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Physical Review A

Laser cooling of stored high-velocity ions by means of the spontaneous force

Wolfgang H. Petrich, M. Grieser, Rudolf Grimm, A. Gruber, Dietrich Habs, H.‐J. Miesner, D. Schwalm, B. Wanner, H. Werno e, A. Wolf, R. Grieser, G. Huber, R. Klein, T. Kühl, Ronny Neumann, S. Schröder

Published Sep 1, 1993• 44 citations
Publisher

Abstract

A longitudinal laser cooling of ion beams at about 5% of the velocity of light has been performed at the Heidelberg Test Storage Ring with various cooling schemes employing the spontaneous force. For a 7.29-MeV $^{9}\mathrm{Be}^{+}$ beam with an initial longitudinal temperature of 2700 K, the main characteristics of laser cooling in a storage ring are discussed. When undamped, the transverse betatron oscillations of the coasting ions limit the longitudinal temperature after laser cooling to typically 1 K. After damping the transverse motion by precooling the ions with an electron cooler, longitudinal temperatures of below 30 mK have been obtained in the subsequent laser cooling. In this case, the longitudinal ion-beam temperature can be understood as an equilibrium of the laser cooling rate with the heating rate due to intrabeam scattering. Moreover, single binary Coulomb collisions between the (still transversely hot) ions can cause such longitudinal velocity changes that ions are lost out of the critical capture range of the laser cooling force. In these two ways, intrabeam scattering imposes a substantial limit on the temperature or number of laser cooled ions in a storage ring. In our experiments, this process presently limits the ratio between the density-dependent Coulomb energy and the longitudinal thermal energy spread to a value on the order of 1, where liquid rather than gaseous behavior of the ion beam is expected to set in.

DOI
10.1103/physreva.48.2127

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A longitudinal laser cooling of ion beams at about 5% of the velocity of light has been performed at the Heidelberg Test Storage Ring with various cooling schemes employing the spontaneous force. For a 7.29-MeV 9Be+^{9}\mathrm{Be}^{+}9Be+ beam with an initial longitudinal temperature of 2700 K, the main characteristics of laser cooling in a storage ring are discussed. When undamped, the transverse betatron oscillations of the coasting ions limit the longitudinal temperature after laser cooling to typically 1 K. After damping the transverse motion by precooling the ions with an electron cooler, longitudinal temperatures of below 30 mK have been obtained in the subsequent laser cooling. In this case, the longitudinal ion-beam temperature can be understood as an equilibrium of the laser cooling rate with the heating rate due to intrabeam scattering. Moreover, single binary Coulomb collisions between the (still transversely hot) ions can cause such longitudinal velocity changes that ions are lost out of the critical capture range of the laser cooling force. In these two ways, intrabeam scattering imposes a substantial limit on the temperature or number of laser cooled ions in a storage ring. In our experiments, this process presently limits the ratio between the density-dependent Coulomb energy and the longitudinal thermal energy spread to a value on the order of 1, where liquid rather than gaseous behavior of the ion beam is expected to set in.
The interaction of laser-induced and intrabeam forces has been studied in a dense stored beam of 100-keV 7Li+^{7}\mathrm{Li}^{+}7Li+ ions. A fraction of the ions (\ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}4}$) exist in the metastable 1s2s 3^{3}3S state. Using this state as a laser spectroscopic probe, we observe fast longitudinal heating in the injected, nonequilibrium distribution due to Coulomb scattering. Laser cooling of the metastable ions is ineffective during this heating period. The metastable fraction of the equilibrated beam is subsequently laser cooled to a longitudinal temperature of \ensuremath{\sim}1 mK, the lowest temperature ever reported in a stored ion beam.
The crystallization of ion beams has recently been established in the rf quadrupole storage ring PALLAS (PAul Laser CooLing Acceleration System) for laser-cooled 24 Mg + ion beams at an energy of about 1 eV. Yet, unexpectedly sharp constraints had to be met concerning the confinement strength and the longitudinal laser cooling rate. In this paper, related and up to now unseen heating mechanisms are pinpointed for crystalline beams. The weak but inevitable diffusive transverse heating associated with the laser cooling process itself is investigated, possibly allowing the future measurement of the latent heat of the ion crystal. As a function of the beam velocity, the influence of bending shear on the attainability of larger crystalline structures is presented. Finally, rf heating of crystalline beams of different structure is studied for discontinuous cooling.
S-LSR is a compact ion storage ring constructed at Kyoto University several years ago. The ring is equipped with a Doppler laser cooling system aimed at beam crystallization. Bearing in mind hardware limitations in S-LSR, we try to find an optimum set of primary experimental parameters for the production of an ultracold heavy ion beam. Systematic molecular dynamics simulations are carried out for this purpose. It is concluded that the detuning and spot size of the cooling laser should be chosen around |−-−|42 MHz and 1.5 mm, respectively, for the most efficient cooling of 40 keV |24^{24}24|Mg|+^++| beams in S-LSR. Under the optimum conditions, the use of the resonant coupling method followed by radio-frequency field ramping enables us to reach an extremely low beam temperature on the order of 0.1 K in the transverse degrees of freedom. The longitudinal degree of freedom can be cooled to close to the Doppler limit; i.e., to the mK range. We also numerically demonstrate that it is possible to establish a stable, long one-dimensionally ordered state of ions.
We report the first observation of indirect resonantly enhanced transverse laser cooling of a bunched, stored ion beam of 40 keV 24Mg+^{24}\mathrm{Mg}^{+}24Mg+. The longitudinal velocity distribution and the horizontal beam size of the laser-cooled 24Mg+^{24}\mathrm{Mg}^{+}24Mg+ ion beam with 280 nm laser light were simultaneously observed by the use of standard fluorescence-based techniques. Keeping the operation point at (2.068, 1.105), the synchrotron tune (${\ensuremath{\nu}}_{s}$) was changed from 0.0376 to 0.1299. A strong decrease in the cooled horizontal beam size and a corresponding increase in the equilibrium cooled momentum spread were observed at the expected synchrobetatron resonance coupling condition of ${\ensuremath{\nu}}_{s}=0.068$, which is the first observation of a resonantly induced coupling for enhanced indirect transverse laser cooling of an ion beam, and is an important step towards creating a crystalline ground state of the beam.
Laser cooling of ion beams generally operates only upon the longitudinal motion of an ion beam. In order to extend this powerful dissipative force to the transverse directions, we consider introducing a Wien filter in a cooing straight section. It is theoretically shown that longitudinal cooling within a Wien filter naturally develops a transverse (mostly horizontal) cooling effect as well. Molecular dynamics simulations demonstrate that this method enables us to reach an ultralow-temperature state of a stored ion beam.
A simple method of cooling the transverse motion of an ion cloud in a linear Paul trap with a single axial laser is proposed. Transverse thermal oscillations of ions are indirectly damped by the longitudinal laser friction via an additional radio-frequency potential that resonantly couples two degrees of freedom. The fundamental mechanism of the present cooling scheme is theoretically described with the help of a harmonic oscillator model. It is shown that the indirect cooling rate can be considerably enhanced when the frequencies of the transverse and longitudinal ion oscillations satisfy a certain relation. The validity of theoretical predictions is confirmed through molecular dynamics simulations in which the detailed three-dimensional configuration of a typical Paul trap is incorporated.