allow us to describe antihydrogen motion in a realistic way. After analysing the kinematics of the charge exchange reaction producing antihydrogen and of antihydrogen deexcitation, we discuss the dynamics in cases of special fields configurations. Finally, we propose an expression for the force acting on an antihydrogen atom when the field configuration is arbitrary. The general formula -- when reduced in the special field configurations -- matches the results which we obtained independently before. The focus is both on the centre of charge dynamics and on the accurate internal quantum characteristics.
We have simulated the formation of antihydrogen through three-body recombination using classical trajectories of antiprotons and positrons. The simulations include several effects which are important in current antihydrogen experiments: the full motion of the antiproton repeatedly passing into and out of the positron plasma, the energy loss of antiprotons due to the interaction with the positron plasma, and the field-ionization of antihydrogen en route from the plasma to the detector. We find that whereas the overall simulated rate of formation of antihydrogen has a density dependence close to n 2 e , the rate of antihydrogen detection follows a power law less than 2. The difference is due to the effect of density dependent field ionization.