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Journal of Experimental and Theoretical Physics Letters

Three-particle recombination coefficient of a weakly nonideal ultracold plasma in a high magnetic field

Boris B. Zelener, B. V. Zelener, Edward A. Manykin

Published Dec 1, 2011• 11 citations
Publisher

Abstract

An expression for the recombination coefficient α B in a weakly nonideal ultracold plasma in a high magnetic field has been proposed. According to this expression, α B ∼ T −1.5 B −2, where T e is the temperature of electrons and B is the strength of the magnetic field. Comparison of calculated values with experimental data including the results of the recent experiments on recombination in antihydrogen confirms the theoretical dependence.

DOI
10.1134/s0021364011190192

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An expression for the recombination coefficient α B in a weakly nonideal ultracold plasma in a high magnetic field has been proposed. According to this expression, α B ∼ T −1.5 B −2, where T e is the temperature of electrons and B is the strength of the magnetic field. Comparison of calculated values with experimental data including the results of the recent experiments on recombination in antihydrogen confirms the theoretical dependence.
The electron distribution function and diffusion coefficient in energy space have been calculated for the first time for a weakly coupled ultracold plasma in a magnetic field in the range of magnetic fields B = 100−50000 G for various temperatures. The dependence of these characteristics on the magnetic field is analyzed and the distribution function is shown to depend on the electron energy shift in a magnetic field. The position of the “bottleneck” of the distribution function has been found to be shifted toward negative energies with increasing magnetic field. The electron velocity autocorrelators as a function of the magnetic field have been calculated; their behavior suggests that the frequency of collisions between charged particles decreases significantly with increasing magnetic field. The collisional recombination coefficient α B has been calculated in the diffusion approximation for a weakly coupled ultracold plasma in a magnetic field. An increase in magnetic field is shown to lead to a decrease in α B and this decrease can be several orders of magnitude.
The distribution functions and diffusion coefficient of electrons in the Rydberg energy space in an ultracold plasma are obtained as functions of temperature by numerically solving a system of kinetic balance equations. As the initial conditions, the results obtained in previous papers by the molecular dynamics method are used. From calculation of Rydberg electron fluxes, the temperature dependence of the recombination coefficient is obtained, in good agreement with the recombination coefficient calculated previously by the molecular dynamics method.
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.
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.
Signals of ultracold plasma are observed by two-photon ionization of laser-cooled caesium atoms in a magneto-optical trap. Recombination of ions and electrons into Rydberg atoms during the expansion of ultracold plasma is investigated by using state-selective field ionization spectroscopy. The dependences of recombination on initial electron temperature (1–70 K) and initial ion density (∼10 10 cm −3 ) are investigated. The measured dependence on initial ion density is N 1.547+0.004 at a delay time of 5 μs. The recombination rate rapidly declines as initial electron temperature increases when delay time is increased. The distributions of Rydberg atoms on different values of principal quantum number n, i.e. n = 30–60, at an initial electron temperature of 3.3 K are also investigated. The main experimental results are approximately explained by the three-body recombination theory.